Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Trischuk, Dominique
Doctor of Philosophy - PhD
University of British Columbia
This dissertation presents a search for long-lived heavy neutral leptons (HNLs) in proton-proton collisions at the Large Hadron Collider (LHC). The Standard Model (SM) of particle physics is an extremely successful theory and many of its major predictions have been precisely confirmed. However, the existence of neutrinos, with small nonzero masses, suggests that the SM is incomplete. Introducing HNLs into the SM is a natural way to generate the light neutrino masses through a seesaw mechanism. Theories that postulate the existence of such particles can also explain the asymmetry between matter and anti-matter in our universe and models with at least three HNLs provide a dark matter candidate. This experimental search uses ATLAS data collected between 2015 and 2018 at a centre-of-mass energy of 13 TeV. A non-standard technique is used to search for a displaced vertex from particle trajectories produced in the HNL decay to leptons. The dominant background from uncorrelated leptons crossing in the ATLAS detector is estimated using an object shuffling method. The reconstructed HNL mass is used to discriminate between signal and background. No excess of events is observed and constraints on the strength of the interactions between HNLs and neutrinos are imposed in various scenarios. This dissertation also presents new methods to study the readout system and performance of a silicon strip tracking detector. The LHC is currently undergoing upgrades that will enable it to produce more than ten times the data that has already been collected. To meet the requirements of this challenging new environment, an all-silicon particle tracking system will be installed in ATLAS.
Displaced Vertex Search For HeavyNeutral Leptons Using The ATLASDetectorbyDominique TrischukB.Sc., The University of Toronto, 2017A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)February 2022© Dominique Trischuk 2022The following individuals certify that they have read, and recommend to the Faculty of Grad-uate and Postdoctoral Studies for acceptance, the dissertation entitled:Displaced Vertex Search For Heavy Neutral Leptons Using The ATLASDetectorsubmitted by Dominique Trischuk in partial fulfillment of the requirements forthe degree of Doctor of Philosophyin PhysicsExamining Committee:Colin Gay, Physics & Astronomy, UBCSupervisorAlison Lister, Physics & Astronomy, UBCCo-SupervisorDouglas Bryman, Physics & Astronomy, UBCUniversity ExaminerRoman Krems, Chemistry, UBCUniversity ExaminerAdditional Committee Members:Gary Hinshaw, Physics & Astronomy, UBCSupervisory Committee MemberAriel Zhitnitsky, Physics & Astronomy, UBCSupervisory Committee MemberiiAbstractThis dissertation presents a search for long-lived heavy neutral leptons (HNLs) in proton-proton collisions at the Large Hadron Collider (LHC). The Standard Model (SM) of particlephysics is an extremely successful theory and many of its major predictions have been preciselyconfirmed. However, the existence of neutrinos, with small nonzero masses, suggests that theSM is incomplete. Introducing HNLs into the SM is a natural way to generate the light neutrinomasses through a seesaw mechanism. Theories that postulate the existence of such particlescan also explain the asymmetry between matter and anti-matter in our universe and modelswith at least three HNLs provide a dark matter candidate. This experimental search usesATLAS data collected between 2015 and 2018 at a centre-of-mass energy of 13 TeV. A non-standard technique is used to search for a displaced vertex from particle trajectories producedin the HNL decay to leptons. The dominant background from uncorrelated leptons crossing inthe ATLAS detector is estimated using an object shuffling method. The reconstructed HNLmass is used to discriminate between signal and background. No excess of events is observedand constraints on the strength of the interactions between HNLs and neutrinos are imposedin various scenarios.This dissertation also presents new methods to study the readout system and performanceof a silicon strip tracking detector. The LHC is currently undergoing upgrades that will enableit to produce more than ten times the data that has already been collected. To meet therequirements of this challenging new environment, an all-silicon particle tracking system willbe installed in ATLAS.iiiLay SummaryThe Standard Model (SM) of particle physics describes the fundamental building blocks ofmatter and their interactions. While many of its major predictions have been precisely con-firmed, the SM is incomplete. For instance, the SM predicts that neutrinos, a type of fun-damental particle, are massless. Thus, the observation of nonzero neutrino masses suggestthat the SM is incomplete. This dissertation uses data from the ATLAS Experiment at theLarge Hadron Collider to search for a particle that explains the very tiny neutrino masses.The analysis is designed to search for clues left by this theoretical particle after it travels along distance through the ATLAS detectors. No evidence for the existence of a new particleis found. Various signal hypotheses are ruled out and this analysis thereby provides guidanceto future searches about where new physics that explains fundamental characteristics aboutour universe might be found.ivPrefaceThe research in this dissertation is based on ATLAS experiment data. ATLAS is a globalcollaboration of physicists, engineers, technicians, students and support staff. The collectiveeffort of over 5500 members make the operation of the experiment, including the data col-lection, possible. For example, collaboration members are responsible for the developmentand maintenance of reconstruction software for physics objects such as muons and electrons.Other collaboration members are responsible for the proton collision simulation software. Thissimulation also relies on input from theory and generator experts outside of the collaboration.This dissertation would not have been possible without the collective effort of all members.The ATLAS collaboration releases both public results in peer-reviewed journals and pre-liminary results that are not externally reviewed. However, all public and preliminary resultsare extensively reviewed within the collaboration. All of the nearly 3000 qualified authorsare listed alphabetically on each publication or public result from the ATLAS collabora-tion. Figures presented in this text have labels that indicate the level to which they havebeen reviewed. Figures taken from a peer-reviewed publication are labelled with “ATLAS”or “ATLAS Simulation”. Figures taken from preliminary results are labelled with “ATLASPreliminary”. Figures that are not approved by the collaboration are labelled with “ATLASWork in Progress” or do not have a label are all prepared by me, with the exception of sta-tistical analysis results in section 5.11, which were prepared by C. Appelt. The results areall undergoing the final stages of the internal ATLAS review process, after which they willbe made public. All other figures not prepared by me have their references indicated in thecaptions.Abbreviations are used in this dissertation to refer to a variety of objects and conceptsranging from hardware components to physics object reconstruction algorithms. Discipline-specific terms are also used throughout the text. These abbreviations and terms are definedin the glossary and accompanied by a short description. Throughout the text you will findreferences to the terms listed in the glossary.I wrote all of the text for this dissertation. Chapters 5 and 6 are written by me, but partsof the text also appear in internal ATLAS documentations. Chapters 1 to 4 present materialthat serves as an introduction for the reader. Chapters 5 and 6 summarize my work. Thishas led to two journal publications, one of which (at the time of writing) is undergoing thefinal stages of the internal ATLAS review process. The remainder of this preface describesvPrefacemy relevant contributions in each area. The search for displaced heavy neutral leptons ispresented in chapter 5. This search is performed using 139 fb−1 of proton-proton collisiondata collected with the ATLAS detector. The analysis is approved internally by the ATLAS“Exotics” group and a journal publication is undergoing the final stages of the internal ATLASreview process. My work was performed under the supervision of A. Lister with guidance fromM. Danninger. The analysis team consists of 16 members and I am one of three main analyzersin this search. Collaborators who helped me in this analysis are C. Appelt, J. Burzynski, D.Casper, S. Galantzan, C. Gay, M. Lutz, S. Oda, R. Newhouse, O. Ruchayskiy, J. Tastet andM. Wielers. This list below outlines my main contributions to the analysis. In addition, Iprovided support and feedback to others, including in group meetings.• I was responsible for validating and coordinating the production of all signal samplesused in the analysis.• In collaboration with theory associates J. Tastet and O. Ruchayskiy, I developed themethod used to interpret the results for the eight different signal models (see section 5.3).I also implemented and validated the method in our analysis framework.• In collaboration with J. Tastet, I developed the method used to take into account spincorrelations in the signal model (see section 5.4.3). I also implemented and validated themethod in our analysis framework. M. Wielers provided assistance with the productionof signal samples for the validation.• I optimized the secondary vertexing algorithm described in section 5.5.2. D. Casperprovided guidance.• I developed the HNL mass reconstruction described in section 5.5.3 following guidancefrom C. Gay.• I developed a custom derivation and coordinated the processing of all the data and sim-ulated samples for the analysis. A derivation step is used in the data analysis frameworkto skim away information that is not required for the analysis (see section 5.7.1).• I developed the analysis event selection code (see fig. 5.18. I also contributed to thedevelopment of the code that creates custom data structures (ntuples) for the relevantinformation in the search. R. Newhouse and J. Burzynski are the main developers ofthis ntuple maker code. C. Appelt developed the statistical analysis code.• I designed and optimized the event selection (see section 5.7). S. Oda and R. Newhousedeveloped the filter and filter emulator respectively. I also optimized the additionalanalysis regions defined in section 5.7.4.viPreface• I performed the studies of the main backgrounds and optimized the selections thatremove non-random background events (see sections 5.8.2 to 5.8.4).• I developed the novel technique to estimate the probability of uncorrelated particlescrossing in the ATLAS inner detector described in section 5.8.6. I also developed themethods to estimate the background uncertainties.• In collaboration with S. Galantzan, I implemented another random crossing estimateusing a track shuffling method (see appendix A.4). I integrated the shuffling algorithminto the main analysis framework, performed the validation studies and performed thesmall-scale data test.• I am the main author and editor of the internal analysis documentation. C. Appelt, M.Lutz, R. Newhouse and M. Danninger also contributed to the document.To be listed as an author on ATLAS publication, collaboration members must perform atleast 80 days technical work. My qualification work is described in section 6.2. I developeda temperature stress test for the ATLAS Inner Tracker (ITk) silicon strip detectors. Thisquality assurance test provides valuable information about the design and construction of theITk-Strip detectors that will be included in future design reviews. My supervisor for this workwas N. Hessey and my collaborators F. Guescini and T. Stack provided guidance and support.This work used a large-scale detector object (petal) that was designed and built by membersof the ITk-Strip collaboration.• I worked with industrial partners to select a climate chamber that performed the tem-perature stress tests.• I set up a monitoring system to study the environment in the chamber during thetemperature cycling in collaboration with F. Guescini.• I built a small-scale prototype detector object (petalet) in collaboration with F. Guescini.• I developed the temperature cycling program for the stress test.• I wrote the measurement programs that evaluated the dimensional stability of the de-tector components.• I performed all the temperature cycling tests and analyzed the results.• I wrote the internal documentation.viiPrefaceMy contribution to the ITk-Strip readout is described in section 6.3. My work was performedunder the supervision of C. Gay. To study the demands of the detector readout:• I developed a firmware emulator that mimics both the detector and the readout sys-tem (see section 6.3.1). My collaborators W. Fedorko, M. Trovato and M. Warren alsoprovided guidance and support.• I was part of a small team who set up a system that, for the first time, read outinformation from a new generation of on-detector electronic chips. This work was donein collaboration with B. Gallop, K. Krizka, S. Stucci, J.J Teoh and W. Wu.• I built one of only a handful of readout systems in our lab at UBC that uses many ofthe final components that will be part of the ITk-Strip readout system at CERN.This readout effort led to the following journal publication:ATLAS ITk Collaboration. The ABC130 barrel module prototyping programmefor the ATLAS strip tracker. Journal of Instrumentation, 15:P09004, 2020.In addition to the contributions listed above, I have presented my work, and other’s work ontheir behalf, in a number of internal ATLAS collaboration meetings and regional conferences:D. Trischuk. Recent Results from UEH Searches, ATLAS Physics and Perfor-mance Week: Exotics Plenary, online, 2021.D. Trischuk. Semi-Electrical Petal Thermocycling, ATLAS ITk Week, online,2021.D. Trischuk. Secondary Vertexing with Displaced Leptons, ATLAS Week: Early-Career-Scientists Session, online, 2021.D. Trischuk. Search for Displaced Heavy Neutral Leptons, Virtual Physics Con-ference, online, 2020.B. Gallop, C. Meyer, C. Gay, D. Trischuk†, E. Zhivun, J. Pinzino, J. Beacham,J.J. Teoh, O. Arnaez, P. Phillips, S. Stucci, T. Calvet and W. Wu. ITk StripsFELIX Demonstrators, ATLAS ITk Week, Geneva, Switzerland, 2019.D. Trischuk. ATLAS Strip Detector Upgrade for the Inner Tracker: Tackling BigData Readout Systems, Winter Nuclear & Particle Physics Conference, Banff,Canada, 2019.D. Trischuk†, W. Fedorko and C. Gay. ITK Strips HCCStar Emulator, ATLASITk Week, Geneva, Switzerland, 2018.†Indicates the speaker.viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxviAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxxv1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Particles in the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Chiral Fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Structure of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Electroweak Symmetry Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . 51.5 Successes and Limitations of the Standard Model . . . . . . . . . . . . . . . . 62 Heavy Neutral Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.1 Neutrino Masses From Right-Handed Neutrinos . . . . . . . . . . . . . . . . . 82.2 Interactions with the Standard Model . . . . . . . . . . . . . . . . . . . . . . . 102.3 HNL Decays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.4 Lepton Number Violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 HNL Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 The ATLAS Detector at the Large Hadron Collider . . . . . . . . . . . . . . 173.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.1.1 LHC Filling Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.1.2 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18ixTable of Contents3.1.3 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.1.4 Pileup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.1.5 High-Luminosity LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2 The ATLAS Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.1 Coordinate System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.2 Detector Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.3 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2.4 Calorimeter System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.5 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.6 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . 293.2.7 ATLAS Detector Simulation . . . . . . . . . . . . . . . . . . . . . . . . 314 Object Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1 Standard Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.1.2 Tracks, Primary Vertices and Energy Clusters . . . . . . . . . . . . . . 334.1.3 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.1.4 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.2 Non-Standard Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.1 Displaced Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424.2.2 Displaced Leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.2.3 Displaced Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 Search for Heavy Neutral Leptons . . . . . . . . . . . . . . . . . . . . . . . . . 505.1 Previous Searches for HNLs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2 Search Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.3 HNL Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.4 Data and Signal Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.4.1 Data Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.4.2 Signal Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.4.3 Modelling Spin Correlations . . . . . . . . . . . . . . . . . . . . . . . . 585.4.4 Signal Kinematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.5 Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.5.1 Displaced Vertex Reconstruction for the HNL Signal . . . . . . . . . . 645.5.2 Custom Displaced Vertex Configuration . . . . . . . . . . . . . . . . . . 665.5.3 Reconstructed HNL Mass . . . . . . . . . . . . . . . . . . . . . . . . . . 745.6 Object Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785.7 Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79xTable of Contents5.7.1 Analysis Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.7.2 Pre-Selections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 815.7.3 Signal Region Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 845.7.4 Additional Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.8 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.8.1 Random Track Crossings . . . . . . . . . . . . . . . . . . . . . . . . . . 895.8.2 Material Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.8.3 Metastable Particle Decays . . . . . . . . . . . . . . . . . . . . . . . . . 925.8.4 Leptonic Z Boson Decays . . . . . . . . . . . . . . . . . . . . . . . . . . 965.8.5 Muons from Cosmic-Ray Interactions . . . . . . . . . . . . . . . . . . . 975.8.6 Data-Driven Estimate of Random Track Crossings Using a Prompt Lep-ton Shuffling Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.9 Signal Systematic Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.10 Statistical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.11 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126 ATLAS Inner Tracker Upgrade . . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.1 ATLAS Inner Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.1.1 Inner Tracker Strip Detector . . . . . . . . . . . . . . . . . . . . . . . . 1216.2 Quality Assurance for ITk-Strip Petals . . . . . . . . . . . . . . . . . . . . . . 1226.2.1 Thermocycling Program . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.2.2 Thermocycling the Petalet . . . . . . . . . . . . . . . . . . . . . . . . . 1256.2.3 Thermocycling the Semi-Electrical Petal . . . . . . . . . . . . . . . . . 1286.3 ITk-Strip Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1386.3.1 HCCStar Emulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1397 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144AppendicesA Data-driven Estimate of Random Track Crossings Using a Track ShufflingMethod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152A.1 Shuffling Analysis Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . 153A.2 Track Shuffling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154A.3 Validation of the Track Shuffling Method . . . . . . . . . . . . . . . . . . . . . 155A.4 Small-Scale Test of the Track Shuffling Method . . . . . . . . . . . . . . . . . . 157xiList of Tables1.1 The four fundamental forces with their relative strengths and mediators. Tablefrom [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 The Standard Model (SM) fermion fields and their electric charges Q, thirdcomponents of the weak isospin T 3 and hypercharges Y . . . . . . . . . . . . . . 42.1 The relative strength of the mixing, xα = |Uα|2/|U |2, with the three neutrinoflavours for the inverted (IH) and normal (NH) hierarchy benchmark and single-flavour mixing scenarios. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114.1 Main differences between standard and large radius tracking (LRT). . . . . . . 435.1 A summary of the eight models used in the interpretation of the analysis re-sults. Models are defined according to the number of HNLs (1SFH or 2QDH),the fraction of LNC and LNV decays and the relative strength of the mixingbetween the lepton generations. The inverted (IH) and normal (NH) hierar-chy benchmarks are used for 2QDH models only, while the 1SFH models havesingle-flavour mixing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545.2 The cross section for LNC and LNV decays for one Majorana HNL, one DiracHNL, a quasi-Dirac HNL pair with “Majorana-like” decays and a quasi-DiracHNL pair with “Dirac-like” decays. The total cross section is the sum of theLNC and LNV contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.3 The main differences in the track selection between the default VSI configura-tion and the lepton-only selection used in the custom VSI configuration in thisanalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.4 Single muon and electron triggers from 2015-2018 that are used to select eventsof interest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.5 The HNL filter and overall filter rate for a set of test events in each of the fourdata taking years (2015-2018). . . . . . . . . . . . . . . . . . . . . . . . . . . . 83xiiList of Tables5.6 Requirements of the four HNL analysis filters. Definitions of the lepton se-lections (e.g. ID or isolation requirements) used in the filter can be found inthe descriptions of the lepton reconstruction algorithms in section 4.1.3 andsection 4.1.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.7 Signal region selections that are applied in each channel. . . . . . . . . . . . . . 865.8 Description of the selection criteria used to defined the SR. All criteria arefurther explained within this chapter. . . . . . . . . . . . . . . . . . . . . . . . 865.9 Definition of the inverted-prompt-lepton VR. A prompt lepton is defined asany muon or electron object with Loose or better quality that has |d0| < 3 mmand |z0 sin(θ)| < 0.5 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.10 Description of the heavy-flavour decay veto. . . . . . . . . . . . . . . . . . . . . 965.11 Description of the Z mass veto. . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.12 The relative systematic uncertainties on the background estimate, estimatedby creating shuffled events from SS DVs or from prompt leptons taken fromevents with different DV channels. The total uncertainty is the quadrature sumof the two contributions. The uncertainties are treated as uncorrelated amongthe different channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.13 Estimated background predictions with statistical and systematic uncertaintiesin the signal region and the control region. The observed yields are shown forOS DVs and SS DVs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1025.14 The KS test probabilities obtained when comparing the shuffled and SS back-ground estimate HNL mass (mHNL) and tri-lepton mass (mlll) distributions.The KS test is done separately for each channel. Two distributions are consid-ered incompatible if the KS probability is much less than one. . . . . . . . . . 1075.15 Table summarizing the systematic uncertainties that impact the signal predic-tion. Systematic uncertainties in this table are the impacts on the signal yieldsin the SR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1075.16 Post-fit background predictions, observed event-yields and scale factors µb withstatistical and systematic uncertainties in the control and signal regions. Theresults are shown for the 2QDH model with inverted-hierarchy mixing in the“Majorana-limit”. The results are also shown for all final states and for the1SFH Dirac-limit, LNC configuration l±α − l∓α l±γ . . . . . . . . . . . . . . . . . . 1136.1 Measurement results for flatness of Side A and B, as well as the bow for thesensor on side A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1276.2 Measurement uncertainties for the features on the semi-electrical petal. . . . . 1326.3 Overview of the custom made ASICs for the ITk Strip Detector [91]. . . . . . . 139xiiiList of TablesA.1 The different regions used in the random track crossing background estimation. 153xivList of Figures1.1 The elementary particles that make up the Standard Model. Figure adaptedfrom [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 The potential V (Φ) = µ2|Φ|2+λ|Φ|4 in a theory without (a) and with (b) localsymmetry breaking around a minimum of the potential. . . . . . . . . . . . . . 51.3 Summary of several Standard Model cross-section measurements. The measure-ments are corrected for branching fractions, compared to the correspondingtheoretical expectations. Figure taken from [8]. . . . . . . . . . . . . . . . . . . 72.1 The elementary particles that make up the Standard Model with the additionof N = 3 right-handed sterile neutrinos. Figure adapted from [2]. . . . . . . . . 92.2 A plot that shows the allowed combinations of |Uα|2/|U |2 that are consistentwith the recent NuFIT [21] fit to neutrino oscillation data. The allowed re-gions under normal (blue) and inverted (green) hierarchy are shown. The redcross markers represent two benchmark scenarios that are defined for the twodifferent hierarchy assumptions. Figure adapted from [20]. . . . . . . . . . . . . 112.3 Feynman diagrams for HNL production from the decay of a W boson and theHNL decay into leptonic and semi-leptonic final states. . . . . . . . . . . . . . . 122.4 Lepton number conserving (LNC) and lepton number violating (LNV) diagramsfor the charge-current leptonic HNL decay. . . . . . . . . . . . . . . . . . . . . . 132.5 Branching ratio of N → llν with a sum of all neutrino flavours as a function ofmN for muon-only (a), electron-only (b), NH (c) and IH (d) mixing scenarios.In each mixing scenario, the branching ratio is shown for N → eeν (blue),N → eµν (orange), N → µeν (pink) and N → µµν (purple) decays. . . . . . . 142.6 The total mixing |U |2 as a function of HNL mass mN for the muon-only mixingscenario. Each |U |2 is computed for mN between 2 and 20 GeV with properdecay lengths cτN = 1, 10 and 100 mm. . . . . . . . . . . . . . . . . . . . . . . 15xvList of Figures3.1 An illustration of various experimental facilities and beam lines at the CERNaccelerator complex relevant to the LHC. The protons are accelerated throughthe injection chain and into the LHC. The path they follow is: LINAC2 →BOOSTER → Proton Synchrotron (PS) → Super Proton Synchrotron (SPS)→ LHC. Figure adapted from [34]. . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Total integrated luminosity versus time (a) delivered to ATLAS (green), recordedby ATLAS (yellow), and certified to be good quality data (blue) during Run 2.Distribution of the mean number of interactions per bunch crossing (b) recordedby the ATLAS experiment in the years 2015-2018. Figures taken from [37]. . . 193.3 The LHC/HL-LHC timeline and run schedule as of Fall 2021. This diagramincludes the planned shutdown and upgrade periods. Figure taken from [38]. . . 203.4 A cut-away view of the the ATLAS detector. Figure taken from [39]. . . . . . 223.5 A transverse view in the R-φ plane of the barrel region of the inner detector.Tracks from the proton collisions traverse outward in radius, with most of thempassing through the four silicon pixel layers, four silicon-microstrip (SCT) layersand approximately 36 straw tubes (TRT). In this figure, the fourth innermostlayer of the pixel detector detector (IBL) is not shown. Figure taken from [39]. 233.6 A longitudinal view of the active region of the pixel detector. In this figure, thefourth innermost layer of the pixel detector (IBL) is not shown. Figure takenfrom [41]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.7 An SCT module showing the 4 silicon detectors connected to a readout hybridassembly. Figure taken from [40]. . . . . . . . . . . . . . . . . . . . . . . . . . . 253.8 A cut-away view of the ATLAS calorimeter system. Figure taken from [39]. . . 263.9 A cut-away view of the ATLAS muon system. Figure taken from [39]. . . . . . 283.10 The ATLAS trigger and data acquisition system (TDAQ) system in Run 2showing the various parts of the system relevant to triggering, detector readoutand data flow. Figure adapted from [47]. . . . . . . . . . . . . . . . . . . . . . 304.1 A schematic of different particles interacting with the ATLAS detector in asection of the x− y plane. Figure adapted from [52]. . . . . . . . . . . . . . . . 334.2 A schematic of the path of an electron through the ATLAS detector. The solidred trajectory shows the path of the electron traversing through the trackingsystem (pixel, SCT and TRT layers) and entering the electromagnetic calorime-ter. The dashed red trajectory indicates the path of a photon produced by theinteraction of the electron with the material in the tracking system. Figuretaken from [59]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37xviList of Figures4.3 The total reconstruction efficiency for simulated electrons in a single-electronsample as a function of the true transverse energy, ET, for each step of theelectron reconstruction: the energy cluster reconstruction (red triangles), trackreconstruction using the Global χ2 Track Fitter (blue open circles), clusterand track reconstruction using GSF tracking (yellow squares), and the finalelectron-candidate reconstruction, which includes the track-to-cluster matching(black circles). Since the cluster reconstruction requires that cluster seeds haveET > 2.5 GeV, the total reconstruction efficiency is less than 60% below 4.5GeV (dashed line). Figure taken from [59]. . . . . . . . . . . . . . . . . . . . . 384.4 The electron identification efficiency in Z → ee events in data as a functionof ET. The efficiencies are obtained by applying data-to-simulation efficiencyratios measured in J/ψ → ee and Z → ee events to Z → ee simulation. TheLHMedium operating point efficiency curve is plotted using red squares. Figuretaken from [60]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.5 The muon reconstruction efficiency for the Medium identification working pointas a function of muon pT in the region 0.1 < |η| < 2.5. This reconstructionefficiency is obtained with Z → µµ and J/Ψ → µµ events. The error bars onthe efficiencies indicate the statistical uncertainty. The panel at the bottomshows the ratio of the measured to predicted efficiencies, with statistical andsystematic uncertainties. Figure taken from [64]. . . . . . . . . . . . . . . . . . 414.6 Track reconstruction efficiency for displaced charged particles produced by thedecay of long-lived signal particles. The efficiency for standard tracking, LRTand the sum of the two is shown as a function of the radius of production ofthe displaced particles (r2prod = x2 + y2). Displaced leptons are shown on theleft and displaced hadrons on the right. Figure taken from [65]. . . . . . . . . . 444.7 The main steps in the VSI displaced vertexing algorithm. . . . . . . . . . . . . 454.8 A schematic illustration of the fake tracks rejection method. In example (a), thevertex is between the pixel B-Layer and Layer-1. The tracks of the reconstructedsecondary vertex must not have hits in the layers behind the vertex (i.e. IBLand B-Layer), and must have hits in the closest layer ahead of the vertex (i.e.Layer-1). In example (b), the vertex is close to the Pixel B-Layer. The tracksin this vertex are not allowed to have hits in the IBL, but may have hits in theB-Layer, and must have hits on the Layer-1. Analogous requirements are madeon vertices close to the other layers. Figure taken from [66]. . . . . . . . . . . . 474.9 An example of finding N -track vertices using an incompatibility graph. Thelayout of tracks and vertices in an event (a) and the incompatibility graph(b) that is formed by connecting two tracks when the two-track vertices aredetermined to be incompatible. Figure taken from [67]. . . . . . . . . . . . . . . 48xviiList of Figures4.10 An example of track sharing by multiple vertices. Figure taken from [67]. . . . 495.1 Observed 95% confidence level (CL) exclusion limits for HNL to muon neutrinomixing angle |Uµ|2 versus HNL mass mN for the prompt signature (the regionabove the black line is excluded) and the displaced signature (the region en-closed by the red line is excluded). The solid lines show limits assuming lepton-number violation (LNV) for half of the decays and lepton-number conservation(LNC) for the other half. The long-dashed line shows the limits assuming LNCfor all decays. The green and yellow bands indicate the ranges of expected limitsobtained within ±1 and ±2 standard deviations of the median limit reflectinguncertainties in the signal and background yields. Figure taken from [70]. . . . 515.2 Sensitivity to HNLs with dominant mixing to first, second and third leptongenerations. Current bounds on the mixing (filled regions) and prospects fornew results in the next 5-15 years are shown as a function of the HNL massmN . Figures taken from [71]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525.3 Feynman diagrams included in the combinations for the muon-only mixing(µ−µµ, µ−µe and µ−ee) and electron-only mixing (e−eµ, e−ee and e−µµ)scenarios. Neutral current decays are also possible for the µ−µµ and e−eechannels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565.4 Additional Feynman diagrams for signal processes that contribute to the sig-nal strength if both |Uµ|2 and |Ue|2 are nonzero. Diagrams are shown for thecharged-current interaction only. . . . . . . . . . . . . . . . . . . . . . . . . . . 585.5 Comparison of the lepton pT distributions for LNC decays betweenMadGraphsamples (purple) and the weighted (pink) and unweighted (gray) Pythia8 sam-ples for a µ−µµ signal using the NC+CC event weights. Samples are generatedwith mN = 10 GeV and cτN = 10 mm signal sample. . . . . . . . . . . . . . . . 605.6 Comparison of the lepton pT distributions for LNC decays betweenMadGraphsamples (blue) and the weighted (orange) and unweighted (gray) Pythia8samples for a µ−µe signal using the CC event weights. Samples are generatedwith mN = 10 GeV and cτN = 10 mm signal sample. . . . . . . . . . . . . . . . 615.7 Simulated lepton pT distributions for the three charged leptons in the HNLevent and the invariant mass of the tri-lepton system (mlll). The leading dis-placed lepton is defined as the lepton in the DV with the largest pT, while thesubleading displaced lepton has the smaller pT. Simulated µ−µµ signals areplotted for three different mass points: mN = 5, 7.5, 10 GeV with cτN = 10 mm. 625.8 HNL kinematics for simulated µ−µµ signals for three different mass points:mN = 5, 7.5, 10 GeV with cτN = 10 mm. . . . . . . . . . . . . . . . . . . . . . 63xviiiList of Figures5.9 The DV mass (a) and DV radius (b) distributions for simulated µ−µµ signalsamples. For the DV mass distribution, three different mass points are shown:mN = 5, 7.5, 10 GeV with cτN = 10 mm. For the DV radius plot, the simulatedsamples have mN = 10 GeV with cτN = 1, 10 and 100 mm. . . . . . . . . . . . 635.10 The µ−µµ signal efficiency (a) and ratio of the signal efficiency between VSILeptons and VSI (b) as a function of simulated HNL mass with 3 < mN <20 GeV. Signal samples with cτN = 1, 10, 100 mm are shown in red, blue andgreen respectively. The signal efficiency is defined as the ratio of the selectedreconstructed events to the total number of simulated events. . . . . . . . . . . 655.11 Simulated events for a µ−µµ, 10 GeV, 10 mm signal in purple and the data-driven same-sign background in grey as a function of the reconstructed HNLmass. The total number of events in the signal and background can be foundin the legends in each plot. Events are selected by applying the pre-selectioncuts described in section 5.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.12 The number of µ−µµ 10 GeV, 10 mm signal (a) and two-muon background (b)events for default VSI (blue) and VSI Leptons (orange) vertex configurations.The original number of events is given by the default configuration. Eventslabels “LRTR3” are the number of events after modifying the track selectionsas described in table 5.3 without the ∆θ and |z0| correlation selection. The“LRTR3 w Geo cut”, which is the final selection applied in the custom vertexconfiguration, is the number of events including this final correlation selection.The signal significance (c) is estimated using the number of signal events dividedby the square root of the number of background events (s/√b). . . . . . . . . . 685.13 Signal events for a 10 GeV, 10 mm µ−µµ sample (a) and two-muon backgroundevents (b) as a function of the two-track forming d0 cut for VSI (blue) andVSI Leptons (orange) vertex configurations. The original number of events isgiven by the default configuration. Then the number of events with two-trackforming d0 cut threshold equal to 2, 1.5, 1, 0.5 and 0 mm is shown. The signalsignificance (s/√b) for 10 GeV, µ−µµ signal is shown for the 10 mm (c) and1 mm (d) signal samples as a function of the same d0 cut. . . . . . . . . . . . . 695.14 Signal (a) and background (b) events with exactly two muons in the displacedvertex as a function of the number of tracks (ntracks) in the vertex reconstructedusing the VSI configuration with a 1 mm two-track forming d0 cut. Verticeswith ntracks = 2 are selected in the signal region, while events with ntracks > 2are rejected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70xixList of Figures5.15 Ratio of the number of selected signal events reconstructed with the customconfiguration to the default VSI configuration. Ratios are shown for the 10 GeVsignal samples in the µ−µµ, µ−µe, e−eµ and e−ee channels as a function ofthe proper decay length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.16 The three components of the vertex reconstruction efficiency and the totalefficiency, measured as a function of radial decay position, Lxy, for µ−µµ, µ−eeand e−ee signals with mN=10 GeV and cτN =10 mm. . . . . . . . . . . . . . . 735.17 Two HNL mass distributions for a simulated µ−µµ with mN = 10 GeV andcτN = 10 mm. The mHNL is computed using mW fixed to the pole mass of80.4 GeV (blue) and the median W mass in the allowed kinematic region (pur-ple). Events where the HNL mass has no real solution are set to -1. . . . . . . . 775.18 The analysis framework pipeline that shows how data and simulated signalevents are processed in the displaced HNL analysis. . . . . . . . . . . . . . . . . 825.19 OS displaced vertices in the VR shown in bins of mDV versus Lxy. All ver-tices are required to pass the VR selections. Leptons in the selected DVs arealso required to pass VeryVeryLoose electron and Medium muon identificationworking points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.20 OS displaced vertices from data events using the VR selections as a functionof Lxy. Displaced vertices are separated by flavour into three channels: ee, eµand µµ. Distributions labeled “All” (solid circles) have no additional selectionsapplied. The distribution with open circles in the ee channel has only the ma-terial veto applied and distributions with open squares have the heavy-flavourdecay veto applied. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.21 OS and SS displaced vertices in the Validation Region as a function of the DVmass. Leptons in the DVs are required to pass the Medium (VeryVeryLoose)quality working points for muons (electrons). The material map veto is alsoapplied for the ee channel. The ratio of OS to SS vertices is shown in thebottom ratio plot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935.22 Correlation plot of DV mass (mDV) versus radius (Lxy = rDV) for the differencebetween OS and SS vertices in the three DV type channels. The data eventsstudied in these plots are selected from events in the VR. The heavy-flavourdecay veto applied in each channel is shown by the solid red line. The z-axismaximum in the plots is saturated at 30 in order to provide a colour scale thatcan distinguish regions with small negative entries (more SS than OS DVs)from those with small positive entries (more OS than SS DVs). . . . . . . . . . 945.23 OS and SS displaced vertices with the heavy-flavour decay veto applied for dataevents in the VR. The material veto is also applied for displaced ee vertices. . . 95xxList of Figures5.24 The invariant mass between the prompt lepton and same-flavour displacedlepton (mll) for selected VR data events in the Z mass veto study. Eventsaround the Z mass with 80 GeV < mll < 100 GeV are identified as Z decaysand are removed from the SR. . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.25 The HNL mass (mHNL) shapes for the background estimate (shaded purple),DV systematic (solid blue line), prompt lepton systematic (dashed blue line),observed SS events (grey triangles) and observed OS events (black circles) forthe six different channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.26 SS displaced vertices in the VR with the heavy-flavour decay veto applied.The material veto for ee DVs is also applied. SS DVs are separated by trackcharge into vertices with two positively charged tracks (SS ++) and two neg-atively charged tracks (SS −−). This study does not include the ∆pT/pT cutfor displaced electrons described in section 5.6. . . . . . . . . . . . . . . . . . . 1035.27 HNL mass distribution for the SS background estimate (orig. plep) and for theshuffled background estimate (random plep), where plep is an abbreviation for“prompt lepton”. The shuffling factor, f , which is defined as the ratio of thenumber of shuffled events to number of original SS background events, is shownon the plots for each channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.28 Tri-lepton mass distribution for the SS background estimate (orig. plep) andfor the shuffled background estimate in colours (random plep), where plep is anabbreviation for “prompt lepton”. The shuffling factor, f , which is defined asthe ratio of the number of shuffled events to number of original SS backgroundevents, is shown on the plots for each channel. . . . . . . . . . . . . . . . . . . . 1065.29 Pre-fit (a-b) and post-fit (c-d) plots for the 2QDH model with inverted-hierarchy(IH) mixing in the “Dirac-limit” (left column) and “Majorana-limit” (right col-umn). The signal region (SR) includes events with mHNL < 20 GeV and thecontrol region (CR) includes events with 20 < mHNL < 50 GeV. . . . . . . . . . 1135.30 Pre-fit plots for the 1SFH model with muon-only mixing (a-b), electron-onlymixing (c-d) and the 2QDH model with normal hierarchy (NH) mixing (e-f)in the “Dirac-limit” (left column) and “Majorana-limit” (right column). Thesignal region (SR) includes events with mHNL < 20 GeV and the control region(CR) includes events with 20 < mHNL < 50 GeV. . . . . . . . . . . . . . . . . . 1145.31 Post-fit plots for the 1SFH model with muon-only mixing (a-b), electron-onlymixing (c-d) and the 2QDH model with normal hierarchy (NH) mixing (e-f)in the “Dirac-limit” (left column) and “Majorana-limit” (right column). Thesignal region (SR) includes events with mHNL < 20 GeV and the control region(CR) includes events with 20 < mHNL < 50 GeV. . . . . . . . . . . . . . . . . . 115xxiList of Figures5.32 The mHNL distribution in the SR and CR for the observed data and the post-fit background for the 2QDH model with inverted-hierarchy mixing in the“Majorana-limit”. Simulated signal samples with three different mass pointsare also shown normalized to the pre-fit signal strength. After the global fit isperformed, the signal strength is zero. . . . . . . . . . . . . . . . . . . . . . . . 1165.33 The expected (dashed line) and observed (solid line) 95% confidence level (CL)contours for the 1SFH model with muon-only (a) and electron-only (b) mixingin the “Dirac-limit” and the observed 95% CL contours for the four HNL modelslisted in table 5.1 in the “Dirac-limit” (c) and “Majorana limit” (d). The limitsare shown for the mixing angle (|U |2) as a function of the HNL mass (mN ). Theregions enclosed by the contours are excluded. The observed contours for the1SFH models are also shown for the 1997 DELPHI [68] and the 2019 ATLAS[70] results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175.34 The expected (dashed line) and observed (solid line) 95% CL contours for themixing angle, |U |2, in the 1SFH model with muon-only (a) and electron-only(b) mixing in the “Majorana-limit” and the contours for the 2QDH model withNH (c-d) and IH (e-f) mixing in the “Dirac-limit” and “Majorana-limit” asa function of the HNL mass, mN . The green and yellow bands indicate theranges of expected limits obtained within ±1 and ±2 standard deviations ofthe median limit reflecting uncertainties in the signal and background yields.The regions enclosed by the contours are excluded. . . . . . . . . . . . . . . . . 1196.1 A longitudinal view of the active regions of the ITk detector. The pixel detectoris shown in the inner region (smaller radius) and is surrounded by the stripdetector. The strip end-cap disks can be seen on either side of the barrel region,coloured with blue and green stripes. Figure taken from [91]. . . . . . . . . . . 1206.2 An expanded view of a strip module in the barrel. Petal modules consist ofthe same basic components, but with different hybrid and sensor geometries.Figure take from [91]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.3 A full sketch of a strip petal and the modules labelled R0-R5. The sensors, inblue, are glued onto the core surface shown in yellow. Light green and yellowchips are housed on the green hybrids and glued onto the sensors. The powerboards are shown in orange. Figure modified from [91]. . . . . . . . . . . . . . 122xxiiList of Figures6.4 The final validated thermocycling program (a) with a ramp rate of 1.33◦C/minand soak times of 15 hours and 30 min at 21◦C and ±40◦C respectively. Thisplot shows the temperature and RH for the full 46-hour program. The redcurves show the measured temperature inside the climate chamber and theblue curves show the RH inside the chamber. The temperature and RH curves(b) for the first thermocycle where the RH spike is the largest. The plot in(b) also indicates the dew point inside the chamber (dashed red line) and themeasured pressure differential (green line), which is defined as ∆P = Pin − Pout.1246.5 The location of the stable markers glued directly to the carbon surface labeled1-5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1256.6 The petalet hanging in the climate chamber right before thermocycling. . . . . 1266.7 Plots of the surface scans of the sensor on side A and the bus-tape surfaceof side B before and after thermocycling. The flatness, bow and other sensormeasurements are also shown in the text on the right-hand side of the plots. . . 1276.8 Plot of the displacement vectors (∆~R) for the features on side A, includingthe two hybrids in purple, the sensor in blue and the bus-tape in brown. Thevector magnitudes are uniformly scaled by a factor of 2000 to visually examineif there is a common direction for the displacements. . . . . . . . . . . . . . . . 1286.9 A photo of the first semi-electrical petal. This petal was the prototype used inthe thermocycling tests discussed in this section. This photo was taken by theTRIUMF communications team. . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.10 The petal coordinate system. The x- and y-axes are defined using the two petalfiducials on the inner and outer petal locators. The origin is defined as the innerfiducial and the x-y plane is defined as the flat surface of the petal locators. . . 1306.11 Pictures of the different fiducial markers on the sensors, hybrids and bus-tape.These markers are measured by the CMM to determine the position of thevarious components on the semi-electrical petal. . . . . . . . . . . . . . . . . . . 1316.12 The support bar in the vertical orientation in the climate chamber. The threeattachment points on the bar are where the three petal locators are attachedand secured to hang the petal in the chamber. . . . . . . . . . . . . . . . . . . . 1326.13 The petal hanging in the climate chamber before and during thermocycling. . . 1336.14 Arrow plot and ∆R displacements of the four sensor fiducials (in blue) and thefour fiducials on the hybrid (in purple) for one of the R5 sensors on side A. Thearrows in the plot are magnified by a factor of 2000 to visually see the directionof motion. The magnitudes and uncertainties of the displacements are shownin the boxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134xxiiiList of Figures6.15 Statistical analysis of the roughly 100 different points measured on Side A ofthe petal. The pull in the y-direction (∆y/σy) and the pull x-direction (∆x/σx)are shown immediately after thermocycling and the measurements are repeated48 hours and four weeks later. After 48 hours, the mean of the pull is closer tozero, which indicates that after some time the structures relax and are moreconsistent with no movement after thermocycling. . . . . . . . . . . . . . . . . 1346.16 The crack on the R4 sensor and the bowing of a hybrid on the same module.Photos are taken immediately after thermocycling the semi-electrical petal 100times. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1366.17 Arrow plot and displacements (∆R and ∆z) of the four fiducials (in purple) forone of the hybrids on side A. The arrows in the plot are scaled by a factor of2000 to visually see the direction of motion. The magnitudes and uncertaintiesof the displacements are shown in the boxes. . . . . . . . . . . . . . . . . . . . . 1376.18 Statistical analysis of the roughly 100 different points measured on Side A of thepetal. The pull in the y-direction (∆y/σy) and the pull x-direction (∆x/σx) areshown immediately after thermocycling and two weeks later. After two weeks,the central distribution is more consistent with zero, except for outliers withlarge pulls that are from the measurements of the hybrid on the module wherethe failure occurred. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.19 Current and HL-LHC era DAQ systems for the ATLAS experiment. The FELIXcards will replace the current readout drivers (RODs) and readout systems(ROSs) used in the current DAQ system. Figure adapted from [93]. . . . . . . 1386.20 A diagram of the ITk-Strip readout showing how all the custom ASICs (ABC-Star, HCCStar and AMAC) are connected to each other and merged in theend-of-structure (EoS) card before being converted to an optical signal andsent to FELIX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.21 A sketch of the HCCStar emulator and LCB wrapper integrated into the FELIGdata generation structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140A.1 An illustration of the main steps of the shuffling analysis framework thatdemonstrated the types of files are needed as inputs to each step. . . . . . . . . 154A.2 Displaced vertices as a function of DV mass and radius for events producedusing the “do-nothing” configuration (in purple) and the original data events(in blue). In the “‘do-nothing” configuration, the original non-selected tracksare also saved such that, the only difference between each event is the primaryvertex. Differences at low Lxy can be observed, from the locations of the primaryvertices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156xxivList of FiguresA.3 Displaced vertices as a function of DV mass and radius (Lxy) for events pro-duced using the “do-nothing” configuration with the original non-selected tracks(in purple) and non-selected tracks from host data events (in pink). Differencesbetween the distributions show that using hadrons from a random host-eventmisses some correlations between the non-selected tracks in the original eventand the lepton-only displaced vertices. . . . . . . . . . . . . . . . . . . . . . . . 157A.4 DV mass distribution for shuffled and “do-nothing” events for SS and OS dis-placed vertices. The ratio between shuffled and not shuffled events is the shuf-fling factor. For this test, with only one collision run from 2016, the expectedshuffling factor of 18.8 is the dashed black line in the ratio plot. OS and SSvertices are directly compared in (c) and (d) for the not shuffled and shuffledevents respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158A.5 Data transfer volume on the worldwide LHC computing network as a functionof time. The two large spikes is this plot can be attributed to the large amountsof data being transferred for this track shuffling estimate. Figure obtained fromthe computing monitoring systems. . . . . . . . . . . . . . . . . . . . . . . . . 159xxvGlossary1SFH refers to an HNL model used to interpret the results of the analysis described in thisthesis. This model has one heavy lepton state that mixes 100% of the time with a singleneutrino flavour.2QDH refers to an HNL model used to interpret the results of the analysis described in thisthesis. This HNL model has two quasi-degenerate heavy lepton states with m1 ∼ m2.The lepton states can mix with any flavour of neutrino..ABCStar refers to one of the custom front-end chips for the ATLAS Inner Tracker. It’s roleis to convert incoming charge signal into hit information. “ABC” stands for ATLASBinary Chip and “Star” refers to the independent pathways from each ABCStar to theHCCStar that create a star shape.AFII refers to the ATLAS Fast Simulation that is used to simulate events in the ATLASdetector. This fast simulation includes a parametrization of the calorimeter response inorder to reduce the simulation time.ALICE is a detector dedicated to studying heavy-ion physics and is one of the four mainLHC experiments. It stands for A Large Ion Collider Experiment.AMAC refers to one of the custom front-end chips for the ATLAS Inner Tracker. It providesmonitoring and interrupt functionality. “AMAC” stands for Autonomous Monitor andControl.ASIC refers to a chip with customized integrated circuits that are designed for particularuse cases. It stands for Application-Specific Integrated Circuits.ATLAS is a general purpose detector and is one of the four main LHC experiments. Thisdetector is used to collect the data analyzed in this thesis. It stands for A Toroidal LHCApparatus.BCR refers to a is 1-bit command sent to all front-end chips that is synchronous with theLHC bunch crossings. This command resets the bunch crossing counter to zero and isused to ensure front-end synchronization. It stands for Bunch Counter Reset.xxviGlossaryBooster is the proton synchrotron booster. It is one of the accelerators in the LHC protoninjection chain.BRAM refers to a module in an field programmable gate array (FPGA) that provides on-chip storage for large amounts of data. It stands for Block Random Access Memory.Bremsstrahlung is electromagnetic radiation produced by the deceleration or deflection ofa charged particle passing through matter near the strong electric fields of nuclei.BSM refers to a beyond the Standard Model theory that proposes descriptions of physicalphenomena that are not currently explained by the Standard Model.Bus-tape provides the modules in the ATLAS Innner Tracker with low and high-voltagepower. Modules are glued directly onto the bus-tape.Calorimeter-tagged muon refers to a track in the ATLAS ID that matches an energydeposit in the calorimeter consistent with a minimum ionizing particle. This type ofmuon has the lowest purity of all the muon types.CC is a charged current interaction mediated by a W+ or W− boson.CERN is the Centre for European Nuclear Research. It is a European research organizationthat operates the largest particle physics laboratory in the world.CFF is a common-file format used in the output of the custom track shuffling algorithm.This file consists of a list of tracks and a set of shuffling instructions that maps variouscombinations of tracks into unique fake events.CL refers to a Confidence Level. This is the probability that, if the test were repeated manytimes, the same outcome would be observed.CMM refers to a coordinate measuring machine. It is used to measure the location in three-dimensional space of an object with respect to a reference point.CMS is a general purpose detector and is one of the four main LHC experiments. It standsfor Compact Muon Solenoid.Combined muon refers to a track that is reconstructed using a global fit of the hits inthe ATLAS ID and MS. During the fit, MS hits may be added or removed in order toimprove the fit quality. An outside-in approach is used for the reconstruction, startingwith the reconstruction of tracks in the MS and then extrapolating inwards to matchMS to ID tracks.xxviiGlossaryCP refers to a combined performance group in the ATLAS collaboration that provides rec-ommendations on how to reconstruct and identify standard physics objects.CPU refers to a central processing unit that consists of electronic circuitry that executesinstructions from a computer program.CR refers to the region in the HNL search used to constrain the background estimate inthe global HNL mass fit. It is defined as the region that passes all the event selections,except that the mHNL is required to be between 20 and 50 GeV.CSC refers to a cathode-strip chamber in the ATLAS MS that is primarily responsible fortracking and measuring the momentum of muons.DAQ refers to a hardware and software system that is used to collect data. It stands forData Acquisition.DELPHI is a general purpose detector that was one of the four main experiments at theLarge Electron-Positron collider built at CERN to study electroweak interactions.DP is the temperature of an environment below which, given the moisture in the chamber,water droplets will start to form. It stands for Dew Point.DV refers to a place of common origin for two or more tracks that is displaced with respectto the primary proton interaction point. It stands for Displaced Vertex.ECal refers to the Electromagnetic Calorimeter that is part of the ATLAS calorimeter systemand is primarily responsible for measuring the energy of electrons and photons.EoS refers to the End of Structure cards on each large-scale structure in the ATLAS InnerTracker strip detector. This card contains, among other things, a custom chip thattransmits the clock and control signals and receives data from the front-end chips.FCal refers to the ATLAS Forward Calorimeter that is primarily responsible for measuringthe energy of particles in the forward region of ATLAS.FE refers to a front-end readout chip responsible for buffering and reading out data fromdetectors.FELIG refers to the Front-End Link Generator card used to mimic the ATLAS Inner TrackerStrip readout in the HCCStar emulator that is described in this thesis.FELIX refers to the Front-End Link Exchange card that will be used in LHC Run 3 (seetimeline in fig. 3.3) and beyond to send and receive data from front-end chips on thedetectors.xxviiiGlossaryFiducial marker refers to an object used by an imaging machine to determine the locationand orientation of an object. For example, during petal mounting, fiducial markers areused to locate the modules and place them onto the petal surface.FPGA refers to a field programmable gate array that consists of integrated circuits designedto be configurable after manufacturing.GBT refers to a data protocol developed by CERN for use in data transmission for exper-iments requiring high data rate links and electronic components capable of sustaininghigh radiation doses. It stands for GigaBit Transceiver.Geant4 is a geometry and tracking platform used to simulate the passage of particles throughmatter. This software toolkit is used to simulate the ATLAS detector system.GSF refers to a Gaussian-Sum Filter used to re-fit tracks matched to electrons. The GSFtakes into account non-linear effects in the trajectory of an electron related to bremsstrahlung.Hard-scatter refers to the primary interaction of interest in each proton bunch crossing. Itis defined as the interaction with the largest momentum transfer.HCCStar refers to one of the custom front-end chips for the ATLAS Inner Tracker stripdetectors. It is the digital interface between the hybrids and the EoS card. “HCC”stands for Hybrid Controller Chip and “Star” refers to the architecture that enables theHCC to build and transmit module wide events.HEC refers to the Hadronic End-Cap Calorimeter that is part of the ATLAS calorimetersystem. It is primarily responsible for measuring the energy of hadrons.HL-LHC is the High-Luminosity Large Hadron Collider, which is the upgraded LHC machinethat will produce proton collisions with ten times the current luminosity.HLT refers to the high-level trigger and is the second software-based trigger step used inATLAS to trigger on interesting events.HNL refers to a heavy neutral lepton and is the subject of the search described in this thesis.HNLs are heavy right-handed states that carry no Standard Model (SM) charges. Intro-ducing HNLs into the SM introduces a mechanism that can explain the light neutrinomasses.Hybrid refers to an electrical circuit board that houses the ATLAS Inner Tracker Stripfront-end chips and is glued onto the silicon sensors.xxixGlossaryIBL refers to the Insertable B-Layer that is part of the ATLAS ID. It is the first layer of thepixel detector and was inserted into the ATLAS ID in 2014 to increase the robustnessand precision of the tracking, as well as to mitigate luminosity effects and radiationdamage.ID refers to the Inner Detector. It is the innermost detector system of the ATLAS detectorand is primarily responsible for reconstructing the trajectory of particles.IH refers to the inverted neutrino mass hierarchy wherein the two heavier mass eigenstateshave a small mass difference and the third state has the lightest mass.Inside-out refers to a tracking sequence that initially forms track seeds in the inner silicondetector and then extends the tracks outward in radius.ITk refers to the ATLAS Inner Tracker. It is an all-silicon tracking system that will replacethe current ID in time for the start of the HL-LHC. It consists of layers of pixel detectorssurrounded by a large-area strip detector system.ITk-Strip refers to the silicon-strip tracking detector and is a sub-system of the ATLASInner Tracker. These detectors are the subject of the performance and readout researchdescribed in chapter 6.Kalman filter refers to a track reconstruction method to find additional space-points thatare compatible with the initial track seed.L-1 refers to the level-1 hardware-based trigger that uses information collected from theATLAS muon and calorimeter detector systems to make decisions about which protoncollisions might contain interesting physics events.L0a refers to a beam crossing synchronous pulse that transfers data from the pipeline in theInner Tracker front-end chips to an event buffer. This data is then sent upstream forfurther data processing. It stands for Level-0 accept.LAr is liquid argon, which is a cryogenic liquid used to detect particles in various ATLASdetectors, including the tile and forward calorimeters.LCB refers to the Level-0 accept (L0a), Control and Bunch counter reset (BCR) signal. Itis a custom data protocol used in the Inner Tracker Strip detectors to transmit L0as,control commands and BCRs.LEP is the Large Electron-Positron collider built at CERN to study electroweak interactions.LEP was closed down in November 2000 for the construction of the LHC in the sametunnels.xxxGlossaryLHC is the Large Hadron Collider, which is the world’s largest and highest energy particleaccelerator and collider. It comprises two superconducting rings and is designed to collideprotons at four interaction points.LHCb is a detector dedicated to studying b-physics and is one of the four main LHC exper-iments. It stands for Large Hadron Collider Beauty Experiment.LHLoose refers to an electron identification criterion used to select leptons with a certainefficiency and purity. This identification has a larger efficiency and lower purity thanthe LHMedium criterion. An identification criterion is also known as a working point.LHMedium refers to an electron identification criterion used to select leptons with a certainefficiency and purity. An identification criterion is also known as a working point.LINAC2 is the Linear Accelerator. It is one of the accelerators in the LHC proton injectionchain.LLP refers to a long-lived particle. In this context, long-lived usually means that the particletravels a distance larger than the position resolution of the detector before it decays.This term typically refers to an exotic particle and not an existing SM particle with along lifetime, such as a b-hadron or muon.LNC refers to a process or decay that conserves lepton number. It stands for lepton numberconserving.LNV refers to a process or decay that violates lepton number. It stands for lepton numberviolating.Loose refers to a muon identification criterion used to select muons with a certain efficiencyand purity. This identification has a larger efficiency and lower purity than the mediumidentification criterion. An identification criterion is also known as a working point.LRT is the large radius tracking reconstruction algorithm used in ATLAS to reconstructdisplaced tracks that do not point back to the interaction point.Luminosity In particles physics, instantaneous luminosity refers to the number of particlespassing per unit area per unit time and thus is a measure of how densely packed thetwo beams are. The integrated luminosity is the time integral of the instantaneousluminosity.MC refers to a Monte-Carlo simulation and is computational mathematical technique that isused to model the probability of different outcomes in the particle collision events thatare studied in the search described in this thesis.xxxiGlossaryMDT refers to a monitored drift tube in the ATLAS MS that are primarily responsible fortracking and measuring the momentum of muons.Medium refers to a muon identification criterion used to select muons with a certain effi-ciency and purity. An identification criterion is also known as a working point.MS refers to the ATLAS Muon Spectrometer is the outermost layer of the ATLAS detector.It is primarily responsible for detecting and measuring the momenta of muons.NC is a neutral current interaction mediated by a Z boson.NH refers the normal neutrino mass hierarchy wherein the two lightest mass eigenstates havea small mass difference and the third state has a larger mass.Ntuple refers to a data structure that contains an ordered set of n-elements. Ntuples areused to store physics event information in a format that is simple and quick to processthe data events.OS refers to opposite-sign and is used to describe a vertex that has two tracks with oppositecharges.Outside-in refers to a tracking sequence that starts with track segments in the outer TRTlayers and extends the tracks inward toward to interaction point.Pair production is the formation of a particle and anti-particle pair from a neutral boson.It often refers to the creation of an electron and positron from a photon near a nucleus.Pileup refers to all the additional collisions that occur at the same time as the hard-scatterprimary interaction in a proton-proton collision.Pixel detector is the silicon pixel detector used to reconstruct tracks in the ATLAS ID.PS is the Proton Synchrotron. It is one of the accelerators in the LHC proton injection chain.Pseudorapidity is a spatial coordinate that describes the angle of a particle relative tothe z-axis. It is defined as η = − ln tan(θ/2). In the massless limit where m →0, thedifference in pseudorapidity, ∆η, is Lorentz invariant under boosts along the z-axis.QA refers to Quality Assurance tests that study the performance and reliability of detectorcomponents during the research, development and production stages.Rapidity is a kinematic variable defined as y = 12 ln(E+pzE−pz ), which is Lorentz invariant forboosts along the z-axis, but is not fixed in physical space.xxxiiGlossaryRH refers to the relative humidity. It is defined as the ratio of moisture present in the systemrelative to moisture that would be present if the air was completely saturated.ROD refers to a custom hardware-based readout driver responsible for processing the datafrom front-end electronics and passing the data to the central readout system.RoI refers to a region of interest in the ATLAS detector identified by the L-1 trigger forfurther study in the second high-level trigger step.ROS refers to custom electronics boards that are central to the ATLAS readout system.They receive, buffer and process data events from segments of a given sub-detector andhave access to the first-level trigger descisions.RPC refers to a resistive plate chamber in the ATLAS MS that is primarily responsible fortriggering on muons.SCT is the Semiconductor Tracker, which is a large-area silicon micro-strip detector used toreconstruct tracks in the ID.SM is the Standard Model, which is a mathematical theory that is currently the best-knowndescription of fundamental particles and their interactions (except for gravity).SPS is the Super Proton Synchrotron. It is one of the accelerators in the LHC proton injectionchain.SR refers to the signal region for the search described in this thesis. Events in this region arerequired to pass the all the selections described in section 5.7.SS refers to same-sign and is used to describe a vertex that has two tracks with the samecharge.TDAQ is the trigger and data acquisition system in ATLAS. It is responsible for the trig-gering and reading out data from various detector systems.TGC refers to a thin-gap chamber in the ATLAS MS that is primarily responsible for trig-gering on muons.Tower is a region in η×φ space in the calorimeter. Towers are used to build energy clusters.TRIUMF is Canada’s particle accelerator centre located in Vancouver, British Columbia.TRT is the Transition Radiation Tracker, which is the outermost sub-system of the ID. It isprimarily responsible for extending track reconstruction to larger radii. It is also used todistinguish electrons and pions based on their differing amounts of transition radiation.xxxiiiGlossaryVeryVeryLoose refers to a custom electron identification criterion used to select displacedelectrons with a certain efficiency and purity. An identification criterion is also knownas a working point.VR refers to the validation region with negligible signal contamination used to study back-ground events and selected displaced vertices for the background estimate in the HNLsearch.VSI refers to a vertex reconstruction algorithm used in ATLAS to reconstruct a place ofcommon origin from tracks that do not point back to the interaction point. It standsfor Vertex Secondary Inclusive. This term also refers to the default secondary vertexingconfiguration used in the ATLAS reconstruction software.VSI Leptons refers to the default lepton-only secondary vertexing configuration used toreconstructed displaced vertices with tracks that are matched to leptons.Working point is also known as an identification criterion. In this context it refers to alepton identification criterion used to select leptons with a certain efficiency and purity.xxxivAcknowledgementsTo Alison, thank you for your continuous guidance and support through my PhD. Thank youfor constantly pushing me to be a better physicist and encouraging me to “do a little bit” ofanalysis work, even though I wanted to spend more time in the lab. I will forever be gratefulfor your mentorship, especially over the past few months while I was figuring out what to doafter my PhD. I would also like to thank Matthias for his guidance and support while I wasworking on the displaced HNL search. I am fortunate to have had many insightful researchdiscussions with you and your mentorship over the past few years has been invaluable. ToColin, thank you for getting me started on the hardware readout project. I always valued ourchats and I am grateful for your support in the development of the ITk-Strip readout programat UBC. I am also grateful to Wojtek who got me started with firmware programming.Thank you to all of the displaced HNL team, especially Robin N. and Christian, whoworked tirelessly to complete this physics analysis. Thank you also to my PhD committeemembers, Gary and Eric, for their feedback during my committee meetings. I am also gratefulto all the members of the ATLAS Collaboration that I have had the privilege to work with.I also wish acknowledge the financial support from the Natural Sciences and EngineeringResearch Council of Canada, which gave me the freedom to pursue a variety of researchprojects.My PhD would not have been the same without the members of the UBC ATLAS group.To Robin N., Robin H., Se´bastien, Zhengcheng, Fe´lix, Chris, Elham, Vincent, Ryan, Russelland Colm, I will always cherish the memories of our lunch-time chats, camping trips andGlu¨hwein nights in the office. To Robin H., thank you for keeping me sane during the longpandemic months. You are one of my biggest cheerleaders and I am grateful for your endlesssupply of optimism.To my parents, you taught me to be curious and to think critically. Your support andadvice has given me the confidence to pursue my passions. I am also incredibly lucky to havethe love and support of my sister Hope, grandparents, Carol, Ernie, Rosemary and Peter, aswell as my second family, Larissa, John, Augustine and Samuel.Most of all, thank you to Nicholas. You are my hero, not only for editing every page ofthis thesis with no physics background (while also studying to become a lawyer!), but also formaking me believe “this is fine”, even when it felt like there were fires burning everywhere. Ican’t wait to see what our next adventure will bring!xxxvChapter 1The Standard ModelThe Standard Model (SM) is currently the best-known description of fundamental particlesand their interactions, with the exception of gravity. While this theory provides precise pre-dictions that are consistent with many experimental measurements, there is also evidence thatthe SM is incomplete. This chapter provides a basic description of the SM and discusses someits successes and limitations, which provide insight into where to search for new physics.1.1 Particles in the Standard ModelThe matter around us is made up of two groups of fundamental particles, namely leptons (l)and quarks (q). Both groups follow Fermi statistics with half-integer spins and, thus, are alsoreferred to as fermions. The charged leptons, which consist of electrons (e), muons (µ) andtaus (τ) are organized into three generations. Each charged lepton also has a correspondingcharge-neutral neutrino (ν). The other matter particles, known as quarks, come in six flavoursand are also paired in three generations: up (u)/down (d), charm (c)/strange (s) and top(t)/bottom (b). Due to colour confinement, quarks are bound in composite colourless systemsknown as hadrons. Hadrons can be divided into two sub-groups: mesons, which are made upof quark and anti-quark pairs, and baryons, which consist of three quarks, such as protonsand neutrons.As far as we know, our universe has four fundamental forces: strong, electromagnetic,weak and gravitational. Each force is mediated by a particle (or particles) known as a gaugeboson. The four fundamental forces, their mediators and their relative strengths1 are listedin table 1.1.There are multiple theories that describe each force. The classical theory of the gravi-tational force is described by Newton’s law of universal gravitation. The relativistic theoryof gravity is described by Einstein’s general theory of relativity. However, gravity’s effect onfundamental particles in the SM is so weak that it is almost always negligible in particlephysics experiments. The strong force is responsible for confining quarks and binding protonsand neutrons together to form nuclei. The theory of electromagnetic force is known as elec-trodynamics and governs how light and charged matter particles interact. The weak force is1The “strength” of a force depends on its nature and the distance over which it is acting. Table 1.1 providesan approximate order of magnitude for each force to illustrate their relative strengths.11.1. Particles in the Standard ModelTable 1.1: The four fundamental forces with their relative strengths and mediators. Tablefrom [1].Force Strength Mediator(s)Strong 10 GluonsElectromagnetic 10−2 PhotonWeak 10−13 W and ZGravitational 10−41 Unknownresponsible for decays of unstable subatomic particles, such as mesons, and plays an importantrole in nuclear radiation. The electromagnetic and weak forces have been unified into a singletheory known as electroweak theory. In the SM, all fermions interact via the weak force andcharged leptons also interact via the electromagnetic force. Quarks carry both electromagneticcharge and colour2, which means quarks interact with the electromagnetic, strong and weakforces. There is one final particle in the SM known as the Higgs boson. This boson was the lastSM particle to be discovered and it is a scalar boson that is responsible for giving particlesmass. A summary of the elementary particles in the SM is found in fig. 1.1.LeftLeftRightLeftRightLeftLeftRightLeftLeftRightLeftRightLeftRightLeftRightLeftRightLeftRight                                                (! "  #$   (! "  % %% %%% &' (  Figure 1: Particle content of the SM and its minimal extension in neutrino sector. In the SM(left) the right-handed partners of neutrinos are absent. In the ⌫MSM (right) all fermionshave both left and right-handed components.Y can vary from 1013 (Dirac neutrino case) to ⇠ ⇡ (the onset of the strong coupling). Theadmitted region is sketched in Fig. 2.Independently on their mass, the new Majorana leptons can explain oscillations of activeneutrinos. So, an extra input is needed to fix their mass range. It can be provided by theLHC experiments.Suppose that the resonance found at the LHC by Atlas and CMS in the region 125 126GeV is indeed the Higgs boson of the Standard Model. This number is remarkably close tothe lower limit on the Higgs mass coming from the requirement of the absolute stability ofthe electroweak vacuum and from Higgs inflation, and to prediction of the Higgs mass fromasymptotic safety of the Standard Model (see detailed discussion in [1] and in a proposalsubmitted to European High Energy Strategy Group by Bezrukov et al. [2]). The existenceof the Higgs boson with this particular mass tells that the Standard Model vacuum is stableor metastable with the life-time exceeding that of the Universe. The SM in this case is avalid e↵ective field theory up to the Planck scale, and no new physics is required above theFermi scale from this point of view. Suppose also that the LHC finds no new particle and nodeviations from the Standard Model. In this case the “naturalness paradigm”, leading thetheoretical research over the last few decades will be much less attractive, as the proposals fornew physics stabilizing the electroweak scale by existence of new particles in the TeV regionand based on low energy supersymmetry, technicolor or large extra dimensions would requiresevere fine-tunings.The solution of the hierarchy problem does not require in fact the presence of new particlesor new physics above the Fermi scale. Moreover, the absence of new particles between theelectroweak and Planck scales, supplemented by extra symmetries (such as the scale invari-ance) may itself be used as an instrument towards a solution of the problem of stability of2124.9Figure 1.1: The elementary particles that make up the Standard Model. Figure adapted from[2].2Here, colour refers to colour charge, which is a quantum number related to the strong interaction.21.2. Chiral Fermions1.2 Chiral FermionsIn general, the Lagrangian for a massless fermion is:L = ψ¯iγµ∂µψ (1.1)where ψ represents a particle field, γµ are the gamma matrices and ∂µ are partial time andspace derivatives. In quantum theory, this Lagrangian can either describe a massless particleψL with left-handed helicity, in which its spin is anti-parallel to its direction of motion, or amassless anti-particle ψR with right-handed helicity, in which its spin is parallel to its directionof motion. In general, ψL or ψR represent ‘chiral’ fermion states, which are not equal to helicitystates. However, in the case of a massless fermion (or when E >> m), helicity and chiralityare equivalent. Thus, chiral states are often labelled by their handedness.To describe massive fermions, a Dirac mass term could be written down. This term wouldmix together left and right-handed fermions and combine them into a single Dirac fermion:LDirac mass = −mD(ψ¯RψL + ψ¯LψR) (1.2)In the SM, all fermions are Dirac fermions, except for the neutrinos whose nature remainsunknown. If neutrinos are not Dirac, they could be Majorana fermions with a mass term suchas:LMajorana mass = −mM (ψ¯LψL + ψ¯RψR) (1.3)The origin of neutrino masses will be discussed in chapter 2, as it motivates the search forthe theoretical particle described in this dissertation.1.3 Structure of the Standard ModelThe structure of the SM is based on symmetries of local transformations known as gaugetransformations. It is described by the gauge group SU(3)C × SU(2)L × U(1)Y . The stronginteractions are described by the SU(3)C gauge group, where the subscript C denotes thecolour. The electroweak interactions are described by the SU(2)L×U(1)Y gauge group, whichrepresents the unification of weak and electromagnetic forces. The subscript L denotes thatonly left-handed particles participate in weak interactions and the subscript Y denotes theweak hypercharge. This weak hypercharge Y = Q − T 3 relates the electric charge Q of theparticle and third component of the weak isospin T 3, all of which are quantities that must beconserved in an electroweak interaction.In the SM, the strong, weak and electromagnetic gauge fields are represented by Giµ, Wjµ,and Bµ. The quarks are represented by left-handed quark doublets QL = (uL, dL)T and right-31.3. Structure of the Standard Modelhanded uR and dR singlet states. The leptons are represented by left-handed lepton doubletsLL = (νL, eL)T and right-handed eR singlet states. Leptons do not have corresponding νRsinglet states because neutrinos are massless in the SM. The values of the electric charge, thethird component of the weak isospin and the hypercharge for the fields are summarized intable 1.2.Table 1.2: The SM fermion fields and their electric charges Q, third components of the weakisospin T 3 and hypercharges Y .Fermion Type Field Q T 3 YQuarksQL =(uLdL)+2/3 +1/21/6-1/3 -1/2uR +2/3 0 +2/3dR -1/3 0 -1/3LeptonsLL =(νLeL)0 +1/2 −1/2−1 −1/2eR −1 0 −1The left and right fermion fields carry different electroweak charges because of the chiralnature of the weak interaction. Therefore, a Dirac mass term of the form in eq. (1.2) cannotbe directly added to the Lagrangian. Instead, masses for the quarks and charged leptons aregenerated via interactions between the fermion and Higgs fields.The Lagrangian of the SM takes the form:LSM = Lgauge + LHiggs + LYukawa (1.4)The gauge Lagrangian Lgauge consists of kinetic terms for the fermions and gauge bosons:Lgauge =− 14(Giµν)2 − 14(W jµν)2 +−14(Bµν)2+ iQ¯L /DQL + iu¯L /DuR + id¯L /DdR+ iL¯L /DLL + ie¯L /DeR(1.5)where these terms are products of the gauge field strength tensors and the fermion fields. Theterms are written in a compact notation using a covariant derivative of the form:/D = γµ(∂µ + igstiCGiµ + igwtjLWjµ + ig′Y Bµ) (1.6)where gs is the coupling strength of the strong interaction, gw is the coupling strength ofthe weak interaction and g′ is the coupling strength for the electromagnetic interaction. Thematrices tjL form a representation of the SU(2)L group and can be expressed in terms of the41.4. Electroweak Symmetry BreakingPauli matrices, σj , such that tjL = σj/2. The Gell-Mann matrices tiC form a representation ofthe SU(3)C group. The Higgs Lagrangian LHiggs describes the kinetic and potential terms forthe Higgs doublet Φ:LHiggs = | /DΦ|2 − (−µ2|Φ|2 + λ|Φ|4) (1.7)where µ and λ are parameters of the Higgs potential. This potential is discussed in more detailin section 1.4. The Yukawa Lagrangian, LYukawa, describes the interactions between the scalarbosons and fermions:LYukawa = −FuQ¯LΦ˜uR − FdQ¯LΦdR − FeL¯LΦeR (1.8)where Φ˜ = iσ2Φ and Fu, Fd, Fe are the Yukawa couplings between the Higgs and fermionfields.1.4 Electroweak Symmetry BreakingAs mentioned in section 1.3, the mass terms for the charged fermions and massive W and Zbosons cannot be added directly to the SM Lagrangian. Instead, these masses are generatedvia the Higgs mechanism, with the spontaneous breaking of the local SU(2)L × U(1)Y gaugeinvariance.In a theory without symmetry breaking, the Higgs Lagrangian, LHiggs, has a potential ofthe form V (Φ) = µ2|Φ|2+λ|Φ|4 with µ2 > 0, where Φ is a doublet in the SM. This is sketchedin fig. 1.2 (a). This potential has a unique minimum, or ground state, at Φ = 0 that issymmetric: rotations about this minimum leave the ground state unchanged. For spontaneoussymmetry breaking to occur µ2 < 0. This potential is sketched in fig. 1.2 (b).x202y202V()0102030(a) µ2 > 0x202y202V()404(b) µ2 < 0Figure 1.2: The potential V (Φ) = µ2|Φ|2 + λ|Φ|4 in a theory without (a) and with (b) localsymmetry breaking around a minimum of the potential.51.5. Successes and Limitations of the Standard ModelIt is clear from the figure that there is no longer a unique ground state for the system.Instead, there is a ring of ground states that lie at a radius equal to√−µ22λ ≡ v√2 . This value vis known as the “vacuum expectation value” or VEV of the Higgs field. In this new potential,the local field close to any given choice of ground state is not invariant under rotation. Thistype of symmetry is thus referred to as “spontaneously broken”.In the Higgs mechanism, it is convenient to represent the Higgs doublet as:Φ =1√2(0v + h)(1.9)This choice minimizes the number of scalar degrees of freedom and expresses Φ in terms of asingle scalar Higgs field h. Substituting eq. (1.9) back into the Higgs Lagrangian in eq. (1.7)results in mass terms for the scalar Higgs field h and the massive gauge bosons W and Zwith:m2h = 2λv2,m2W =14g2wv2 andm2Z =14(g2w + g′2)v2.(1.10)1.5 Successes and Limitations of the Standard ModelThe SM is an elegant theory that has been experimentally tested at collider experiments toa high degree of precision across a wide range of energy regimes. In fig. 1.3, cross sectionmeasurements for various SM processes are shown. These measurements are performed usingproton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider.So far the SM predictions have been incredibly successful and show overall excellent agreementbetween data and theory.However, there is experimental evidence that suggests this theory is incomplete. For in-stance, astrophysical observations of gravitational lensing [3], rotational velocities of galaxies[4, 5] and measurements of the cosmic microwave background [6] all suggest that the visiblematter described in the SM represents only a small fraction of the total matter present inour universe. The SM does not describe the nature of this “dark” matter. Another exampleis the ratio of matter to anti-matter present in the universe. Our universe is largely matter-dominated and currently, the SM offers no explanation for this. Most relevant to the searchdescribed in this dissertation is the observation of neutrino flavour oscillations [7]. In the SM,neutrinos are strictly massless, due to the absence of right-handed neutrino fields. However,experiments have observed the probability of measuring a neutrino with a definite flavourcan vary as the neutrino propagates through space. This flavour oscillation probability is pro-portional to the mass splitting between the neutrino mass states. Thus, the observation of61.5. Successes and Limitations of the Standard Modelnonzero neutrino masses also suggests there exists physics beyond the SM.pp W Z t¯t tt-chanWt H WW WZ ZZ ts-chant¯tW t¯tZWWVtot.t¯tt¯t500 µb−180 µb−12 fb−1WHZHtotaltt¯H(×0.3)VHVBFWWWWWZ(×0.2)10−210−111011021031041051061011σ[pb]Status: July 2021ATLAS Preliminary√s = 7,8,13 TeVTheoryLHC pp√s = 13 TeVData 3.2 − 139 fb−1LHC pp√s = 8 TeVData 20.2 − 20.3 fb−1LHC pp√s = 7 TeVData 4.5 − 4.6 fb−1Standard Model Total Production Cross Section MeasurementsFigure 1.3: Summary of several Standard Model cross-section measurements. The measure-ments are corrected for branching fractions, compared to the corresponding theoretical ex-pectations. Figure taken from [8].7Chapter 2Heavy Neutral LeptonsMany theories have been proposed for physics beyond the Standard Model (BSM) in order toprovide a complete theory of the universe. In particular, theories with several right-handedneutrino states have been proposed to explain (some of the) observed BSM phenomena. Heavyneutral leptons (HNLs) are massive particles that interact similarly to neutrinos with interac-tion strengths that are described by flavour dependent mixing angles (U2e , U2µ and U2τ ). HNLswere first proposed in left-right symmetric theories as heavy right-handed states that interactvia the weak force [9–12]. Introducing right-handed heavy states also provides a type-I seesawmechanism that can explain the light SM neutrino masses [13–15]. Not only does this theoryprovide a natural explanation to the nature of the relatively small neutrino masses (whencompared with charged leptons), it also provides an explanation for the asymmetry betweenmatter and anti-matter in the universe through a process known as leptogenesis. In HNLscenarios with masses around the electroweak scale, the seesaw mechanism implies that theneutrino Yukawa couplings are relatively small such that neutrino production in the early uni-verse is very slow. If charge-parity violating oscillations occurred during neutrino productionin the early universe, then this could explain the matter-antimatter asymmetry [16]. More-over, models with three HNLs can also incorporate a dark matter candidate [17, 18]. Thischapter provides a brief overview of the seesaw mechanism that can explain why neutrinoshave extremely light masses and reviews how HNLs interact with the SM.2.1 Neutrino Masses From Right-Handed NeutrinosThis section describes how right-handed HNLs can give rise to light SM neutrino masses.This description of the type-I seesaw mechanism is adopted from [19]. The Lagrangian for Nright-handed neutrinos NRI is described by:LSM+HNL = LSM + iN¯RIγµ∂µNRI − (FαI L¯αNRI Φ˜ +12MIN¯cRINRI ) (2.1)where LSM is the usual SM Lagrangian, FαI is the Yukawa couplings matrix, MI is themass matrix for the right-handed states NRI , Lα = (να, eα)T are left-handed lepton doubletswith α = {e, µ, τ}, Φ is the Higgs doublet with Φ˜ = iσ2Φ and N¯ cRI is the charge conjugatetranspose of the NI state. The right handed neutrino states carry no standard model charges82.1. Neutrino Masses From Right-Handed Neutrinos(i.e. they are “sterile”) and therefore it is possible to add a Majorana mass term of the formMIN¯cRINRI to the Lagrangian, which is usually prohibited by gauge invariance. A summary ofthe elementary particles in the SM with the addition of N = 3 right-handed sterile neutrinosis found in fig. 2.1.LeftLeftRightLeftRightLeftLeftRightLeftLeftRightLeftRightLeftRightLeftRightLeftRightLeftRightuup2.4 MeV⅔ ccharm1.27 GeV⅔ ttop171.2 GeV ⅔ddown4.8 MeV-⅓ sstrange104 MeV-⅓ bbottom4.2 GeV-⅓νeelectronneutrino0 νμmuonneutrino0 ντtauneutrino0eelectron0.511 MeV-1 μmuon105.7 MeV-1 τtau1.777 GeV-1ggluon0 0γphoton00Z091.2 GeV0weakforceW±80.4 GeV± 1weakforcemass→charge→QuarksLeptonsThree Generations of Matter (Fermions) spin ½Bosons (Forces) spin 1I II IIIname→H>114 GeV 00Higgsbosonspin 0N 1 N2 N3sterileneutrinosterileneutrinosterileneutrinoFigure 1: Particle content of the SM and its minimal extension in neutrino sector. In the SM(left) the right-handed partners of neutrinos are absent. In the ⌫MSM (right) all fermionshave both left and right-handed components.Y can vary from 1013 (Dirac neutrino case) to ⇠ ⇡ (the onset of the strong coupling). Theadmitted region is sketched in Fig. 2.Independently on their mass, the new Majorana leptons can explain oscillations of activeneutrinos. So, an extra input is needed to fix their mass range. It can be provided by theLHC experiments.Suppose that the resonance found at the LHC by Atlas and CMS in the region 125 126GeV is indeed the Higgs boson of the Standard Model. This number is remarkably close tothe lower limit on the Higgs mass coming from the requirement of the absolute stability ofthe electroweak vacuum and from Higgs inflation, and to prediction of the Higgs mass fromasymptotic safety of the Standard Model (see detailed discussion in [1] and in a proposalsubmitted to European High Energy Strategy Group by Bezrukov et al. [2]). The existenceof the Higgs boson with this particular mass tells that the Standard Model vacuum is stableor metastable with the life-time exceeding that of the Universe. The SM in this case is avalid e↵ective field theory up to the Planck scale, and no new physics is required above theFermi scale from this point of view. Suppose also that the LHC finds no new particle and nodeviations from the Standard Model. In this case the “naturalness paradigm”, leading thetheoretical research over the last few decades will be much less attractive, as the proposals fornew physics stabilizing the electroweak scale by existence of new particles in the TeV regionand based on low energy supersymmetry, technicolor or large extra dimensions would requiresevere fine-tunings.The solution of the hierarchy problem does not require in fact the presence of new particlesor new physics above the Fermi scale. Moreover, the absence of new particles between theelectroweak and Planck scales, supplemented by extra symmetries (such as the scale invari-ance) may itself be used as an instrument towards a solution of the problem of stability of2124.9Figure 2.1: The elementary particles that make up the Standard Model with the addition ofN = 3 right-handed sterile neutrinos. Figure adapted from [2].After electroweak symmetric breaking, the Higgs field Φ obtains a vacuum expectationvalue v and Φ˜ = 1√2(v + h0). Thus, eq. (2.1) can be rewritten as:LHNL = LSM + iN¯RIγµ∂µNRI − ((v + h)/√2)FαI ν¯LαNRI −12MIN¯cRINRI (2.2)Thus, the effect of the Yukawa interaction term in eq. (2.1) is to generate a Dirac massterm that couples left and right-handed neutrino states and the HNLs “inherit” weak-likeinteractions with the W and Z bosons that are suppressed by the mixing angles, ΘαI .The mass terms in eq. (2.2) can always be diagonalized, but in the limit where |MI | >>v|FαI |, this diagonalization leads to N heavy and three light states. The eigenvalues of thediagonalized atrix corresponds to the HNL and SM neutrino masses. These light neutrino92.2. Interactions with the Standard Modelmasses are suppressed by the HNL-neutrino mixing angles, ΘαI , such that:ΘαI =v|FαI |MI(2.3)This is known as a seesaw mechanism because increasing the eigenvalues increases themasses of the HNLs, while pushing the masses of the SM neutrinos down.Experimental observations of neutrino flavour oscillations tell us that there are two massdifferences for the SM neutrinos [7]. In order for the above description to explain the observedneutrino mass splittings, the number of NI states must be N ≥ 2. The search described inthis dissertation uses a model-independent approach where only one HNL is kinematicallyaccessible and, if other HNLs are present in the theory, they are considered sufficiently heavythat they do not affect the analysis. An additional model-dependent interpretation, whichconsiders two HNLs with nearly degenerate masses (M1 ∼M2), is also included. In this case,the HNL mass, mN = (M1 + M2)/2. Further motivation for this model-dependent approachis discussed in [20].2.2 Interactions with the Standard ModelHNLs interact with the SM through mixing with neutrinos. The experimentally relevantobservable for this interaction is the mixing of the HNLs with a given neutrino flavour:|Uα|2 ≡∑I|ΘαI |2 (2.4)where α = e, µ, τ and I is the number of HNLs. This mixing is also referred to as the“coupling” to a definite flavour neutrino, α, since it measures the strength of the interactionbetween the two particles. The total mixing between HNLs and neutrinos is:|U |2 ≡∑αI|ΘαI |2 ≡∑α|Uα|2 (2.5)The mixing angles, ΘαI , are related to the neutrino Yukawa couplings, FαI . There aremeasured constraints on the Yukawa couplings that can be expressed as constraints on thevalues of |Uα|2 that are compatible with neutrino oscillations data. An analysis done in [20]used NuFIT, the most recent global fit to neutrino oscillation data [21], to map out values ofthe relative strength of the mixing with electron, muon and tau neutrinos, xα = |Uα|2/|U |2,that are consistent with neutrino oscillations measurements (see fig. 2.2). Two regions are de-fined that are consistent with the data assuming inverted and normal neutrino mass hierarchy.Normal (NH) and inverted hierarchy (IH) benchmark models are defined in the two allowedregions according to the ratio between the flavour specific mixing angles (see table 2.1). Ex-102.2. Interactions with the Standard Modelperimental searches typically report the interpretation of their results under the assumptionof mixing with a single neutrino flavour. For this reason, electron-only and muon-only mixingscenarios are also defined.3L2r #2M+?K `Fb pbX M2mi`BMQ Qb+BHH iBQM +QMbi` BMib3 f NElectron-onlyMuon-onlyIHNHFigure 2.2: A plot that shows the allowed combinations of |Uα|2/|U |2 that are consistent withthe recent NuFIT [21] fit to neutrino oscillation data. The allowed regions under normal (blue)and inverted (green) hierarchy are shown. The red cross markers represent two benchmarkscenarios that are defined for the two different hierarchy assumptions. Figure adapted from[20].Table 2.1: The relative strength of the mixing, xα = |Uα|2/|U |2, with the three neutrinoflavours for the inverted (IH) and normal (NH) hierarchy benchmark and single-flavour mixingscenarios.Model xe xµ xτIH 1/3 1/3 1/3NH 0.06 0.48 0.46Muon-only 0 1 0Electron-only 1 0 03In the search presented in this dissertation, the acceptance to decays with tau leptons is zero. For thisreason, a single tau-only mixing scenario is not considered.112.3. HNL Decays2.3 HNL DecaysThe analysis described in this dissertation searches for HNLs produced through a W bosonthat decays into a lepton and a neutrino, which mixes with the HNL. HNL decays are mediatedby the weak interaction via charged current or a neutral current decays. The decay, shown infig. 2.3, can either be fully leptonic if the bosons decay to lepton final states or semi-leptonicif the bosons decay hadronically. If the charged leptons from the decay of the HNL have thesame flavour (i.e. β = γ), then both the charged current and neutral current decays contributeto the total process.W+l+αl−βl+γ , q¯νγ , q′N W+?(a) Charged current decayW+l+ανβl+γ , q¯l−γ , qN Z?(b) Neutral current decayFigure 2.3: Feynman diagrams for HNL production from the decay of a W boson and theHNL decay into leptonic and semi-leptonic final states.2.4 Lepton Number ViolationThe SM Lagrangian has a global U(1) symmetry that corresponds to a conserved quantumnumber known as the lepton number L, where leptons have +L and anti-leptons have −L.If HNLs behave as Majorana fermions, with identical particle and anti-particle states, thenlepton number violating (LNV) decays are possible. In some models, LNV decays can besuppressed compared to the lepton number conserving (LNC) processes, while in others, sucha Dirac fermion HNL model, LNV decays are forbidden [20, 22–25]. Diagrams of LNC andLNV decays are shown in fig. 2.4. The distinction between an LNC and LNV decay comesfrom the relative charge between the first lepton (lα) and the lepton (lβ or νβ) that couplesto the HNL. For LNC decays, these two leptons must have opposite charges, while for LNVdecays, these leptons have the same charge.Due to the chiral nature of the weak interaction, the HNL is produced with a preferredhelicity state (spin polarization) that is correlated with the spin of the lepton lα. Since theHNL is a very weakly interacting particle (and in particular is electrically neutral), its spin122.5. HNL Cross Sectionis preserved during its propagation through space. Thus, when the HNL decays, the spin ofthe lepton that couples directly to the HNL lβ will be correlated to the spin of the HNL andcorrespondingly to the spin of lα. Depending on how the HNL decays (either via an LNC orLNV known decay), the angular distributions of the leptons will be different. Such kinematicdifferences can have small impacts on the experimental efficiencies of selecting HNL signalevents. The impact of spin correlations in LNC and LNV decays on the search described inthis dissertation is described in more detail in section 2.4.W+l+αl−βl+γνγNW+?(a) LNCW+l+αl+βl−γν¯γNW−?(b) LNVFigure 2.4: Lepton number conserving (LNC) and lepton number violating (LNV) diagramsfor the charge-current leptonic HNL decay.2.5 HNL Cross SectionThe probability of producing a heavy neutral lepton can be described by the production crosssection, σN , measured in units of area. To compute the HNL cross section, the mass, mN , andmixing angles, |Θα|2, need to be specified. The branching ratio for the W boson decaying toan HNL and a charged lepton, lα, is directly proportional to the coupling strength and canbe expressed as [26]:BR(W → lαN) = BR(W → lαν) · |Θα|2(1− m2Nm2W)2(1 +m2N2m2W)(2.6)where BR(W → lαν) is the known W branching ratio to a lepton-neutrino pair, Θα arethe mixing angles between the HNL and SM neutrinos and mN and mW are the mass of theHNL and W boson respectively.132.5. HNL Cross SectionThis means that the total HNL cross section from the decay of W boson, σN , is given by:σN = σ(pp→W ) ·BR(W → lαN)= σ(pp→W ) ·BR(W → lαν) · xα · |Θ|2 ·(1− m2Nm2W)2(1 +m2N2m2W) (2.7)where xα · |Θ|2 has been substituted for |Θα|2.To compute the rate for the HNL decay to leptons, σN is multiplied by the branchingratio for the fully-leptonic HNL decay BR(N → llν). This branching ratio takes into accountthe strength of the mixing angles between the HNL and its decay products. The relevantHNL branching ratios used in the analysis in this dissertation are shown in fig. 2.5 for thefully-leptonic decay channels.2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0mN [GeV] 0.000.020.040.060.080.100.12BR(Nll) - any flavour neutrinoMuon-only mixing (xe = 0 , x = 1 , x = 0)BR(N ee )BR(N e )BR(N e )BR(N )(a)2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0mN [GeV] 0.000.020.040.060.080.100.12BR(Nll) - any flavour neutrinoElectron-only mixing (xe = 1 , x = 0 , x = 0) BR(N ee )BR(N e )BR(N e )BR(N )(b)2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0mN [GeV] 0.010.020.030.040.050.060.070.08BR(Nll) - any flavour neutrinoNormal hierarchy mixing (xe = 0.06 , x = 0.48 , x = 0.46)BR(N ee )BR(N e )BR(N e )BR(N )(c)2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0mN [GeV] 0.0250.0300.0350.0400.0450.050BR(Nll) - any flavour neutrinoInverted hierarchy mixing (xe = 1/3 , x = 1/3 , x = 1/3)BR(N ee )BR(N e )BR(N e )BR(N )(d)Figure 2.5: Branching ratio of N → llν with a sum of all neutrino flavours as a function ofmN for muon-only (a), electron-only (b), NH (c) and IH (d) mixing scenarios. In each mixingscenario, the branching ratio is shown for N → eeν (blue), N → eµν (orange), N → µeν(pink) and N → µµν (purple) decays.142.5. HNL Cross SectionIndividual HNL decay branching ratios, BR(N → llν) depend on mN and the relativestrengths of the mixing angles: xe, xµ and xτ . The branching ratios are computed assumingone HNL state in the “Majorana-limit” with both LNC and LNV decays contributing equally.These branching ratio values include a sum of all possible flavours of neutrinos. The differencebetween BR(N → lγlγν) and BR(N → lβlγν) (with β, γ = e or µ) is due to the interferencebetween the charged and neutral current decays in cases where the leptons, l, are identical.In the muon-only (electron-only) mixing scenario, N → ee (N → µµ) decays have a smallbranching ratio from exclusively neutral current decays and N → eµ (N → µe) decays are notpossible. In the multi-flavour mixing scenarios, all decays are possible. In the NH benchmarkthe mixing with µ/νµ is stronger than the mixing with e/νe, resulting in larger branchingratios for N → µµ and N → µe decays. The IH benchmark has equal mixing with all threelepton flavours and thus, the difference between the four decays comes from the interferencebetween neutral and charge-current decays.2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0mN [GeV] 10 910 810 710 610 510 410 310 2|U|2=I,|I,|2Muon-only mixing (xe = 0 , x = 1 , x = 0)c N = 1 mmc N = 10 mmc N = 100 mmFigure 2.6: The total mixing |U |2 as a function of HNL mass mN for the muon-only mixingscenario. Each |U |2 is computed for mN between 2 and 20 GeV with proper decay lengthscτN = 1, 10 and 100 mm.The proper lifetime of the HNL, τN , strongly depends on the mass, mN , and the mixingangle, |Θ|2, such that [27]:τN ∝ 1m5N |Θ|2(2.8)The dependence on the mass in this expression can be derived by approximating the HNLdecay as a four-fermion contact interaction where the width, Γ, is proportional to the squareof the Fermi constant G2F . The value of G2F has negative four mass dimensions and Γ has onemass dimension. Thus, using dimensional analysis, Γ must be proportional to m5. Since τ is152.5. HNL Cross Sectioninversely proportional to Γ, the lifetime is proportional to 1/m5.The total mixing angle, |Θ|2, for one HNL model in the “Majorana-limit” can be analyt-ically computed for a given generated mass and lifetime using a Fermi theory computationdescribed in [28]. These computations include all exclusive decay widths and a sum over allthe decay channels that contribute to the process. The mixing angle, |U |2 = ∑αI |ΘαI |2,as a function of HNL mass, mN , for the muon-only mixing scenario is shown in fig. 2.6 forcτN = 1, 10, 100 mm. The relationships between |U |2 and mN in the other mixing scenariosare similar and the corresponding |U |2 have similar orders of magnitude to the muon-onlymixing scenario.16Chapter 3The ATLAS Detector at the LargeHadron ColliderThe research described in this dissertation uses proton collision data collected by the ATLASexperiment at the European Centre for Nuclear Research (CERN). The proton collisions areprovided to the ATLAS experiment by the Large Hadron Collider (LHC). This chapter givesan overview of the LHC and describes the ATLAS detector.3.1 The Large Hadron ColliderThe LHC is the world’s largest particle accelerator and collider. Consisting of two supercon-ducting rings, the LHC is designed to collide protons with a centre-of-mass energy of√s = 14TeV and a nominal luminosity of L =1034 cm−2 s−1 [29]. It is installed in a 27 kilometre-longtunnel under the countryside surrounding Geneva, Switzerland. Protons are accelerated inopposite directions in each of the superconducting rings and collide at four interaction points.These points, where the two proton beams cross, are the locations of the four main LHCexperiments: ATLAS [30], CMS [31], ALICE [32] and LHCb [33].Building the LHC at CERN meant that this new machine would be able to reuse theexisting tunnels and injection chain that were originally built for the Large Electron Position(LEP) machine. The injection chain starts with a linear accelerator (LINAC2), where theprotons, sourced from hydrogen gas with their electrons stripped off by an electric field, areaccelerated to 50 MeV. Then, a series of smaller accelerators gradually increase the energyof the protons. The Proton Synchrotron Booster (Booster), the Proton Synchrotron (PS)and the Super Proton Synchrotron (SPS) accelerate the protons up to 1.4, 25 and 450 GeV,respectively. Thereafter, the protons are injected into the LHC where they can be furtheraccelerated up to a maximum energy of 7 TeV. Figure 3.1 shows an illustration of the pathfollowed by the protons.173.1. The Large Hadron Collider 3. LHC and ATLASFigure 3.1: The CERN accelerator complex relevant for proton–proton collisions in the LHC. Grayarrowheads indicate the proton path. BOOSTER refers to the Proton Synchrotron Booster, PS is theProton Synchrotron, and SPS is the Super Proton Synchrotron. The figure is adapted from refer-ence [49].minutes to fill the LHC with pre-accelerated proton bunches. Within around 20 minutes after thefilling, the LHC accelerates the beams to their target collision energies.3.1.2 Luminosity and pile-upThe number of events produced by the LHC is a function of the instantaneous luminosity L deliveredby the machine over time t ,Nevents =æeventZLdt =æeventL, (3.1)and is proportional to the relevant cross-section æevent for producing such events. The time integralover instantaneous luminosity is called the integrated luminosity L. The instantaneous luminosity isgiven by [9]L = f n1n24ºæxæyF. (3.2)With the nominal LHC spacing between proton bunches of 25 ns, the collision frequency is f = 40MHz.The amount of protons per bunch is n1 and n2 for the two beams, with up to 1011 protons per bunch.Not all bunches are filled with protons in practice. The bunches have root mean square extensions æxand æy in the two directions perpendicular to the beam propagation direction. Collisions at the LHCare not exactly head-on, and the factor F contains a description of the geometric effects due to thecrossing angle between the beams at the interaction point.Due to the large amount of protons per bunch at the LHC, each bunch crossing usually resultsin more than one hard scattering interaction. Interactions besides the interaction of interest are23Figure 3.1: An illustration of various experimental facilities and beam lines at the CERN accel-erator complex relevant to the LHC. The protons are accelerated through the injection chainand into the LHC. The path they follow is: LINAC2 → BOOSTER → Proton Synchrotron(PS) → Super Proton Synchrotron (SPS) → LHC. Figure adapted from [34].3.1.1 LHC Filling SchemeThe beams in the LHC consist of bunches of protons spaced by 25 ns intervals. This is equalto a bunch crossing rate of 40 MHz. At the LHC’s desig luminosity, each bunch of protonscontains about 1.15 × 1011 protons. When filling the LHC, not all of these bunch spaces,also known as buckets, are filled with protons. Instead, empty buckets are left in the beamin order to meet various operational constraints, such as allowing time for the injection ofprotons from the SPS or time to dump the beam if/when this is required. This means thatwhen the LHC is full there are a total of 2808 bunches circulating in each LHC beam. TheLHC filling scheme changes with time, but any changes are always done to give ATLAS andCMS the same number of protons collisions. The full filling scheme is described in detail inRef. [35].3.1.2 LuminosityThe number of events per second produced at the LHC for a given process is proportionalto the cross section of the process of interest (σprocess) and the instantaneous luminosity (L)183.1. The Large Hadron Colliderthat is delivered by the LHC over time (t):Nprocess = σprocess∫Ldt = σprocessL (3.1)where L is the time integral of the instantaneous luminosity, known as the integratedluminosity, L. The instantaneous luminosity is given by [36]:L = fn1n24piσxσyF (3.2)where n1 and n2 are the number of protons in each bunch, f is the collision frequency andσx and σy are the root-mean-square of the horizontal and vertical bunch size respectively. Sincecollisions at the LHC are not exactly head-on, an additional factor F accounts for geometriceffects arising from the nonzero crossing angle between the two beams.(a)0 10 20 30 40 50 60 70 80Mean Number of Interactions per Crossing0100200300400500600/0.1]-1Recorded Luminosity [pb Online, 13 TeVATLAS-1Ldt=146.9 fb∫> = 13.4µ2015: <> = 25.1µ2016: <> = 37.8µ2017: <> = 36.1µ2018: <> = 33.7µTotal: <2/19 calibration(b)Figure 3.2: Total integrated luminosity versus time (a) delivered to ATLAS (green), recordedby ATLAS (yellow), and certified to be good quality data (blue) during Run 2. Distribution ofthe mean number of interactions per bunch crossing (b) recorded by the ATLAS experimentin the years 2015-2018. Figures taken from [37].3.1.3 DatasetAlthough the LHC was designed to collide protons with a centre-of-mass energy of up to√s = 14 TeV, it has not yet been run at this maximum energy. The first LHC run (Run1) operated at√s = 7 TeV (2011) and√s = 8 TeV (2012). The second run (Run 2) beganin 2015 and finished collecting data in 2018 at a centre-of-mass energy of√s = 13 TeV.The search described in this dissertation uses the data collected during Run 2. This datasetcontains a total integrated luminosity of 139 fb−1 after accounting for recording efficiency andgood detector operation. The evolution of luminosity delivered to the ATLAS experiment is193.1. The Large Hadron Collidershown in fig. 3.2 (a). During Run 2, a total of 156 fb−1 of stable proton-proton collisions weredelivered to ATLAS by the LHC. Out of the total luminosity delivered, 147 fb−1 was recordedby ATLAS, due to various data taking inefficiencies. Of this recorded luminosity, 139 fb−1met the requirement that the data was of good quality for all sub-detectors needed for thesearch presented in this dissertation.3.1.4 PileupWhen the proton bunches collide at the interaction points around the ring, multiple protoncollisions can be recorded. The primary collision of interest, known as the hard-scatter inter-action, is the one with the largest momentum transfer. The additional collisions are calledpileup and can occur in time or out of time with the hard-scatter event. In-time pileup refersto other collisions that are from the same bunch crossing as the hard-scatter collision. Incontrast, out-of-time pileup occurs when readout times for the detector systems are longerthan the time between two bunch crossings resulting in the detector sometimes recording en-ergy deposits from earlier or later bunch crossings. Figure 3.2 (b) shows the mean number ofinteractions per bunch crossing recorded by the ATLAS experiment between 2015 and 2018at√s = 13 TeV.3.1.5 High-Luminosity LHCThe LHC is undergoing a series of upgrades to enable the machine to produce collisions withten times the current luminosity. This upgraded machine, known as the High-Luminosity LHC(HL-LHC) will provide a challenging new environment for future detector operations. Thereis a two-and-a-half-year shutdown planned in order to install the necessary upgrades for thecurrent LHC machine and for the various detectors on the LHC ring. One of these detectorupgrades for the ATLAS experiment is discussed in detail in chapter 6. The details of theLHC/HL-LHC run schedule are shown in fig. 3.3.5 to 7.5 x nominal Lumi13 TeVintegrated luminosity2 x nominal Lumi2 x nominal Luminominal Lumi75% nominal Lumicryolimitinteractionregionsinner triplet radiation limitLHC HL-LHCRun 4 - 5...Run 2Run 1DESIGN STUDY PROTOTYPES CONSTRUCTION INSTALLATION & COMM. PHYSICSDEFINITION EXCAVATIONHL-LHC CIVIL ENGINEERING:HL-LHC TECHNICAL EQUIPMENT:Run 3ATLAS - CMSupgrade phase 1ALICE - LHCbupgradeDiodes ConsolidationLIU InstallationCivil Eng. P1-P5experiment beam pipessplice consolidationbutton collimatorsR2E project13 - 14 TeV 14 TeV7 TeV 8 TeVLS1 EYETS EYETS LS3ATLAS - CMSHL upgradeHL-LHC installationLS230 fb-1 190 fb-1 350 fb-1 3000 fb-14000 fb-120402027BUILDINGSFigure 3.3: The LHC/HL-LHC timeline and run schedule as of Fall 2021. This diagram includesthe planned shutdown and upgrade periods. Figure taken from [38].203.2. The ATLAS Detector3.2 The ATLAS DetectorThe ATLAS experiment is a general purpose detector designed to search for the Higgs bosonover a large mass range, perform precision measurements of the SM and search for evidenceof BSM physics. In order to accomplish these objectives, ATLAS is equipped with a varietyof very fast and radiation-hard electronics and particle detection elements that provide goodobject resolution and reconstruction efficiency over a wide range of energies [39]. This sectionprovides an overview of the different detector components of the ATLAS experiment.3.2.1 Coordinate SystemThe ATLAS experiment uses a right-handed global coordinate system that defines the loca-tions of the various detector subsystems and describes the kinematics of particles producedin the proton-proton collisions. The origin of the coordinate system is at the nominal protonbeam interaction point. The x-axis points from the origin towards the centre of the LHC ring,while the y-axis points up from the interaction point towards the surface. The z-axis is thenperpendicular to the x− y plane, pointing along the LHC beam axis. The azimuthal angle φand the polar angle θ are defined in the usual way with φ measured around the x-axis and θmeasured as the angle between the z-axis and a line segment from the origin to the point ofinterest.In hadron colliders, it is rare that the centre-of-mass frame of the interaction is thesame as the detector’s rest frame, since the individual quarks or gluons that collide are notequally balanced in momentum. For this reason, it is useful to define the pseudorapidity,η = − ln tan(θ/2), because, in the massless limit where m→0, the difference in pseudorapid-ity, ∆η, is Lorentz invariant under boosts along the z-axis. Alternatively, we can also define therapidity, y = 12 ln(E+pzE−pz ), which is truly Lorentz invariant for boosts along the z-axis, but is notfixed in physical space. This variable is typically used to measure massive objects and is ap-proximately equal to the pseudorapidity η for highly relativistic particles with m << E. Othercommonly used quantities include the transverse momentum, pT =√p2x + p2y, transverse en-ergy, ET =√m2 + p2T, and the angular distance between two objects, ∆R =√∆η2 + ∆φ2.3.2.2 Detector OverviewA schematic of the ATLAS detector is shown in fig. 3.4. It is the largest of the four main LHCexperiments, measuring 45 m in length, 25 m in height and weighing approximately 7,000tonnes [39]. ATLAS is a multi-purpose detector that consists of three layers designed to takecomplementary and redundant measurements in order to fully reconstruct particles emergingfrom the proton collisions. These layers are symmetrically distributed around the nominalinteraction point. In the central region, the sub-detectors are arranged in a cylindrical barrel213.2. The ATLAS Detectorstructure around the beam pipe, while disk-shaped end-cap structures are located on eitherside of the barrel.Figure 3.4: A cut-away view of the the ATLAS detector. Figure taken from [39].The ATLAS inner detector (ID) is located closest to the beam pipe and is contained in a2 T solenoid magnetic field [39]. The ID is primarily responsible for the precision tracking ofcharged particles in the central |η| < 2.5 region. Moving out in radius, the next system consistsof an electromagnetic and hadronic calorimeter designed to measure the energy of chargedand neutral particles. The muon spectrometer (MS) is the outermost layer of the ATLASdetector and is designed to detect charged particles (primarily muons) that are not stoppedin the calorimeter system. The MS system also independently measures the momentum ofthese charged particles in the |η| < 2 region. For this reason, the system also has threetoroidal magnets that generate magnetic fields of approximately 0.5 T and 1 T in the barreland end-cap regions respectively, in order to bend the charged tracks and obtain momentummeasurements [39].3.2.3 Inner DetectorThe ATLAS inner detector (ID) system is contained in a 2 T solenoid magnetic field andis designed to provide precision tracking and momentum measurements of charged particles223.2. The ATLAS Detectorwithin the pseudorapidity range of |η| < 2.5. To accomplish this goal, the ID is divided intothree complimentary sub-systems. Closest to the interaction point, where the detector requiresthe most granularity, is a dense silicon pixel detector. Further away from the interaction point,the semiconductor tracker (SCT) uses silicon-microstrip detectors to reduce material effectsand cost [40]. Surrounding the silicon pixel and strip detectors is the transition radiationtracker (TRT), which is made up of straw tube gas detectors. These three detector sub-systems are arranged in concentric circles in the barrel region and in disks in the end-caps.The transverse view of the ID is shown in fig. 3.5.Figure 3.5: A transverse view in the R-φ plane of the barrel region of the inner detector. Tracksfrom the proton collisions traverse outward in radius, with most of them passing through thefour silicon pixel layers, four silicon-microstrip (SCT) layers and approximately 36 straw tubes(TRT). In this figure, the fourth innermost layer of the pixel detector detector (IBL) is notshown. Figure taken from [39].233.2. The ATLAS DetectorPixel DetectorThe silicon pixel detector is designed to provide high precision measurements as close to theproton interaction point as possible. When charged particles pass through the semiconductingsilicon layers, they create electron-hole pairs that are collected by the sensors. A longitudinalview of the pixel detector is shown in fig. 3.6. The pixel system consists of four layers. TheFigure 3.6: A longitudinal view of the active region of the pixel detector. In this figure, thefourth innermost layer of the pixel detector (IBL) is not shown. Figure taken from [41].innermost layer is called the insertable B-layer (IBL) and was installed in 2014 between Run 1and Run 2 to increase the robustness and precision of the tracking and help mitigate luminosityeffects [41]. The IBL is located at a radius of r = 33 mm and covers the |η| < 3 region of thedetector. It also has the highest granularity of the four layers with a nominal pixel size of 50× 250 µm2 in φ× z. The other three layers of the detector have a nominal pixel size of 50 ×400 µm2 in φ× z (about 90% of the pixels) [39]. The intrinsic detector resolution of the IBLis 8 µm in φ and 40 µm in z, while the remaining pixel layers have a resolution of 10 µm inφ and 115 µm in z [40, 41]. The entire pixel detector detector consists of approximately 1744sensors and 80 million readout channels.Semiconductor TrackerThe semiconductor tracker (SCT) consists of a barrel detector and two symmetric end-capdetectors with approximately 61 m2 of silicon-microstrip sensors [40]. The barrel detector has243.2. The ATLAS Detectorfour layers of silicon modules placed at a constant radius around the beam-pipe, while theend-cap detectors are located on either side of the barrel perpendicular to the beam. In thecentral region, each silicon module consists of four detectors with a constant strip pitch of 80µm. Two detectors are wire bonded together and then two such pairs are mounted togetherat a 40 mrad stereo angle to provide three-dimensional tracking. This results in an intrinsicdetector resolution of 16 µm in φ and 580 µm in z. Figure 3.7 illustrates an SCT module withfour detectors connected to the hybrid readout electronics and a small stereo angle betweenthe two pairs of detectors.Figure 3.7: An SCT module showing the 4 silicon detectors connected to a readout hybridassembly. Figure taken from [40].Transition Radiation TrackerThe outermost layer of the ID is the transition radiation tracker (TRT) [42]. The TRT usesstraw tube gas detectors that have a diameter of 4 mm and can be up to 150 cm in length.The TRT has about 50,000 straws in the barrel region and 320,000 straws in the end-capregion. In total, the TRT has about 420,000 readout channels and has a detector resolutionof about 130 µm. Inside each straw tube, a 0.03 mm diameter gold-plated tungsten wire actsas the anode. The straw tubes are filled with a gas mixture that consists of Xe4, CO2 and O2[39]. Charged particles that pass through the straw tubes ionize the gas creating electron-ionpairs. These electrons drift toward the anode wire where they are read out by the electronics.Relativistic charged particles crossing the material boundary in the TRT produce transitionradiation photons in the X-ray range. These photons are absorbed in the active gas inside the4Since the beginning of Run 2, TRT tubes with high gas leak rates have been replaced with a less expensiveAr-based gas mixture. During Run 1 a number of tubes in inaccessible areas developed leaks. To save costs,Ar was used in these modules, even though it is less efficient at absorbing X-ray photons than Xe [43].253.2. The ATLAS Detectorstraw tubes and serve as a detecting method for tracking and particle identification. Lighterparticles, such as electrons, have larger gamma factors, γ = E/mc2, and will produce largeramounts of radiation compared to heavier particles, such as pions. This is used to help withelectron identification.3.2.4 Calorimeter SystemOutside of the solenoid magnet is a large volume calorimeter system. Electromagnetic andhadronic calorimeters measure the energy of the incident particles passing through them andprovide coverage in the |η| < 4.9 region. The goal of the ATLAS calorimeter system is toabsorb and measure the energy of most particles and limit the number of particles that passthrough into the muon system [39]. Figure 3.8 shows a cut-away view of the calorimetersystem.Figure 3.8: A cut-away view of the ATLAS calorimeter system. Figure taken from [39].Electromagnetic CalorimeterThe electromagnetic calorimeter (ECal) consists of a barrel and two end-cap detectors andis designed to measure the energy of incident electrons and photons [44]. It consists of al-ternating layers of “active” liquid argon (LAr) and “passive” lead absorbers. This type ofcalorimeter, with alternating “active” and “passive” layers, is known as a sampling calorime-ter. The granularity varies across the different layers of the ECal and is highest in the |η| < 2.5region, where tracking information from the ID is also available. The highest granularity of263.2. The ATLAS Detectorthe system is 0.025 × 0.025 in ∆η ×∆φ.Measuring the energy of the particles relies on the behavior of an electromagnetic shower.In the high energy regime of the LHC, electrons mainly lose their energy via bremsstrahlung,while photons mainly lose their energy via pair production [45]. As the electrons and photonslose energy in the material, a multiplication of particles occurs. These electromagnetic showerstypically occur in the absorbing material and are then detected in the active medium. Thiscascade of particles can be described in terms of the radiation length of the material X0, whichis the distance over which an electron loses, on average, 1/e of its energy due to radiation. Inthe case of photons, one radiation length is roughly 7/9 times the mean distance travelled bya photon before it undergoes pair production. The ATLAS ECal has a thickness of more than22X0 in the barrel and 24X0 in the end-cap regions. This provides adequate containment ofelectromagnetic showers originating from bremsstrahlung and pair production.Hadronic CalorimeterThe hadronic calorimeter is designed to measure strongly interacting particles such as hadrons.The ATLAS hadronic calorimeter consists of three components: the tile calorimeter, theLAr hadronic end-cap calorimeter (HEC) and the LAr forward calorimeter (FCal). The tilecalorimeter is also a sampling calorimeter and uses steel as an absorber and scintillating tiles asthe active material. Similar to electromagnetic showers, strongly interacting particles producehadronic cascades. While an electromagnetic shower is characterized by its radiation length,X0, a hadronic shower can be described by its (usually much longer) interaction length, λ,which is the mean distance between hadronic interactions in a given material [45]. The tilecalorimeter has three layers and a total thickness of 9.7λ at η = 0. The highest granularityof the tile calorimeter is 0.1 x 0.1 in ∆η × ∆φ. The HEC has two independent wheels perend-cap and extends out to |η| < 3.2. It is also a sampling calorimeter with alternating layersof passive copper plates and active LAr. The highest granularity of the hadronic end-capcalorimeter is 0.1 x 0.1 in ∆η ×∆φ. Finally, the forward calorimeter is designed to measureboth electromagnetic and hadronic interactions. It covers the very forward region of the de-tector 3.1 < |η| < 4.9 and its highest granularity is also 0.1 x 0.1 in ∆η ×∆φ. The forwardcalorimeter is approximately 10λ thick and consists of three layers. The first layer is madeof copper and is optimized for electromagnetic measurements, while the two other layers aremade of tungsten and liquid argon.3.2.5 Muon SpectrometerThe outermost layer of the ATLAS detector is the muon spectrometer (MS). Muons require adedicated system to detect and measure their momenta because, unlike most particles, theyare not stopped in the calorimeter system. A particle’s energy loss per unit path length largely273.2. The ATLAS Detectordepends on its velocity (β) and reaches an energy loss minimum near βγ ∼ 4 [45]. Since muonsat the LHC are typically produced around this threshold, they are known as minimum ionizingparticles. Muons energy loss per unit path length (dE/dx) is a tiny fraction of their energyand therefore they are not contained by the many layers of material in the calorimeter system.A cut-away view of the MS is shown in fig. 3.9.Figure 3.9: A cut-away view of the ATLAS muon system. Figure taken from [39].The MS consists of four different detector technologies that are designed to accomplish twomain goals. The monitored drift tubes (MDTs) and cathode-strip chambers (CSCs) providehigh precision tracking and momentum measurements of the incoming muons, while the thin-gap chambers (TGCs) and resistive plate chambers (RPCs) are primarily used to make initialtrigger decisions. The entire system is embedded in a large toroidal magnetic field that isused to bend the charged muons in order to measure their momentum based on their curvedtrajectories. The magnetic field in the muon system points in the φ direction, which is mostlyorthogonal to the muon trajectories and deflects charged particles in the η direction.Precision Muon Tracking ChambersTwo gas detector systems provide precision tracking information in the MS. Monitored drifttube (MDT) chambers are 30 mm drift tubes that are full of a pressurized Ar/CO2 gas mix-ture. Charged particles moving in a gas primarily lose energy due to excitation and ionizationof nearby gas molecules. This results in electron-ion pairs that are free to move around in themedium. These ionization electrons are then collected at tungsten-rhenium wires located at283.2. The ATLAS Detectorthe centre of the drift tubes. The time difference between the initial passage of the particle andthe arrival time of the ionization electrons at the central wire is related to how far away theincoming particle was from the centre of the tube and is used to provide a position measure-ment. The maximum electron drift time is about 700 ns. The MDTs provide pseudorapiditycoverage up to |η| < 2.7 and are aligned tangentially to the φ direction to provide precisionmeasurements along the z direction. The average spatial resolution of a single tube is about80 µm.Cathode-strip chambers (CSCs) are multi-wire proportional chambers that also containan Ar/CO2 gas mixture. These chambers are installed in the forward region of ATLAS (2.0 <|η| < 2.7), where the particle rate is much higher. The anode wires in the chambers areoriented in the radial direction. The cathode plates are segmented into strips that are paralleland perpendicular to the wires in order to provide 2D tracking. The position of the track isinterpolated between the charge collected on neighbouring strips. On average the CSC has aposition resolution of 60 µm per plate.Muon Trigger ChambersThe MS also has two detector systems with fast readout to provide information about themuon tracks traversing through the detector that is used to make trigger decisions. In thebarrel region (|η| < 1.05), layers of resistive plate chambers (RPCs) are used for triggeringon muons. RPCs are gaseous parallel electrode-plate detectors with a typical position-timeresolution on the order of 1 cm × 1 ns [46]. They are kept at a constant potential difference,which provides an electric field of about 5 kV/mm between the plates. The gas used is amixture of C2H2F4/Iso-C4H10/SF6. Charged particles passing through the plates ionize thegas and the resulting charges are collected on the anode plates. Each RPC station consists oftwo independent layers, providing measurements in the η and φ directions.The thin-gap chambers (TGCs) in the end-cap region (1.05 < |η| < 2.7) provide triggerinformation, as well as the azimuthal position of the tracks to complement the MDT mea-surements in the radial direction. TGCs are also multi-wire proportional chambers with ahigh-quenching gas mixture of CO2 and n-pentane. The TGCs provide a timing resolution ofless than 25 ns for 99% of tracks.3.2.6 Trigger and Data AcquisitionThe LHC delivers proton collisions to ATLAS at a rate of 40 MHz. With such a high collisionrate, it is impossible (in terms of data readout speed and storage) to record every protoncollision event. As a result, the ATLAS trigger and data acquisition system reduces the readoutrate down to about 1 kHz of events that are saved for further analysis. The ATLAS experimentcurrently uses two stages of triggers known as the Level-1 trigger and High-Level trigger. A293.2. The ATLAS Detectorschematic of the trigger and data acquisition system is shown in fig. 3.10.Figure 3.10: The ATLAS trigger and data acquisition system (TDAQ) system in Run 2 show-ing the various parts of the system relevant to triggering, detector readout and data flow.Figure adapted from [47].Level-1 TriggerThe Level-1 (L-1) trigger is a hardware-based system that uses information collected from themuon and calorimeter detector systems to make decisions about which proton collisions mightcontain interesting physics events [47]. The calorimeter information is used to find chargedleptons, photons, jets and missing transverse energy, while the muon system informationis primarily used to search for high-transverse momentum muons. For every event that isaccepted by the L-1 trigger, the front-end (FE) electronics read out the data for that event.The data is initially processed and formatted in the Readout Drivers (RODs) before passingto the Readout System (ROS) where the data is buffered. In addition to selecting interestingevents, the L-1 trigger also identifies so-called Regions-of-Interest (RoIs) within the detectorthat are further studied in the second trigger step. The L-1 trigger reduces the event rateto a maximum detector readout rate of 100 kHz. The maximum latency, which is the timethat the detector systems must buffer the data in their front-ends while waiting for an L-1decision, is 2.5 µs. There is also a limit to how many events can be read out consecutively to303.2. The ATLAS Detectoravoid overlapping readout windows, as well as a limit on the number of events stored withina given number of bunch crossings to prevent the front-ends buffers from overflowing.High-Level TriggerThe second trigger level, called the high-level trigger (HLT), is software based. Dedicatedreconstruction algorithms are used to reconstruct particles and estimate their properties inorder to make the final event selection. Typically the HLT trigger decision is made withina few hundred milliseconds, which is long enough to run multiple reconstruction algorithmsto extract physics information from the RoIs defined by the L-1 hardware trigger and decidewhether the event passes the trigger conditions. If the event passes the L-1 hardware trigger,then the full detector is read out for a final trigger decision. The HLT software is based onthe ATLAS offline software called Athena [48]. On average, the HLT trigger rate during anATLAS data-taking period is 1.2 kHz, which corresponds to about 1.2 GB/s of data beingsent to permanent storage.3.2.7 ATLAS Detector SimulationThe simulation of the ATLAS detector is based on a Geant4 simulation toolkit [49] andimplemented in the ATLAS simulation framework [50]. This framework simulates how stableparticles interact with the detector. Energy deposits in the sensitive detector elements arerecorded as “hits”. Pileup effects and detector noise are added to the simulation by overlappingadditional energy deposits from simulated minimum bias events on top of these “hits”. Thetrigger algorithms are also simulated and then the events are reconstructed with the samealgorithms that are used for actual experimental data (see chapter 4). Simulating the complexdetector geometry and detector response is computationally expensive. In fact, due to complexcalorimeter shower developments, almost 80% of the full simulation time is used to simulate thecalorimeter responses. For this reason, ATLAS fast simulation, or AFII, [51] was developed toparametrize the calorimeter response and reduce the simulation time. For the search describedin this dissertation, AFII is used to simulate the signal. AFII works reasonably well becuasethe signal only contains leptons and does not rely on any complex jet substructure variablesthat are not as well modelled in the ATLAS fast simulation.31Chapter 4Object ReconstructionThis chapter provides an overview of the reconstruction of physics objects with a focus onthose used in the analysis presented in this dissertation. The ATLAS detector is primarilydesigned to reconstruct prompt particles that are produced at the primary interaction point.As a result, standard reconstruction algorithms have been developed to identify differentparticles based on the signatures they produce in the various detector components. Thesestandard reconstruction algorithms are developed and maintained by combined performance(CP) groups that provide recommendations to the entire collaboration on how to use stan-dard physics objects in an analysis. These groups also provide calibrations and associateduncertainties for standard objects. In most cases, this means that analyzers directly use re-constructed physics objects, such as muons or electrons, in their analysis and only interactwith the reconstruction algorithms if they also work in a CP group. The relevant standardobject reconstruction algorithms are described in section 4.1. The reconstruction of basic com-ponents used to identify particles, including tracks, vertices and energy clusters is describedin section 4.1.2. The reconstruction of electrons and muons is described in section 4.1.3 andsection 4.1.4 respectively.The search described in this dissertation also requires non-prompt object reconstruction.Non-standard reconstruction techniques are required to identify displaced objects and searchfor displaced decays of exotic particles. Since these objects are not part of the standardreconstruction chain, there are currently no CP groups that provide recommendations fornon-standard physics objects. As a result, the analyzers often take on a greater role in thereconstruction and identification of non-standard objects. The reconstruction of non-standardobjects relevant to this analysis are described in section 4.2, with a focus on displaced vertexreconstruction in section 4.2.3.4.1 Standard Reconstruction4.1.1 OverviewA schematic of different particles interacting with the ATLAS detector is shown in fig. 4.1.Muons pass through the entire detector and mainly interact with the ID and MS. Electricallyneutral photons do not interact with the inner detector, but instead form a collimated shower324.1. Standard Reconstructionof particles in the ECal. Electrons5 also produce a similar shower in the ECal, but theycarry electric charge and therefore also leave tracks in the ID. Neutrons do not interact withthe inner detector due to their lack of electric charge and instead deposit their energy in thehadronic calorimeter creating a hadronic shower of particles. Protons cause the same hadronicshower, but also leave tracks in the inner detector.Figure 4.1: A schematic of different particles interacting with the ATLAS detector in a sectionof the x− y plane. Figure adapted from [52].4.1.2 Tracks, Primary Vertices and Energy ClustersTracks, primary vertices and energy clusters are the basic inputs used to reconstruct the otherphysics objects discussed in this chapter. Charged particles passing through the ID and MSleave behind tracks that indicate their trajectories. Primary vertices are the location of theproton-proton interaction points and are reconstructed at the point of origin of a collection5Throughout this dissertation, the term “electron” will usually refer to both electrons and positrons. Thisis also the case for all other particles and anti-particles (e.g. muons, quarks, protons etc.)334.1. Standard Reconstructionof tracks. Energy clusters are formed from groups of energy deposits left behind by particlesthat interact with the calorimeters.TracksStandard track reconstruction starts with information from the pixel and SCT detectors. MStrack segments are independently reconstructed and are discussed in section 4.1.4. Once trackcandidates are reconstructed in the silicon detectors, they are extended using the informationfrom the TRT. A detailed description of the tracking reconstruction algorithms can be foundin Refs. [53] and [54]. Track reconstruction begins by forming clusters from measurementsin the pixel or SCT detectors. Charge deposits that are above a threshold in the pixel andSCT sensors are grouped into clusters. Three dimensional measurements, called space-points,are created from these clusters. Each space-point represents a place where a charge particlepassed through the active material in the ID. After clusterization, an iterative combinatorialtrack-finding algorithm is run using the space-point measurements. Track seeds are formed bydefining sets of three space-points. Track candidates are then reconstructed using a Kalmanfilter [55] to find additional space-points that are compatible with the initial track seed.Each time a new space-point is added, the track candidate is updated. In dense environments,particles pass so close to each other that it is possible to have a number of track candidates thatshare space-points. To resolve such ambiguities, the track candidates are processed individuallyand given a score, where a higher score indicates that the track candidate is more likely torepresent the trajectory of a charged particle. This ambiguity solver primarily uses measures oftrack quality, such as the expected cluster multiplicity, the number of holes6 and the goodnessof fit (χ2) of the track, to determine the track score. Track candidates that fail to meetbasic quality thresholds are rejected. After the track score is calculated, candidates that areassigned to multiple clusters are further processed by a neural network algorithm to splitmerged clusters. When all the track ambiguities are resolved, the track finding algorithm isrun again to perform a final fit. Reconstructed tracks found in the silicon detectors are thenused as inputs to find compatible sets of TRT measurements to extend the tracks into theTRT. Up to this point, an inside-out sequence is used to find tracks in the inner silicon trackerand extend the tracks outward in radius. While this method is very efficient, ambiguous hitscan prevent track seeds from passing the ambiguity solver and tracks coming from secondarydecays (e.g. kaon decays) or photon conversions may not have many silicon hits. To recovertracks in these cases, a second reverse outside-in sequence is run, starting with track segmentsin the TRT and extending the tracks inward to find any leftover compatible hits that werenot used in the inside-out sequence. The final output of the track reconstruction algorithm is6A track hole is defined as the intersection of a track candidate with a detector element that does notcontain a matching cluster, but where one is expected.344.1. Standard Reconstructiona list of ID tracks that can be defined by the following set of five parameters:(d0, z0, φ, θ, q/|p|) (4.1)where d0 and z0 are the transverse and longitudinal impact parameters, φ and θ are the usualazimuthal and polar angles and q/|p| is the ratio of the particle’s charge to momentum.Primary VerticesPrimary vertices are defined as points in space where a proton-proton interaction is expectedto have occurred. Details of the primary vertex reconstruction can be found in Ref. [56]. Vertexreconstruction can be separated into two steps: vertex finding and vertex fitting. In the formerstep, reconstructed tracks are associated to candidate vertices. The vertex fitting step thenreconstructs the point of origin of these associated tracks to define the vertex position. Toreconstruct a vertex, a track selection is applied to construct a list of input tracks and an initialseed position is chosen. The selected tracks and initial seed position are used to determine abest-fit position and then the tracks are weighted up or down depending on how compatiblethey are with the best-fit position. Once the final vertex position is determined, any trackthat is not compatible with this position is removed from the vertex. These rejected trackscan then be used to form another vertex. This procedure is repeated with all the remainingtracks in the event until no new vertices are formed.The primary vertex reconstruction is also responsible for identifying the primary vertexassociated to the hard-scatter event. The location of the primary hard-scatter vertex is essen-tial to the reconstruction of the full kinematics of the event. The highest sum of the squaredtransverse momenta of the tracks (∑ |pT|2) is used to distinguish the hard-scatter vertexfrom pileup vertices. This choice is based on the assumption that charged particles producedin a hard-scatter event have, on average, a larger transverse momentum spectra than tracksproduced in pileup collisions. For the analysis in this dissertation, the primary hard-scattervertex is defined as the primary vertex with the highest∑ |pT|2 of the tracks associated to it.Energy ClustersEnergy clusters are formed from a set of calorimeter cells that contain energy deposits andshare common edges. ATLAS has two different clustering algorithms. The sliding-windowreconstruction algorithm was used to build energy clusters for electron and photon recon-struction until the end of 2016. The second topological clustering (topo-cluster) algorithmwas used from 2017 onward for electron and photon reconstruction and was also used to buildenergy clusters for the reconstruction of hadronic showers, also known as jets. For the analysispresented in this dissertation, the primary use of energy clusters is for electron reconstruction354.1. Standard Reconstructionand, for this reason, the remainder of this section will focus on electromagnetic energy clusteralgorithms used to reconstruct electrons.The sliding-window reconstruction method divides the calorimeter in η and φ into a gridof fixed elements known as “towers”. Inside each of these towers, the energy of all cells inthe longitudinal layers is added to form the “tower energy”. Electromagnetic-energy clustercandidates are seeded using energy deposits that are larger than 2.5 GeV in a window of size3 × 5 tower units in η × φ. Then, the centre of the 3 × 5 window slides around in steps of0.025, in either the η or φ direction, to search for other energy deposits to add to the cluster.This seed-to-cluster process is repeated until this has been done for every element in thecalorimeter. The sliding-window algorithm is described in more detail in Ref. [57].The topological clustering algorithm uses signal-significance patterns to form 3D topo-logical cell clusters, also known as topo-clusters. Cluster seeds are formed from cells thathave a high signal significance defined by the ratio of the signal to the expected cell noise.Neighbouring cells above a certain signal significance threshold are iteratively added to thecluster. This process continues until there are no cells left to be added to clusters. For electronreconstruction, topo-clusters are only formed using energy from ECal cells. The topo-clusteralgorithm is described in more detail in Ref. [58].4.1.3 ElectronsElectrons are charged particles that leave tracks in the inner detector and deposit most oftheir energy in the electromagnetic calorimeter. ATLAS uses tracks and energy clusters toidentify and reconstruct electrons. An overview of the electron reconstruction can be foundin the Refs. [59] and [60].ReconstructionElectrons lose most of their energy due to bremsstrahlung when interacting with material.This results in a collimated electromagnetic shower of particles that is normally reconstructedas part of one energy cluster in the ECal. As a result, it is possible to produce and matchmultiple tracks that originated from the primary electron to a single energy deposit. Therefore,an electron is defined as an object that consists of an energy cluster with at least one matchedtrack. Since close matching of tracks to energy clusters is required to identify electrons, thereconstruction of electrons occurs in the central precision region of the ATLAS detector with|η| < 2.5. A schematic illustration of the path of an electron through the detector is shown infig. 4.2.Electron reconstruction starts by finding energy clusters (described in section 4.1.2) inthe electromagnetic calorimeter with a transverse energy ET > 2.5 GeV. The cluster recon-struction efficiency for electrons ranges from 65% at ET = 4.5 GeV, to 95% at ET = 7 GeV,364.1. Standard Reconstructionsecond layerfirst layer (strips)presamplerthird layer hadronic calorimeterTRT (73 layers)SCTpixelsinsertable B-layerbeam spotbeam axisd0ηφ∆η×∆φ = 0.0031×0.098∆η×∆φ = 0.025×0.0245∆η×∆φ = 0.05×0.0245electromagnetic calorimeterFigure 4.2: A schematic of the path of an electron through the ATLAS detector. The solid redtrajectory shows the path of the electron traversing through the tracking system (pixel, SCTand TRT layers) and entering the electromagnetic calorimeter. The dashed red trajectoryindicates the path of a photon produced by the interaction of the electron with the materialin the tracking system. Figure taken from [59].to more than 99% for ET > 15 GeV, as shown in fig. 4.3 [59]. Next, ID tracks are foundusing the reconstruction method described in section 4.1.2. Figure 4.3 shows that the trackreconstruction also varies as a function of ET and is 80% efficient at ET = 1 GeV and morethat 98% efficient above ET = 10 GeV.Since charged electrons lose energy when traversing through material, a subsequent fittingprocedure, using a Gaussian-sum filter (GSF) [61], takes into account non-linear effects, or“kinks”, in the tracks related to bremsstrahlung. Radiative energy losses decrease the momen-tum of the electrons, causing them to bend more in the magnetic field. Taking into accountthis additional energy loss improves the reconstruction of electron track parameters, such asd0, that are related to the bending of the track.A likelihood-based (LH) method is used to identify prompt electrons in order to ensurethat only high-quality electrons are used for analysis and to suppress non-prompt backgroundsfrom photon conversions, jets and heavy flavour decays. The likelihood is calculated usingproperties of the electron track, information about the electromagnetic shower shape and thecompatibility of the energy cluster with the primary electron track. The probability distribu-tion functions for the prompt electron signal and non-prompt backgrounds are derived fromsimulation and corrected to accurately model data. Electron identification operating pointsare defined using a likelihood discriminator that increases in value for more “electron-like”objects and requires the tracks satisfy additional tracking requirements.374.1. Standard Reconstruction0 5 10 15 20 25 [GeV]TTrue E00.20.40.60.81Efficiency Reconstructed seed cluster Reconstructed seed track Reconstructed cluster and track Reconstructed electron candidateATLAS Simulation = 13 TeVsFigure 4.3: The total reconstruction efficiency for simulated electrons in a single-electron sam-ple as a function of the true transverse energy, ET, for each step of the electron reconstruction:the energy cluster reconstruction (red triangles), track reconstruction using the Global χ2Track Fitter (blue open circles), cluster and track reconstruction using GSF tracking (yellowsquares), and the final electron-candidate reconstruction, which includes the track-to-clustermatching (black circles). Since the cluster reconstruction requires that cluster seeds haveET > 2.5 GeV, the total reconstruction efficiency is less than 60% below 4.5 GeV (dashedline). Figure taken from [59].The prompt electron identification working point that is relevant to the work describedin this dissertation is called LHMedium. The LHMedium working point has the followingtracking requirements: at least two hits in the pixel detector with at least one hit in theinnermost (functional) layer, at least seven silicon (pixel + SCT) hits and a minimum ET of4.5 GeV. The LHLoose working point is similar to LHMedium, except that a looser cut onthe likelihood discriminator is used. LHVeryLoose electrons are also similar to those selectedby the LHMedium and LHLoose working points, except there is no longer a required hiton the first working pixel layer and there is only one required pixel hit. The LHLoose andLHVeryLoose working points are not used in the analysis described in this dissertation, butserve as a comparison for the displaced electron identification discussed in section 4.2.2. Theworking point LHTight is not used in the analysis, but is similar to LHMedium except thatit has a smaller identification efficiency. Figure 4.4 shows the electron identification efficiencyfor the LHLoose, LHMedium and LHTight working points as a function of ET.384.1. Standard Reconstruction0.50.60.70.80.91Data efficiency Loose Medium TightATLAS-1 = 13 TeV, 81 fbsElectrons20 40 60 80 100 120 140 [GeV]TE0.911.1Data / MC Figure 4.4: The electron identification efficiency in Z → ee events in data as a function ofET. The efficiencies are obtained by applying data-to-simulation efficiency ratios measuredin J/ψ → ee and Z → ee events to Z → ee simulation. The LHMedium operating pointefficiency curve is plotted using red squares. Figure taken from [60].IsolationIn general, high-pT electrons are expected to be isolated from other particles and, as a re-sult, their detector signatures should be spatially separated from other detector deposits. Tomeasure the isolation, variables are constructed to measure the amount of detector activ-ity near the electron object. Usually this is done by summing the transverse cluster energy(calorimeter-based isolation) or transverse momenta of tracks (track-based isolation) that arein a cone of radius ∆R =√∆φ2 + ∆η2 around the electron candidate. In this dissertation,track-based isolation requirements are applied, which require that the ratio of the sum pTof all tracks in a cone ∆R = 0.3 around the electron to the electron’s pT is less than somethreshold. For prompt electrons this threshold is 0.05 (∑p(0.3)T /pT < 0.05) and for displacedelectrons the threshold is 1.0 (∑p(0.3)T /pT < 1.0).394.1. Standard Reconstruction4.1.4 MuonsMuons are reconstructed mainly using information from the ID and MS system. An overviewof the muon reconstruction can be found in the Refs. [62] and [63].ReconstructionMuon reconstruction begins by independently reconstructing tracks in the ID and MS. Trackreconstruction of charged particles in the ID is described in section 4.1.2. In the MS, muontrack segments are formed by combining hits from the layers of muon chambers. These tracksegments are initially fit using a loose pointing constraint based on the location of the primaryvertex and the approximate trajectory of a charged particle bending in the magnetic field.Segments are then combined, starting with the ones in the middle layers of the MS, to formmuon track candidates. In most regions of the detector, two track segments are required toreconstruct a track candidate and the same segment is initially allowed to be used in severaltrack candidates. A global χ2 fit is performed using the hits associated to each track candidateto determine if the track passes the χ2 selection criteria.Four muon types are defined depending on what detector information is used to reconstructthe muon [63]:• Combined muon: a track is reconstructed using a global fit of the hits in the ID and MS.During the fit, MS hits may be added or removed in order to improve the fit quality.An outside-in approach is used for the reconstruction, starting with the reconstructionof tracks in the MS and then extrapolating inwards to match MS to ID tracks.• Inside-out muon: an ID track is extrapolated to at least three aligned MS hits. Thismethod does not rely on the MS track reconstruction and therefore recovers some ef-ficiency in regions where the MS coverage is limited. These muons are usually mergedtogether with the combined muons.• Segment-tagged muon: a track from the ID is classified as a muon if the track can beassociated to a segment in the MS. These muons are only used when the muon crossesone layer of the MS.• Calorimeter-tagged muon: a track from the ID is classified as a muon if it matches anenergy deposit in the calorimeter that is consistent with a minimum ionizing particle.This type of muon has the lowest purity of all the muon types.• Extrapolated muon: a track is based only on information from the MS and has a looserequirement that the track originated from the primary vertex. Extrapolated muons aregenerally only used to extend the acceptance for muon reconstruction into the 2.5 <|η| < 2.7, which is outside of region covered by the ID.404.1. Standard ReconstructionFor the work described in this dissertation, all muon types, expect for the lowest puritycalorimeter-tagged muons, are initially used to seed the displaced vertex reconstruction (seesection 4.2.3). However, in the final event selection only combined muons (including inside-outmuons) are used.6 7 8 910 20 30 40 50 60 100Efficiency0.960.981 ATLAS-1 = 13 TeV, 3.2 fbs|>0.1η muons, |Medium Dataµµ→ψJ/ MCµµ→ψJ/ Dataµµ→Z MCµµ→Z [GeV]T p6 7 8 910 20 30 40 50 60 210Data / MC0.9811.02 Stat only Stat⊕Sys Figure 4.5: The muon reconstruction efficiency for the Medium identification working point asa function of muon pT in the region 0.1 < |η| < 2.5. This reconstruction efficiency is obtainedwith Z → µµ and J/Ψ→ µµ events. The error bars on the efficiencies indicate the statisticaluncertainty. The panel at the bottom shows the ratio of the measured to predicted efficiencies,with statistical and systematic uncertainties. Figure taken from [64].IdentificationAfter reconstruction, muon identification requirements are applied in order to suppress non-prompt muon backgrounds, such as decays of charged hadrons. The relevant working point forthe muons used in this dissertation is Medium and the reconstruction efficiency for Mediummuons are shown in fig. 4.5. Selection criteria for high-quality muons include requirementson the number of hits in the ID or MS, the properties of track and the compatibility of themeasurements between the two subsystems. Muons originating from the decays of chargedhadrons will produce a “kink”, or change in direction, in the reconstructed track. As a result,this can lead to a poor fit quality for the combined track, as well as incompatible momentummeasurements between the ID and MS tracks.414.2. Non-Standard ReconstructionIdentification criteria, known as working points, are defined mainly using the muon selec-tion efficiency and purity in simulations of Z → µµ and J/ψ → µµ events. For the identifica-tion of combined muons the following variables are used:• q/p significance: defined as the absolute value of the ratio between the charge, q, andthe momentum, p, of the muon divided by the sum in quadrature of the uncertaintieson q and p;• ρ′: defined as the absolute value of the difference between the transverse momentummeasurements in the ID and MS divided by the pT of the combined track;• normalized χ2 of the combined track fit.The Medium working point is used to identify muons in the analysis in this dissertationand is also the default muon working point in ATLAS. This working point is designed tominimize the systematic uncertainties associated with muon reconstruction and calibration.The collection of Medium muons only contains combined and inside-out muons that havehits in at least two MS layers and a q/p significance of less than seven to ensure a loosecompatibility between ID and MS measurements. The muon reconstruction efficiency withthis selection is around 97% for muons with 4 < pT < 20 GeV.IsolationPrompt muons from the decays of heavy particles, such as W , Z or Higgs bosons, are oftenspatially isolated from other particles. Muons from semi-leptonic decays of heavy flavouredhadrons are typically produced near a jet and are not well separated from other particles. Asa result, the muon isolation, which measures how much detector activity is around the muon,can be a useful variable to select prompt muons. Similar to electrons, a track-based isolationis calculated using the scalar sum of the transverse momenta of all tracks within a cone ofradius ∆R =√∆φ2 + ∆η2 around the muon candidate. In this dissertation, a track-basedisolation requirement is used to select prompt muons where the ratio of the scalar sum oftransverse momenta of all tracks in a cone of ∆R = 0.3 to the transverse momentum of theprompt (displaced) muon candidate is∑p(0.3)T /pT < 0.05(1.0).4.2 Non-Standard Reconstruction4.2.1 Displaced TracksStandard track reconstruction, described in section 4.1.2, is optimized to reconstruct chargedparticles that originate from the primary interaction point. However, standard track recon-struction efficiency falls off rapidly for charged particles that originate from decays occurring424.2. Non-Standard Reconstructiona significant distance from the interaction point. Therefore, analyses that search for displacedsignals reconstruct displaced tracks using a dedicated large radius tracking algorithm. Thedetails of this algorithm can be found in Ref. [65].Large radius tracking (LRT) is performed after the standard inside-out and outside-intrack reconstruction. This dedicated tracking step uses the leftover silicon hits to reconstructdisplaced tracks that are not required to point back to the interaction point. LRT follows thesame reconstruction strategy as inside-out tracks, but uses relaxed constraints on the trackimpact parameters (d0 and z0) and number of hits. The key differences between standard andlarge radius track reconstruction are outlined in table 4.1.Table 4.1: Main differences between standard and large radius tracking (LRT).Track parameter Standard LRTMaximum d0 10 mm 300 mmMaximum z0 250 mm 1500 mmMaximum track |η| 2.7 5.0Minimum track pT 500 MeV 900 MeVMinimum silicon hits 7 7Minimum unshared silicon hits 6 5Seed extension Combinatorial SequentialThe large radius track seeding uses a sequential Kalman filter to prevent the creation ofmultiple track candidates from different combinations of space-points. After track candidatesare reconstructed, the track ambiguity solving step uses the same relaxed constraints, andany tracks that pass the ambiguity solver are extended into the TRT. The resulting collectionof displaced tracks is then merged with the collection of standard tracks.LRT is optimized for high track reconstruction efficiency and this comes at the cost of alarge number of fake tracks. This means that the LRT reconstruction algorithm is very CPUintensive and requires a large amount of disk space to store the output track collection. As aresult, the LRT reconstruction step is not run by default. Instead, a subset of the recordeddata events, based on the output of the standard reconstruction, is selected for this specialreprocessing. A description of the selections applied to filter data events for this analysis isfound in section 5.7.2.LRT reconstruction efficiency varies as function of the distance from the primary interac-tion point. BSM signals with large production radii (r2prod = x2 + y2) that decay into leptonsand hadrons are used to study the reconstruction efficiency:reconstruction efficiency =number of signal particles matched to reconstructed tracksnumber of signal particles(4.2)The dependence of the reconstruction efficiency on rprod is shown in fig. 4.6. At low rprod,standard tracking is very efficient and there are not many leftover hits to form tracks in434.2. Non-Standard Reconstruction [mm]prodr0 50 100 150 200 250 300Reconstruction effiency00.20.40.60.811.21.41.6Simulation Preliminary ATLASDisplaced leptons Standard tracksLarge radius tracksCombined(a) [mm]prodr0 50 100 150 200 250 300Reconstruction effiency00.20.40.60.811.21.41.6Simulation Preliminary ATLASDisplaced hadrons Standard tracksLarge radius tracksCombined(b)Figure 4.6: Track reconstruction efficiency for displaced charged particles produced by thedecay of long-lived signal particles. The efficiency for standard tracking, LRT and the sum ofthe two is shown as a function of the radius of production of the displaced particles (r2prod =x2 + y2). Displaced leptons are shown on the left and displaced hadrons on the right. Figuretaken from [65].the LRT step. However, for rprod > 50 mm, fewer than 20% of hadrons (30% of leptons)from displaced decays would be reconstructed without LRT. Beyond rprod > 50 mm, LRThelps to recover efficiency for displaced tracks. However, the efficiency in fig. 4.6 is still wellbelow 100% for large rprod, even with the addition of large radius tracks. This is due toinefficiencies in the tracking reconstruction algorithm, in particular on the minimum numberof silicon hits, material effects from interactions with the detector and the hermetic designof the ATLAS detector that is optimized to reconstruct prompt particles that decay at theprimary interaction point.4.2.2 Displaced LeptonsStandard electron and muon reconstruction and identification algorithms, described in sec-tion 4.1.3 and section 4.1.4 respectively, are primarily designed to reconstruct prompt leptonsproduced at the primary interaction point. Displaced leptons are mainly reconstructed usingthe same standard algorithms, with the exception that the collection of ID tracks now usesa combination of both standard and large radius tracks. However, in order to reconstructdisplaced electrons, the |d0| and the number of silicon hits requirements, that are applied inaddition to the track reconstruction requirements, are removed. This is primarily necessary forelectrons, since the number of silicon hits is used to separate electrons and photons. Withoutthe removal of d0 and hit requirements, many reconstructed displaced electrons end up beingclassified as photons.After reconstruction, identification working points are used to select good quality elec-444.2. Non-Standard Reconstructiontrons and muons. For muons, the standard working points (described in section 4.1.4) arerelatively efficient at identifying muons from the displaced decay of the signal described inthis dissertation. As a result, the default muon working points are not modified. However, fordisplaced electrons, the standard identification working points require the electrons to havehits in the innermost pixel layer or a certain number of hits in the silicon detectors. Thus,the search described in this dissertation uses a custom working point called VeryVeryLoose isdefined to identify displaced electrons. This working point is similar to the standard LHVery-Loose working point, except that any d0 related requirements are removed, along with therequirements on the number of pixel and silicon hits.4.2.3 Displaced VerticesFor certain long-lived particle signals, such as those presented in this dissertation, we arealso interested in determining a place of common origin for displaced tracks, which is calleda displaced vertex (DV). A reconstruction algorithm, known as Vertex Secondary Inclusive(VSI), is used to reconstruct DVs in the ID. ATLAS also has other non-standard reconstructiontechniques designed to reconstruct decays in other parts of the detector (e.g. the MS system),but this section will only described DV reconstruction in the ID, as this is the focus of thesearch described in this dissertation.This section discusses the VSI algorithm in general, while section 5.5.2 discusses the customVSI configuration used in the analysis described in this dissertation. The main steps of theVSI algorithm can be found in fig. 4.7. More details about this algorithm can be found in Ref.[66].Vertex Secondary Inclusive (VSI) Vertexing AlgorithmTrack Selection Two-Track Vertex FindingN-Track Vertex FindingTrack AttachmentVertex MergingFigure 4.7: The main steps in the VSI displaced vertexing algorithm.Track SelectionThe first step in the algorithm is to further select tracks from a full set of reconstructed tracks.This step is very important to maintain a high signal efficiency, while reducing the numberof fake vertices and CPU time. By default, the input to the secondary vertexing includesboth standard (see section 4.1.2) and large radius (see section 4.2.1) tracks. However, thealgorithm is also configurable to alternatively select ID tracks matched to muon or electron454.2. Non-Standard Reconstructionobjects (see section 4.1.3 and section 4.1.4 for a description of how tracks are matched toelectron and muon objects respectively). Selecting only muon and electron-matched tracksconfigures VSI to only reconstruct displaced lepton vertices. This lepton-only track selectionis also important when reconstructing vertices with electrons, since this method can selectthe electron tracks that are reconstructed using the GSF instead of the ATLAS Global χ2fitter. This is important because GSF electron tracks have improved reconstruction of trackbending parameters, such as d0, which are crucial to the vertex reconstruction.Other track selection functions are also included in the algorithm and these selections canbe optimized to maximize signal efficiency and reject background vertices. Examples of trackcuts that can be applied include track pT, fit quality (χ2), d0 and z0. In order for the vertexreconstruction to continue, at least two tracks per event must be selected in the track selectionstep.Two-Track Vertex FindingThe reconstruction sequence continues with a two-track vertex finding step, which attempts toform vertices with all compatible two-track pairs. Again, to help reduce the CPU time and thenumber of fake vertices, this step has a few different selection requirements for each compatibletwo-track pair to pass to the next vertexing stage. First, a fast fit is done for each track pair todetermine an initial vertex position. Then, the position and momentum of the two-track DVare used to apply kinematic cuts using the vertex pointing vector, ~rDV = ~r (rDV , zDV , φDV),which is defined as the relative position of the fitted vertex with respect to the primary hard-scatter vertex. These cuts are designed to reject vertices that are compatible with the decayof a particle originating from the primary vertex. There is also a two-track vertex forming d0cut, which requires that at least one track has a d0 greater than a user-specified value in orderfor the two-track pair to be accepted.Next there is a hit pattern consistency check for the two-track vertex. A classical hitpattern check has two requirements. The first requires ID hits from the tracks just ahead ofthe vertex position (r > rDV) and the second forbids hits from the track just behind the vertexposition (r < rDV), as illustrated in fig. 4.8. The idea here is to check that the two tracks looklike they originate from the fitted vertex position. If there are hits behind the vertex, or nohits just ahead of the vertex, then the vertex is not consistent with the decay of a displacedparticle.VSI can also be configured to use an extrapolation method where the classical hit patternconsistency checks are complemented by information about disabled ID modules. The ATLASdetector is not perfect and, in any given run, various ID modules can be labelled as “not active”either because they are not functioning properly or may not be collecting data at all. As aresult, the efficiency of the hit pattern check that requires hits just in front and forbids hits464.2. Non-Standard ReconstructionSecondary VertexRequired HitsAllowed HitsForbidden HitsTrackTrackPixel Layer-2Pixel Layer-1Pixel B-LayerIBL(a)Secondary VertexRequired HitsAllowed HitsForbidden HitsTrackTrackPixel Layer-2Pixel Layer-1Pixel B-LayerIBL(b)Figure 4.8: A schematic illustration of the fake tracks rejection method. In example (a), thevertex is between the pixel B-Layer and Layer-1. The tracks of the reconstructed secondaryvertex must not have hits in the layers behind the vertex (i.e. IBL and B-Layer), and musthave hits in the closest layer ahead of the vertex (i.e. Layer-1). In example (b), the vertex isclose to the Pixel B-Layer. The tracks in this vertex are not allowed to have hits in the IBL,but may have hits in the B-Layer, and must have hits on the Layer-1. Analogous requirementsare made on vertices close to the other layers. Figure taken from [66].just behind the vertex can be affected by disabled modules. To improve the efficiency, run-by-run ID conditions are taken into account in the VSI algorithm using a disabled hit patterncheck. If a module consistent with a track is “not active” just ahead of the candidate vertex,then the require hits criterion is skipped and the vertex will be accepted. On the other hand,if an ID module consistent with a track is “not active” just behind of the candidate vertex,then the forbidden hits criterion cannot be determined and the vertex will be rejected.N-Track Vertex Finding and Vertex MergingAfter the two-track vertex finding step, N -track vertices are formed using an incompatibilitygraph method that determines the sets of tracks that are fully compatible with each other.Here, the term compatible means that the two tracks form a vertex with the required quality.VSI focuses on incompatible track pairs rather than compatible pairs. A list of incompatibletrack pairs are represented in a graph where the nodes (points) represent tracks and thelines represent incompatible pairs (see fig. 4.9 right). This graph is then used to find thecombination of nodes that leave behind only fully-isolated nodes when they are removed fromthe graph. For the example in fig. 4.9, if nodes (3, 4, 5, 6) are removed from the graph, thenonly nodes 1 and 2 remain and there are no longer any lines connecting incompatible pairs.This means tracks 1 and 2 form a compatible vertex. Alternatively nodes (1, 2, 6) could be474.2. Non-Standard Reconstructionremoved and tracks 3, 4 and 5 would also form a compatible vertex.Notreviewed,forinternalcirculationonlyDRAFT12 3 4 56123 456(3, 4, 5, 6)(1, 2, 6)Incompatibility GraphTracks and vertices in the event Solution to keep only fully-compatible nodesRemovingFigure 6: An example of finding n-track vertices using the incompatibility graph. Left: layout of tracks and verticesin the event; Center: the incompatibility graph is formed by connecting two tracks when the di-track vertices arejudged as incompatible; Right: finding out the set of tracks that are fully compatible each other.The approach that VrtSecInclusive takes focuses on the incompatible track pairs rather than compatible265track pairs. Here, the term incompatible means that the two-track pair is not able to form a vertex with a266required quality. The list of incompatible track pairs in the event is represented as a graph like Figure 6267(center) where the nodes (edges) represent tracks (incompatible pairs). The problem of finding n-track268vertices is to find out sets of tracks in which the constituent tracks are all compatible each other. This269problem can be translated as follows – find the combination of nodes in the graph that achieves to remain270only fully-isolated nodes when they are removed from the graph. In the example of the case in Figure 6,271the solutions are removal of tracks (3, 4, 5, 6) and (1, 2, 6). The remaining isolated tracks are regarded as272the candidate n-track vertices and they are fitted as one vertex. Bad-quality vertices or vertices that are273fully inclusive of other vertices are removed.274While the abovemethodwith the incompatible graph eectivelyworks to form n-track vertices for relatively275small multiplicity and all tracks from the same real vertex are compatible, the number of solutions may276explode when the track multiplicity from the displaced vertex is very large and a fraction of track pairs is277not compatible. Such a probability is expected to roughly increase with O(N2track). The second approach278to form n-track vertices is clustering vertices as a simple and rapid algorithm. In this approach, the279compatible track pairs are merged if their positions are closer than 1 mm. This second approach was280implemented in the code but not commissioned yet, and still the incompatible graph approach is always281used.2822.6 Re-arrangement of tracks and vertex merging283After n-track vertex finding using the incompatibility graph, a track may be compatible with multiple284vertices, as illustrated in Figure 7. In this case, the track index 3 is shared by two dierent vertices, and285there is an ambiguity to which vertex this track should be associated. Since VrtSecInclusive allows a286track to be maximally associated to one secondary vertex, such ambiguity needs to be resolved. This step287is referred to as re-arrangement.288For each used track, the algorithm lists up all vertices which share it. The track that has the maximum289shared vertices is identified. Subsequently, the goodness of association of the track to the shared vertices290are asked, and the vertex with the worst goodness (2 per track) is identified. If the worst 2 per track2918th February 2018 – 14:22 112.1 I Z DVTigre(a)Notreviewed,forinternalcirculationonlyDRAFT12 3 4 56123 456(3, 4, 5, 6)(1, 2, 6)Incompatibility GraphTracks and vertic s in the event Solution to keep only fully-compatible nodesRemovingFigure 6: An example of finding n-track vertices using the incompatibility graph. Left: layout of tracks and verticesin the event; Center: the incompatibility graph is formed by connecting two tracks when t di-track vertices arejudged as incompatible; Right: finding out the set of tracks that are fully compatible each other.The approach that VrtSecInclusive tak s focuses on the incompatible rack p irs r the than compatible265track pairs. Here, the term incompatible means that the wo-track pair is not able to form a vertex with a266required quality. The list of incompatible track pairs in the event is repres nt d as a graph like F gure 6267(center) where the nodes (edges) r present tracks (incompatible pairs). The problem of finding n-track268vertic s s to find out sets of tracks in which the constituent tracks re all compatible each other. This269problem can be translated s follows – find the combinatio of odes in the graph that achieves to remain270only fu ly-isolated no es when t y ar removed from the graph. In the example of the cas in Figure 6,271the soluti ns are removal f tracks (3, 4, 5, 6) and (1, 2, 6). The remaining isolated tracks re regarded as272the candidate n- rack vertic s and they ar fitt d as one vertex. Bad-quality vertices or vertices that are273fully inclusive of other vertic s ar removed.274While t e abovemethodwith the incompatible graph eectiv lyworks to form n-track vertices for relatively275small u tiplicity and all tr cks from the same real v rtex ar compatible, the number of soluti ns may276explode wh n t track multiplicity from the displaced vertex is very large nd a fraction of track p irs is277not compatible. Such a probability s expected to roughly increase with O(N2track). The second approach278to form n-track vertic s s clu tering vertic s as a simple and rapid lgorithm. In this approach, the279compatible track pairs re merged if their positions are closer than 1 mm. This second approach was280imple ented in the code but not commissioned yet, and still the incompatible graph approach is always281used.282.6 Re-arrangement of racks and vertex merging283After n-track vertex finding using the incompatibility graph, track may be compatible with multiple284vertic s, as illu trated in Figure 7. In this case, the track index 3 is shared by two dierent v rtices, and285there is an ambiguity to which vertex this track should be associated. Since VrtSecInclusive allows a286track to be maxi lly associated to one secondary vertex, such ambiguity needs to be resolv d. This step287is referr d to as re-arrangement.288For each used track, the algorithm lists up all vertic s which share it. The track that has t e maxi um289shared vertic s is identifi d. Subsequently, the goodness of association of the track to the shared vertices290are asked, an the vertex with the worst goodness (2 per track) is identifi d. If the worst 2 per track2918th February 2018 – 4:22 112.1 I Z DVTigre(b)Figure 4.9: A xample of finding N -track vertices using an incompatibility graph. The layoutof tracks and vertices in n event (a) and the incompatibility grap (b) that is formed byconnecting two tracks when the two-track vertices are determined to be incompatible. Figuretaken from [67].Once N -tr k ver ices are formed, it is possible that a track may be compatible w thmultiple vertices a illustrated in fig. 4.10. In his cas , there is an ambiguity as to whichvert x th track belongs. At m st, each tr ck is allowed to be associated to one vertex andthus this ambiguity n eds to be resolv . For each track, a list of vertices that share t e trackis created. Then, the track that shares the most vertices is identified. Th goodness of fit (χ2)of this track to each of these vertices is calculated. The vertex with the worst χ2 for the trackis found a d, if χ2 is larger than a user-specified threshold, then the track is removed frothat vertex and this process is repeated. Otherwise, if the significance of the distance betweenthe two vertices that share the track is smaller than another user-specified threshold, or atleast two tracks are shared, then the vertices are erged together. At this point, if the tracksharing ambiguity can not be resolved, then the track is simply removed from the vertex withthe worst χ2. This process is then repeated until no shared tracks remain. Once there are novertices with shared tracks, a vertex fit is performed and, if the distance between any twovertices is less than another user-specified threshold, then these vertices are also merged.Track AttachmentAt this point, all the tracks that were not selected in the track selection step are not yetassociated to any DV. The final step in this reconstruction algorithm attempts to recover losttracks, by running the track attachment step. While this has the potential to recover signaltracks with poor quality that did not pass the track selection, this step can potentially attach484.2. Non-Standard ReconstructionFigure 4.10: An example of track sharing by multiple vertices. Figure taken from [67].irrelevant or fake tracks. This step allows non-selected tracks to be attached or associated tothe vertex provided that the tracks meet some basic quality checks (pT, track χ2 etc.) andthat they are close enough to the existing candidate vertex (both in d0 and z0 significance).This final track attachment step can be turned on or off.Displaced Vertex VariablesAfter the DV reconstruction is completed, the final vertices are recorded and a few differentvariables are calculated for the displaced vertices and the tracks associated to them. Forexample, every track stores if it was initially selected in the track selection step or not. Thisis useful when calculating the VSI track selection efficiency. Another variable records if thetrack was attached to the vertex in the final track attachment step of VSI or not. This can beuseful in some analyses to identify fake or irrelevant tracks that are attached to the verticesand help regain some signal efficiency. Finally, new track variables, calculated with respect tothe reconstructed DV position, are computed. These variables include track kinematics (d0DV ,z0DV , pTDV , ηDV , a and φDV), the square of the uncertainty for d0, z0 and q/p (σd0 , σz0 andσp) and the goodness of fit of the track to the vertex (χ2). These variables are useful since theoriginal track quantities are calculated with respect to the primary vertex, but for displacedtracks this prompt-particle assumption is no longer valid.In addition to the displaced track quantities, DV quantities are also computed. The DVkinematics are found using the sum of the momentum of the associated tracks using thetrack parameters calculated with respect to the DV (pTDV , ηDV , φDV). This same momentumsum along with a pion mass assumption for each track is used to compute the invariantmass of the DV (mDV). The radial position (Lxy) of the vertex is also used as a measureof vertex displacement. This variable is computed using the x and y position of the vertex,Lxy =√x2 + y2.49Chapter 5Search for Heavy Neutral LeptonsThis chapter summarizes a search for long-lived heavy neutral leptons (HNLs) performedwith data from the ATLAS detector at the LHC. Many BSM theories predict new particlesthat have short lifetimes. These signatures decay so quickly that are considered prompt. Thismeans that the distance the particle travels before it decays is less than or equal to theposition resolution of the detector trying to measure it. In contrast, searches for metastableor long-lived particles (LLPs) probe regions of phase space within resolvable distances forthe detectors and look for exotic decays that would be rejected by most prompt searches. Asdiscussed in chapter 2, the HNL lifetime depends on its mass mN and its mixing angle withSM neutrinos |Θ|2 (see eq. (2.8)). HNLs with GeV scale mass and mixing angles between10−3 and 10−6 would produce sufficiently displaced decays that could be detected at high-energy collider experiments. These signals are particularly interesting as they could be foundin relatively under-explored regions of phase space.This analysis searches for a long-lived HNL produced when a W boson decays into a lepton(muon or electron) and a neutrino that mixes with the HNL. This analysis targets final statesthat are consistent with a fully-leptonic HNL decay. The experimental signature consists ofan isolated prompt lepton (e/µ) from the W boson decay accompanied by a displaced vertexfrom the HNL decay with either two muons (µµ), two electrons (ee) or one muon and oneelectron (eµ) between 4 and 300 mm from the primary vertex.This chapter begins with a brief overview of experimental searches for HNLs and thendescribes the analysis strategy and results of the ATLAS search for displaced HNLs performedusing proton-proton collision data collected between 2015 and 2018.5.1 Previous Searches for HNLsPrevious searches for HNL signals on the electroweak scale include analyses with the DELPHIexperiment at the Large Electron-Positron collider and most recently with collider experimentsat the LHC. The DELPHI search studied 106 events from Z decays and placed constraintsin the HNL mass range between 3 and 50 GeV [68]. More recently, with the LHC’s very highrate of W boson production, it is possible to search for HNLs using W decays and identifyHNLs using their fully or semi-leptonic decay modes.505.1. Previous Searches for HNLsCMS has published an analysis that searches for events with three prompt charged leptonsand searches for HNLs in the mass range of 1 GeV - 1.2 TeV [69]. At masses below 20 GeV,the objects in the decay are increasingly displaced and prompt searches become inefficient.Thus, ATLAS has both prompt and displaced HNL searches that provide constraints on theHNL mass up to 50 GeV [70]. Both CMS and ATLAS have also published papers searching forgeneral displaced signatures, but most of these searches do not have sensitivity to HNLs dueto high-pT requirements or a requirement that two or more displaced vertices are constructedin the same event.A 2019 ATLAS result previously searched for displaced HNLs using pp data collected in2016 and set limits on the mixing angle to muon neutrinos, |Uµ|2, and excluded models with|Uµ|2 between 10−3 and 10−6 for HNL masses between 4.5 and 10 GeV [70]. The range ofmodels excluded by the 2019 displaced HNL search are shown in the 95% confidence level(CL) red exclusion curves in fig. 5.1. The 2019 prompt HNL analysis limits are also shown infig. 5.1 and extend out to 50 GeV.Figure 5.1: Observed 95% confidence level (CL) exclusion limits for HNL to muon neutrinomixing angle |Uµ|2 versus HNL mass mN for the prompt signature (the region above theblack line is excluded) and the displaced signature (the region enclosed by the red line isexcluded). The solid lines show limits assuming lepton-number violation (LNV) for half of thedecays and lepton-number conservation (LNC) for the other half. The long-dashed line showsthe limits assuming LNC for all decays. The green and yellow bands indicate the ranges ofexpected limits obtained within ±1 and ±2 standard deviations of the median limit reflectinguncertainties in the signal and background yields. Figure taken from [70].Beam-dump experiments at CERN and Fermilab also search for HNLs with smaller mass(e.g. mN < 2 GeV). Summary plots of the sensitivity to HNLs are shown in fig. 5.2. In eachplot, dominant mixing to either electron, muon or tau neutrinos is assumed. These plots donot include the 2019 ATLAS prompt and displaced search results (or the results from the515.1. Previous Searches for HNLssearch described in this dissertation) because these results were published after the summaryplots were prepared.(a) Electron-only mixing(b) Muon-only mixing(c) Tau-only mixingFigure 5.2: Sensitivity to HNLs with dominant mixing to first, second and third lepton gen-erations. Current bounds on the mixing (filled regions) and prospects for new results in thenext 5-15 years are shown as a function of the HNL mass mN . Figures taken from [71].525.2. Search Overview5.2 Search OverviewThe signal model in this search is a long-lived HNL produced from a W boson decay. Theanalysis signature consists of a prompt lepton that is produced with the HNL and a displacedvertex from the fully-leptonic decay of the HNL (see fig. 2.3). The analysis considers sixchannels that are defined as α−βγ according to the flavour of the prompt lepton (α) and theflavours of the two charged leptons produced in the HNL decay (βγ): µ−µµ, µ−µe, e−eµ,e−ee, e−µµ and µ−ee. Both LNC and LNV decays are considered in this analysis.Simulated signal samples are generated to cover a mass range from 3 to 20 GeV and properdecay lengths (cτN ) of 1, 10, 100 mm. HNL theory predicts a relationship between the mixingangle, mass and lifetime (see eq. (2.8)). Beyond ∼ 20 GeV, HNL models that experiments atthe LHC are currently sensitive to are increasingly prompt. Therefore, this displaced searchtargets models with mN < 20 GeV. At the lower HNL mass limit, signals with mN < 3 GeVare overwhelmed by backgrounds.This analysis exploits the prompt lepton from the W boson decay to make use of theATLAS single-lepton triggers. Selected events are reconstructed using displaced tracking al-gorithms (see section 4.2.1). Signal selections on electron and muon identification workingpoints, the mass and radius of the displaced vertex, the HNL mass and invariant mass of thetri-lepton system are optimized for the six decay channels.The primary background is from leptons that randomly cross in the ID that are recon-structed as a two-lepton DV. For ee vertices, interactions with the detector material andsupport structures also form a source of background. At lower masses, there are also SMresonances, which contribute to the background.This analysis includes many improvements compared to the 2019 ATLAS result. It nowconsiders additional channels, including channels with prompt electrons and channels with dif-ferent flavours between the prompt and displaced leptons (e.g. µ−ee and e−µµ). The customvertexing configuration used to reconstruct lepton-only DVs is also novel, as is the discrimina-tory variable that reconstructs the HNL mass mHNL using the available information from thethree charged leptons in the signal combined with the W boson mass and the HNL flight di-rection. Details about the custom vertexing configuration and HNL mass reconstructions canbe found in section 5.5.2 and section 5.5.3 respectively. A new background estimation methodwas also developed to provide a more sophisticated way to estimate the dominant randomtrack crossing background that reduces some of the statistical limitations faced in the 2019ATLAS analysis. This background estimation method is discussed in section 5.8.6. Finally,this search also sets the first experimental limits on two benchmark models that the LHC-long-lived-particle community developed in recent years to target HNLs under the invertedand normal neutrino mass hierarchy models. These benchmark results, as well as results forthe muon-only and electron-only mixing scenarios, are presented in section 5.11.535.3. HNL Models5.3 HNL ModelsEight HNL models are used to interpret the results in this search. They include modelswith single-flavour and multi-flavour mixing in various lepton number conserving/violating(LNC/LNV) scenarios. In the “Dirac-limit”, all of the HNL decays are LNC, while in the“Majorana-limit,” half of the decays are LNC and half of the decays are LNV. As discussed insection 2.4, the primary difference between LNC and LNV decays comes from spin correlationsthat can alter the kinematics of the leptons in the HNL decay. The results consider fourdifferent mixing scenarios (see section 2.2) in two HNL models: one HNL model with single-flavour mixing (1SFH) and two quasi-degenerate HNL model (2QDH). In the 2QDH model,the mass splitting between the pair of HNLs is smaller than the resolution of the detectorsand, thus, the analysis is unable to distinguish between the two particles. See section 2.1for more details about the motivation for the 2QDH model. Table 5.1 summarizes the eightmodels.Table 5.1: A summary of the eight models used in the interpretation of the analysis results.Models are defined according to the number of HNLs (1SFH or 2QDH), the fraction of LNCand LNV decays and the relative strength of the mixing between the lepton generations. Theinverted (IH) and normal (NH) hierarchy benchmarks are used for 2QDH models only, whilethe 1SFH models have single-flavour mixing.ModelFraction of Fraction of (xe, xµ, xτ )LNV decays LNC decays (xα = |Uα|2/|U |2)1SFH muon-only in the “Dirac-limit” 0 1( 0 , 1 , 0 )1SFH muon-only in the ‘Majorana-limit” 12121SFH electron-only in the “Dirac-limit” 0 1( 1 , 0 , 0 )1SFH electron-only in the “Majorana-limit” 12122QDH IH mixing in the “Dirac-limit” 0 1( 13, 13, 13)2QDH IH mixing in the “Majorana-limit” 12122QDH NH mixing in the “Dirac-limit” 0 1(0.06, 0.48, 0.46)2QDH NH mixing in the “Majorana-limit” 1212The cross section calculation in section 2.5 assumes one HNL in the “Majorana-limit”. Thecross sections for the other models in the “Dirac-limit” and those with more than one HNL(i.e. 2QDH model), can be computed as multiples of this Majorana cross section σM . Table 5.2describes the relationships between the models. For an HNL in the “Majorana-limit”, bothLNC and LNV decays are allowed and, thus, for in the “Dirac-limit”, with only LNC decays,there are half as many decay channels open. This increases the lifetime by a factor of two andthereby enhances the cross section by the same factor. For the 2QDH models, twice as manychannels are opened because there are now two HNL particles that contribute to the process.Thus, the cross section in models with a pair of quasi-Dirac HNLs is twice as large as the oneHNL model.545.4. Data and Signal SamplesTable 5.2: The cross section for LNC and LNV decays for one Majorana HNL, one DiracHNL, a quasi-Dirac HNL pair with “Majorana-like” decays and a quasi-Dirac HNL pair with“Dirac-like” decays. The total cross section is the sum of the LNC and LNV contributions.1SFH 1SFH 2QDH 2QDH“Majorana-limit” “Dirac-limit” “Majorana-limit” “Dirac-limit”LNC decays σM 2σM 2σM 4σMLNV decays σM 0 2σM 0Total 2σM 2σM 4σM 4σM5.4 Data and Signal Samples5.4.1 Data SamplesThis search was performed using 139 fb−1 of LHC proton-proton collision data collected bythe ATLAS experiment between 2015 and 2018. A subset of these data events are selectedand processed using the specialized displaced track reconstruction described in section 4.2.1.All data events are required to pass basic event cleaning, which includes only selecting eventsthat are considered to be “good” for physics analysis (see discussion about data quality insection 3.1.3). Events are also required to have a reconstructed primary vertex with at leasttwo associated tracks with pT > 500 MeV.5.4.2 Signal SamplesMonte Carlo (MC) signal samples were generated using a Pythia87 pp → W boson pro-duction model. W bosons (of both charges) are forced to decay into a lepton (µ or e) and acustom heavy neutral lepton (W → lN). The HNL is given a long lifetime and set to decayleptonically (N → llν). The HNL decay is modeled as a weak decay mediated by either avirtual W or Z boson (see fig. 2.3). If the charged leptons in the HNL decay have the sameflavour (e.g. α − γγ), then both diagrams contribute to the decay. The interference betweenthe neutral and charged current decays is taken into account in the computation of branchingratio, BR(N → llν), that is used to compute the HNL cross section in section 2.5.Figure 5.3 shows the Feynman diagrams that contribute to models with single-flavourmixing. For each channel, events are generated with the following HNL masses: mN =3, 4, 4.5, 5, 7.5, 10, 12.5, 15, 17.5, 20 GeV. Each mass point is generated with three differentproper decay lengths: cτN = 1, 10, 100 mm.7Signal samples were obtained using Pythia 8.212 [72] with the ATLAS A14 set of tuned parameters [73]and the NNPDF2.3LO PDF set [74].555.4. Data and Signal SamplesW+µ+µ−µ+νµN W+?(a) µ−µµW+e+e−e+νeN W+?(b) e−eeW+µ+µ−e+νeN W+?(c) µ−µeW+e+e−µ+νµN W+?(d) e−eµW+µ+νµe+e−N Z?(e) µ−eeW+e+νeµ+µ−N Z?(f) e−µµFigure 5.3: Feynman diagrams included in the combinations for the muon-only mixing (µ−µµ,µ−µe and µ−ee) and electron-only mixing (e−eµ, e−ee and e−µµ) scenarios. Neutral currentdecays are also possible for the µ−µµ and e−ee channels.The six channels that are generated for each mass and proper decay length are:• µ−µµ: W boson decays to a muon and HNL (W → µN) and the HNL decays to a muonpair and a neutrino (N → µµν),• µ−µe: W boson decays to a muon and HNL (W → µN) and the HNL decays to amuon-electron pair and a neutrino (N → µeν),565.4. Data and Signal Samples• µ−ee: W boson decays to a muon and HNL (W → µN) and the HNL decays to anelectron pair and a neutrino (N → eeν),• e−ee: W boson decays to an electron and HNL (W → eN) and the HNL decays to anelectron pair and a neutrino (N → eeν),• e−eµ: W boson decays to an electron and HNL (W → eN) and the HNL decays to anelectron-muon pair and a neutrino (N → eµν) and• e−µµ: W boson decays to an electron and HNL (W → eN) and the HNL decays to amuon pair and a neutrino (N → µµν).Depending on the relative size of the mixing angles (|Ue|2, |Uµ|2 and |Uτ |2) in the HNLmodel that is considered, the decay channels will have various contributions to the overallsignal strength. For models where the HNL mixes with both muon and electron flavouredneutrinos (e.g. IH and NH benchmarks), two additional channels contribute. These channelsare:• µ−eµ: W boson decays to a muon and HNL (W → µN) and the HNL decays to anelectron-muon pair and a neutrino (N → eµν), and• e−µe: W boson decays to an electron and HNL (W → eN) and the HNL decays to amuon-electron pair and a neutrino (N → µeν).Feynman diagrams for these additional two channels, as well as the charged-current decaysfor the µ−ee and e−µµ channels that are also possible in a mixed-flavour mixing scenario, areshown in fig. 5.4. Experimentally, the leptons in the displaced vertex are indistinguishable and,therefore, in models with both nonzero muon and electron mixing angles, the µ−µe (e−eµ)and µ−eµ (e−µe) signals are combined into one channel. These processes only differ due to thekinematics differences from spin correlations and the relative strength of the mixing with theSM neutrinos xα = |Uα|2/|U |2. Thus, the event weighting procedure, described in section 5.4.3,is used to compute separate weights for the µ−µe and µ−eµ processes. A combined weightthat is equal to the sum of the individual weights is used for models where both the µ−µeand µ−eµ processes are allowed. The same method is used for the e−eµ samples to get acombined weight for e−eµ and e−µe processes.The analysis is not sensitive to HNL mixing with tau neutrinos, |Uτ |2. Tau reconstructionis typically more difficult than electron or muon reconstruction due to the short proper decaylength of the tau lepton (cττ ∼ 0.1 mm) and the complicated nature of the decay products.The sensitivity to |Uτ |2 through the leptonic tau decays to muons and electrons was studiedusing N → ττν samples. These sames were run through the analysis using the selections fromall six channels. In all cases, less than one signal event was observed for tau decays after the575.4. Data and Signal Samplesfinal analysis selections were applied. Thus, in models where |Uτ |2 is nonzero, all tau channelsare assumed to have zero acceptance.W+µ+e−µ+νµN W+?(a) µ−eµW+e+µ−e+νeN W+?(b) e−µeW+e+µ−µ+νµN W+?(c) e−µµW+µ+e−e+νeN W+?(d) µ−eeFigure 5.4: Additional Feynman diagrams for signal processes that contribute to the signalstrength if both |Uµ|2 and |Ue|2 are nonzero. Diagrams are shown for the charged-currentinteraction only.5.4.3 Modelling Spin CorrelationsSpin correlations (described in section 2.4) between the prompt lepton and the HNL arenot included in the Pythia8 signal generation. However, these correlations are taken intoaccount in MadGraph using the HeavyN model [75, 76]. The impact of spin correlations inthe modelling of HNL decays was only brought to light after all of the Pythia8 samples wereproduced. Due to the significant amount of time and computing resources required to validateand re-simulate all of the signal samples with MadGraph, an event weighting method is usedto account for the small kinematic differences between LNC and LNV decays.MC simulations model the probability of different outcomes by computing matrix elementsfor the processes. To take spin correlations into account, the MC generator should sample from585.4. Data and Signal Samplesa distribution that is proportional to:f(x) = |Mproduction + decay|2 (5.1)where x denotes the set of all relevant kinematic variables that the matrix element,M , dependson. Instead, Pythia8 factorizes the production and decay matrix elements and samples froma distribution that is proportional to:g(x) = |Mproduction|2 × |Mdecay|2 (5.2)To correct for this sampling effect, a weight that is equal to w(x) = f(x)/g(x) is applied toeach simulated event. This event weight can be computed analytically. The matrix elementsin f(x) and g(x) depend on the mass of the HNL, the 4-momentum of the W boson and the4-momentum of the prompt and displaced leptons. To simplify the computation of the matrixelements, light lepton (e/µ) masses are neglected and the matrix elements are reported up toa constant.Six matrix elements are computed that include spin correlations. Three matrix elementsare computed for LNC decays that correspond to the charge current (CC), neutral current(NC) or charge plus neutral current (CCNC) contributions. Similar matrix elements are alsocomputed for LNV decays. The size of the contribution from each of the CC, NC and CCNCdecays depends on the process and which mixing angles are nonzero. Thus, the computationof the weight, w(x), depends on the lepton number conserving behaviour of the decay (i.e.LNC or LNV), the flavours of the leptons in the HNL decay and the relative strengths of themixing angles, xα = |Uα|2/|U |2.For e−γγ and µ−γγ channels, with γγ = ee or µµ, the following event weight is computed:wCC+NC =xγ |MCCNC |2 + (1− xγ)|MNC |2|MPythia|2 (5.3)where |MCCNC |2 is the matrix element for CC plus NC decays proportional to |Uγ |2, |MNC |2is the contribution from NC decays proportional to |Uα 6=γ |2, |MPythia|2 is the matrix elementgenerated by Pythia8 and xγ is the relative strength of the mixing angle of the lepton flavourin the decay.8 This event weight is used for µ−µµ, µ−ee, e−ee and e−µµ channels.For processes with different flavours of leptons in the HNL decay (i.e. β 6= γ), only the8For example, in a µ−ee decay in a model where the mixing to all three lepton generations is nonzero, the|MCC+NC |2 term would take into account all the diagrams (CC and NC) that are proportional to |Ue|2 andthe |MNC |2 term would take into account NC-only decays where a muon or tau neutrino couples to the HNL(i.e. N → νl 6=eZ∗;Z∗ → e+e−).595.4. Data and Signal Samplescharge current decay contributes and the weight is:wCC =|MCC |2|MPythia|2 (5.4)where |MCC |2 is the matrix element for the charged current decays. This event weight is usedfor µ−µe and e−eµ channels.The validation of this method is performed by comparing samples generated with Pythia8and MadGraph9 Comparisons of the lepton pT distributions between MadGraph samples,the weighted and unweighted Pythia8 samples are shown in fig. 5.5 for the µ−µµ channelwith CC and NC decays.0 10 20 30 40 50 60 70 80 [GeV]TTruth Prompt Lepton p3−102−101−10Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVs, 10 GeV, 10 mmµµ-µLNC, s(a)0 10 20 30 40 50 [GeV]TTruth Displaced Lepton 1 p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVs, 10 GeV, 10 mmµµ-µLNC, (b)0 10 20 30 40 50 [GeV]TTruth Displaced Lepton 2 p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVs, 10 GeV, 10 mmµµ-µLNC, (c)0 10 20 30 40 50 [GeV]TTruth Displaced Lepton 3 p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVs, 10 GeV, 10 mmµµ-µLNC, (d)Figure 5.5: Comparison of the lepton pT distributions for LNC decays between MadGraphsamples (purple) and the weighted (pink) and unweighted (gray) Pythia8 samples for aµ−µµ signal using the NC+CC event weights. Samples are generated with mN = 10 GeV andcτN = 10 mm signal sample.9MadGraph signal samples were obtained with MadGraph5 aMC@NLO v2.9.3 [77] using the HeavyNmodel [75, 76]. The Pythia8 version description can be found in section 5.4.2.605.4. Data and Signal SamplesFigure 5.6 shows the pT comparisons for the µ−µe channel with CC decays only. Goodagreement betweenMadGraph and the weightedPythia8 samples indicates that the reweigh-ing method can be used to successfully include spin correlations in the model and, therefore,no additional signal uncertainty is necessary to account for this effect.0 10 20 30 40 50 60 70 80 [GeV]TTruth Prompt Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVse, 10 GeV, 10 mmµ-µLNC, (a)0 10 20 30 40 50 [GeV]TTruth Displaced Lepton 2 p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVse, 10 GeV, 10 mmµ-µLNC, (b)0 10 20 30 40 50 [GeV]TTruth Displaced Lepton 2 p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVse, 10 GeV, 10 mmµ-µLNC, (c)0 10 20 30 40 50 [GeV]TTruth Displaced Lepton 3 p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 TeVse, 10 GeV, 10 mmµ-µLNC, (d)Figure 5.6: Comparison of the lepton pT distributions for LNC decays between MadGraphsamples (blue) and the weighted (orange) and unweighted (gray) Pythia8 samples for aµ−µe signal using the CC event weights. Samples are generated with mN = 10 GeV andcτN = 10 mm signal sample.5.4.4 Signal KinematicsKinematic distributions of simulated particles involved in the HNL production and decay areshown for a µ−µµ signal in figs. 5.7 to 5.9. In simulation, the kinematic differences betweenthe different channels are negligible because leptons with momenta on the order of a GeV canbe treated as equivalent (massless) objects. Three different mass variables are used in thisanalysis. The DV mass, mDV, is the invariant mass of the two displaced charged leptons. The615.4. Data and Signal SamplesDV mass does not include the neutrino momentum from the HNL decay and thus, mDV willalways underestimate the simulated HNL mass, mN . The tri-lepton mass, mlll, is computedusing the kinematics of the three charged leptons in the signal. It is also missing the neutrinomomentum and is always less than the W boson mass. The HNL mass in fig. 5.8 (a) iscalculated using the HNL flight direction and the momenta of the other charge leptons inthe HNL decay to constrain two out of three degrees of freedom in the neutrino momentum.The final degree of freedom can be solved for using energy-momentum conservation of the Wboson decay. Details about this HNL mass calculation can be found in section 5.5.3.0 10 20 30 40 50 60 70 80 [GeV]TTruth Prompt Lepton p3−102−101−10Fraction of Events / 2 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 40 60 80 100 12)lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(a)0 10 20 30 40 50 [GeV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 4 6 8 100 120)lllTri-lepton mass (m1−110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(b)0 10 20 30 40 50 [GeV]TTruth Subleading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 4 6 8 100 120)lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(c)0 20 40 60 80 100 120 140 160 180 200) [GeV]lllTruth visble mass (m3−102−101−101Fraction of Vertices / 4 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 60 80 100 1Tri-lepton1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation RegionVertices / 4 GeV i 6i l 6i 6l i 611.0 µ0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVNm= 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG V G VG VmP BDUn e na= 13 e 139 bs10µµµ(d)Figure 5.7: Simulated lepton pT distributions for the three charged leptons in the HNL eventand the invariant mass of the tri-lepton system (mlll). The leading displaced lepton is definedas the lepton in the DV with the largest pT, while the subleading displaced lepton has thesmaller pT. Simulated µ−µµ signals are plotted for three different mass points: mN = 5, 7.5, 10GeV with cτN = 10 mm.620 2 4 6 8 10 12 14 16 18 20Truth HNL Mass Calculation [GeV]3−102−101−101Fraction of Events / 0.5 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 2 40 60 80 100 120) [ ]lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in Progress µµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(a) HNL mass (mHNL)0 20 40 60 80 100 [GeV]TTruth HNL p3−102−101−101Fraction of Events / 4 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 4 6 8 1 0 2) [ ]lllTri-lepton mass (m1−10110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Wo k in Progress µµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(b) HNL pT10− 5− 0 5 10ηTruth HNL 3−102−101−101Fraction of Events = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 40 60 80 100 12) [GeV]lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVNm = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VmP BDUn e na= 13 e 139 bs10µµµ(c) HNL η4− 3− 2− 1− 0 1 2 3 4φTruth HNL 3−102−101−101Fraction of Events = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 40 60 80 100 120) [GeV]lllTri-lepton mass (m1−110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVNm = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(d) HNL φFigure 5.8: HNL kinematics for simulated µ−µµ signals for three different mass points: mN =5, 7.5, 10 GeV with cτN = 10 mm.0 2 4 6 8 10Truth DV Mass [GeV]4−103−102−101−10Fraction of Events / 0.2 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 40 60 80 100 120) [ e ]lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ(a)0 50 100 150 200 250 300 [mm]xyTruth DV L4−103−102−101−10110Fraction of Events / 10 mm = 1 mmτc = 10 mmτc = 100 mmτcMaterial LayersATLAS Internal = 13 TeVs = 10 GeVHNL, mµµµLNC, 20 40 60 80 100 120) [GeVlllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region(b)Figure 5.9: The DV mass (a) and DV radius (b) distributions for simulated µ−µµ signalsamples. For the DV mass distribution, three different mass points are shown: mN = 5, 7.5, 10GeV with cτN = 10 mm. For the DV radius plot, the simulated samples have mN = 10 GeVwith cτN = 1, 10 and 100 mm.635.5. Event Reconstruction5.5 Event ReconstructionThe experimental displaced HNL signature consists of two main building blocks: a promptlepton and a two-lepton DV. The prompt lepton is reconstructed using the standard electronand muon reconstruction algorithms described in section 4.1.3 and section 4.1.4 respectivelyand the two-lepton DV is reconstructed using the VSI algorithm described in section 4.2.3.However, since the default VSI configuration was not optimized to reconstruct two-leptonDVs, a custom VSI configuration was developed for this analysis. The details of the customVSI configuration can be found in section 5.5.2.In addition to standard kinematic variables (e.g. pT, η, φ), this analysis also calculates theHNL mass, mHNL, using the kinematics of the three charged leptons in the signal, as well asinformation about the flight direction of the HNL and the W boson mass. The details of thismass variable can be found in section 5.5.3.5.5.1 Displaced Vertex Reconstruction for the HNL SignalThe displaced vertex reconstruction, described in section 4.2.3, produces two collections of ver-tices by default. These collections are created by modifying the VSI algorithm’s configurationsettings to apply different cuts and control which steps in the reconstruction sequence are run.The collection used by most ATLAS displaced vertex analyses, simply referred to as “VSI”,initially selects tracks from the collection of ID tracks (both standard and large-radius). Inorder to reduce the number track pairs, a 2 mm two-track forming d0 cut is used. This cutrequires that at least one track has a d0 > 2 mm in order to be defined as a compatibletwo-track pair. This configuration also runs the final track attachment step with non-selectedtracks.The second collection of vertices, called “VSI Leptons”, only selects lepton-matched tracks.The details of how tracks are matched to electron and muon objects can be found in sec-tion 4.1.3 and section 4.1.4 respectively. Since the number of track pair combinations is nowreduced by selecting lepton-matched tracks, this configuration has no requirements on the d0of the tracks. Since the purpose of this configuration is to reconstruct vertices with displacedleptons, the final track attachment step with non-selected tracks is not run, since these tracksconsist of mostly non-lepton tracks.The signal efficiency using VSI and VSI Leptons vertices is shown in fig. 5.10 (a) forsimulated HNL signals with varying lifetimes and masses. This efficiency is defined as theratio of the selected reconstructed events to the total number of simulated events. Selectingevents using VSI Leptons vertices has a larger signal acceptance for all masses and lifetimeswhen compared toVSI. Figure 5.10 (b) shows the signal efficiency using VSI Leptons verticesis up to 230% of the VSI signal efficiency for cτN = 1 mm signals.645.5. Event Reconstruction0 5 10 15 20HNL mass [GeV]00.050.10.150.20.250.3Signal Efficiency VSI 1 mmVSI 10 mmVSI 100 mmVSI leptons 1 mmVSI leptons 10 mmVSI leptons 100 mmSignal Efficiencyall MC campaignsµµDV type: ATLAS Internal\20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 2.4 Signalµµ-µ20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bk plep systematic, 2.5 Data, 10.0 ATL S Work i Progress = 13 TeVseµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (0 2 4 6 8 10Truth DV Mass [GeV]4−103−102−101−10Fraction of Events / 0.2 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 40 60 80 100 120) [ e ]lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ (a)0 5 10 15 20HNL mass [GeV]11.522.533.5VSI leptons/VSI lifetime = 1 mmlifetime = 10 mmlifetime = 100 mmRatio Signal Efficiencyall MC campaignsµµDV type: ATLAS Internal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 2.4 Signalµµ-µ0 5 10 15 20HNL mass [GeV]11.522.533.5VSI leptons/VSI lifetime = 1 mmlifetime = 10 mmlifetime = 100 mmRatio Signal Efficiencyall MC campaignsµµDV type: ATLAS Internal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−01−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bk plep systematic, 2.5 Data, 10.0 ATL S Work i P ogress = 13 TeVseµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (0 5 10 15 20HNL mass [GeV]11.522.533.5VSI leptons/VSI lifeti e = 1 mlifeti e = 10 mlifetime = 100 mmRatio Signal Efficiencyall MC campaignsµµDV type: ATLAS Internal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 2.4 Signalµµ-µVSI leptons/VSI20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−01−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bk plep systematic, 2.5 Data, 10.0 ATL S Work i P ogress = 13 TeVseµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (0 5 10 15 20HNL mass [GeV]11.522.533.5VSI leptons/VSI lifetime = 1 mmlifeti e = 10 mmlifeti e = 100 mmR tio Signal Efficiencyall MC ca paignsµµDV type: ATLAS Internal20 40 60 80 100 120) [GeV]lllTri-lepton ass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 2.4 Signal-µ0 5 10 15 20HNL mass [GeV]11.522.533.5VSI leptons/VSI lifeti e = 1 mmlifetime = 10 mmlifeti e = 10 mmRatio Signal Efficiencyall MC ca paignsµµDV type: ATLAS Internal20 40 60 80 100 120) [GeV]lllTri-lepton ass (m3−102−01−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bk plep systematic, 2.5 Data, 10.0 ATL S Work i P ogress = 13 TeVseµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (0 2 4 6 8 10Truth DV Mass [GeV]4−103−102−101−10Fraction of Events / 0.2 GeV = 5 GeVHNLm = 7.5 GeVHNLm = 10 GeVHNLmATLAS Internal = 13 TeVs = 10 mmτ, cµµµLNC, 20 40 60 80 100 120) [ e ]lllTri-lepton mass (m1110Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 4.0 DV systematic, 4.0 Prompt lepton systematic, 4.0 Data, 4.0 Work in ProgressµµChannel: e-Validation Region0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CR = 5 GeVN = 7.5 GeVN = 10 GeVNPost-fit BackgroundDataUncertaintyATLAS Internal-1 = 13 TeV, 139 fbs, 10 mmµµ-µ [ ]L2−1−2Events / 2.5 GeV = 5 eN = 7.5 eN = 10 eNmost-fit ackgroundatancertainty I t r l-1 , f, -HNEvents / 2.5 GeVSR CRG VG VG VP BDUn e na= 13 e 139 bs10µµµ (b)Figure 5.10: The µ−µµ signal efficiency (a) and ratio of the signal efficiency between VSILeptons and VSI (b) as a function of simulated HNL mass with 3 < mN < 20 GeV. Signalsamples with cτN = 1, 10, 100 mm are shown in red, blue and green respectively. The signalefficiency is defined as the ratio of the selected reconstructed events to the total number ofsimulated events.There are two main differences between the VSI and VSI Leptons configurations that resultin this increase in signal efficiency. First, the VSI Leptons configuration has no requirement ofthe d0 of the tracks when forming compatible two-track pairs. This is especially important forsignals that are not very displaced, since the tracks from the HNL decay will have a small d0.As a result, the observed increase in efficiency is largest for the 1 mm lifetime signals (see thered points in fig. 5.10 (b)). The second effect comes from the non-selected track attachmentstep that is only run in the VSI configuration. In this configuration, reconstructed signalvertices may have additional tracks attached to the vertex either from fake tracks or pileuptracks near the HNL decay. Since the signal selection requires that the displaced vertex hasexactly two tracks, any signal vertex with additional attached tracks is rejected by this two-track requirement.While the signal acceptance is larger for events reconstructed with the VSI Leptons config-uration, the sensitivity of the analysis depends on both the signal and background acceptance.In fig. 5.11, the signal and data-driven same-sign background estimate is shown as a functionof the reconstructed HNL mass.10 The lepton-only vertexing configuration improves the signalefficiency by 20% for this µ−µµ signal model and up to 300% for other benchmark signals.However, this signal efficiency increase comes at the cost of over a factor of 20 increase in thetwo-muon DV data-driven background.10The details of the reconstructed HNL mass variable can be found in section 5.5.3 and a description of thedata-driven same-sign background estimate is described in section 5.8.655.5. Event Reconstruction0 5 10 15 20 25 30HNL mass [GeV]10203040506070Events=65.64bs/ 2.42µµµ SS bkg, , 10mm 102.11µµµATLAS Internal-1 = 13 TeV, 140.0 fbsVSIsel , mixed signal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress 3 TeVeµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton ma s (m3−102−101−10110210Vertices / 4 GeV t - ri SS bkg, 4.0 Data-driven shuffled bkg, 2.5 DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµµv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL ((a) VSI0 5 10 15 20 25 30HNL mass [GeV]10203040506070Events=19.12bs/ 43.52µµµ SS bkg, , 10mm 126.14µµµATLAS Internal-1 = 13 TeV, 140.0 fbsVSI_Leptonssel , mixed signal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1011210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress 3 TeVeµ-µv8, Data-driven bkg., 2.4, 10 GeV, 10mm), 102.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton ass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, GeV, 10mm), 126.1µµ-µHNL ((b) VSI LeptonsFigure 5.11: Simulated events for a µ−µµ, 10 GeV, 10 mm signal in purple and the data-drivensame-sign background in grey as a function of the reconstructed HNL mass. The total numberof events in the signal and background can be found in the legends in each plot. Events areselected by applying the pre-selection cuts described in section 5.7.5.5.2 Custom Displaced Vertex ConfigurationWith the default lepton-only vertexing configuration, the analysis could not benefit fromthe increase in signal acceptance due to the large increase in the background. Therefore, acustom vertex configuration was developed to maintain most of the signal efficiency increaseand greatly reduce the background. The three main areas in the VSI algorithm that wereoptimized for the two-lepton displaced HNL signal are the track selection, two-track vertexforming d0 cut and track attachment. These three optimizations are discussed below.The custom vertex configuration that is used to reconstruct vertices for this analysisis based on the VSI Leptons configuration with additional track selections applied to bothstandard and LRT tracks and a two-track forming d0 cut of 1 mm. This custom configurationalso runs the final track attachment step.Track Selection OptimizationIt was identified that HNL signal events can be lost due fake tracks being attached or mergedwith the signal vertices. Identifying and removing these fake tracks prior to vertexing improvesthe signal acceptance. As will be discussed in section 5.8, the dominant background comesfrom random track crossings that form a two-lepton vertex. Removing non-signal-like tracksbefore vertexing reduces the probability of a random crossing and therefore also reduces thebackground.At the same time as the vertex optimization studies were being performed, large-radiustrack reconstruction was also undergoing optimization in preparation for the start of the LHC665.5. Event ReconstructionRun 3.11 As a result, new LRT quality selections had been developed specifically to reducethe number of fake tracks. The additional selections on the track parameters that were addedto the custom VSI configuration were inspired by these Run 3 LRT improvements and arelisted in table 5.3.Table 5.3: The main differences in the track selection between the default VSI configurationand the lepton-only selection used in the custom VSI configuration in this analysis.Track Type Track Parameter Default Value Custom ValueStandard Lepton matching Not required Required& LRT Min. # Silicon hits 7 8LRT Max. |z0| 1000 mm 500 mmMin. # SCT hits 2 7Max. # SCT holes 2 1Max. χ2/dof 50 9∆θ and |z0| correlation n.a. ∆θ ≤ 1 or |z0| < 200 mmThe impact of the additional track selections on the signal and background can been seenin fig. 5.12. Applying additional selections removes fake or poor quality tracks and reduces thenumber of two-lepton VSI background events by a factor of 2 and the number of VSI Leptonsbackground events by 20%. This reduction in the background is achieved while maintaining asimilar number of signal events. To measure the performance of the additional track selections,the signal significance was estimated as the number of signal events divided by the square rootof the number of background events (s/√b). Adding the additional track selections increasesthe signal significance, indicating that these selections improve the analysis sensitivity.Two-Track Vertex Forming d0 Cut OptimizationAs described in section 5.5.1, one of the main differences between the VSI and VSI Leptonsconfigurations is the removal of the two-track forming d0 cut that is used to determine thecompatibility of the two tracks. Studying simulated HNL signal events shows that about 80%(20%) of events with 1 mm (10 mm) lifetimes have two tracks with d0 < 2 mm. This meansthat 80% (20%) of the time, signals with 1 mm (10 mm) lifetimes will fail to pass the two-trackcompatibility threshold in the VSI configuration.Signal and background events were studied for different two-track forming d0 cuts rangingfrom 0 mm to 2 mm. It was observed that changing the d0 cut from 2 mm to 0 mm canincrease the signal efficiency by a factor of 1.2 to 3 (see fig. 5.13 (a)). However, the numberof background events also increases as the d0 cut decreases (see fig. 5.13 (b)). To find oneconfiguration for all signal models, a balance must be found when optimizing the vertexingconfiguration for signals with different lifetimes. Using the signal significance (s/√b) as a11Run 3 refers to the period of data collection that is planned to start in 2022. See fig. 3.3 for a timeline ofthe LHC machine.675.5. Event Reconstructionmetric (fig. 5.13 (c) and (d)), it was determined that a 1 mm d0 cut gave the best balancebetween increasing the sensitivity to low lifetime signals, while minimally impacting longerlifetime samples.(a) Signal (b) Background(c) Signal SignificanceFigure 5.12: The number of µ−µµ 10 GeV, 10 mm signal (a) and two-muon background (b)events for default VSI (blue) and VSI Leptons (orange) vertex configurations. The originalnumber of events is given by the default configuration. Events labels “LRTR3” are the numberof events after modifying the track selections as described in table 5.3 without the ∆θ and|z0| correlation selection. The “LRTR3 w Geo cut”, which is the final selection applied in thecustom vertex configuration, is the number of events including this final correlation selection.The signal significance (c) is estimated using the number of signal events divided by the squareroot of the number of background events (s/√b).685.5. Event Reconstruction20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((a) Signal (cτN = 10 mm)20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((b) Background20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((c) Significance (cτN = 10 mm)20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((d) Significance (cτ)N = 1 mm)Figure 5.13: Signal events for a 10 GeV, 10 mm µ−µµ sample (a) and two-muon backgroundevents (b) as a function of the two-track forming d0 cut for VSI (blue) and VSI Leptons(orange) vertex configurations. The original number of events is given by the default config-uration. Then the number of events with two-track forming d0 cut threshold equal to 2, 1.5,1, 0.5 and 0 mm is shown. The signal significance (s/√b) for 10 GeV, µ−µµ signal is shownfor the 10 mm (c) and 1 mm (d) signal samples as a function of the same d0 cut.Track AttachmentThe plot of the number of background events as a function of the d0 cut ( fig. 5.13 (b)) showsthat even when the d0 cut is the same, the VSI Leptons background is still about four timeslarger compared to VSI. However, as described in section 5.5.1, the final difference betweenthe configurations is that VSI runs the final track attachment step and attaches non-selectedtracks to the vertex. This means that non-lepton tracks that are compatible with a two-leptonpair will be added to the vertex and increase the number of tracks (ntracks) in the vertex suchthat ntracks > 2.695.5. Event ReconstructionTo study the impact of the track attachment step, DVs with exactly two lepton-matchedtracks are selected. These events are then separated according to the total number of tracksin the vertex. Vertices that consists of two leptons (i.e. ntracks = 2) are selected as signal(or signal-like) events. Any vertex with ntracks > 2 is rejected from the signal region. Infig. 5.14 (a), about four signal events are removed from the signal region because additionaltracks are attached to the two-track signal vertex. However, in the background distributionin fig. 5.14 (b), there are many vertices with ntracks > 2 that have exactly two-leptons. Sincethe VSI Leptons configuration does not run this additional track attachment step, many ofthese vertices with ntracks > 2 will be reconstructed with exactly two lepton-matched tracksand be selected in the signal region.Without the additional track attachment step, information about the non-lepton tracksnear by the background vertices is missing. This missing information is what causes the factorof four increase in background events that is observed in fig. 5.13 (b) when the two config-urations are run with the same d0 cut. Running the track attachment in the VSI algorithmimproves the signal significance, since the reduction in background is much larger than thesmall amount of signal events that are lost.1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5num_trks5−104−103−102−101−10110210310410510610710entries0.0 0.0152.03.70.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0155.82), ( sig. 0mm d0 w LRT cuts-1 Ldt = 140 fb∫ = 13 TeV, sVSI_LRTR3_0p0 InternalATLAS20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Wo k in Progress = 13 TeVeµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Number of Tracks in Vertex, 10GeV, 10mm), 155.82µµ-µSignal (0 5 10 15 20 25 30HNL mass [GeV]1020304050670Events=65.64bs/ 2.42µµµ SS bkg, , 10mm 102.11µµµATLAS Internal-1 = 13 TeV, 140.0 fbsVSIs l , mixed signal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 155.82µµ-µSignal (Number of Tracks in Vertex(a) Signal2 4 6 8 10 12num_trks050010001500200025003000entries667.32079.01724.31344.0756.0354.7140.0 86.3 14.0 11.7 2.3 2.37182.0), ( SS bkg 0mm d0 w LRT cuts-1 Ldt = 140 fb∫ = 13 TeV, sVSI_LRTR3_0p0 InternalATLAS20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Wo k in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (0 5 10 15 20 25 30HNL mass [GeV]102034050670Events=65.64bs/ 2.42µµµ SS bkg, , 10mm 102.11µµµATLAS Internal-1 = 13 TeV, 140.0 fbsVSIsel , mixed signal20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 155.82µµ-µSignal (Number of Tracks in Vertex20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 0GeV, 10mm), 7182µµ-µSignal (Data-driven background, 7182(b) BackgroundFigure 5.14: Signal (a) and background (b) events with exactly two muons in the displacedvertex as a function of the number of tracks (ntracks) in the vertex reconstructed using the VSIconfiguration with a 1 mm two-track forming d0 cut. Vertices with ntracks = 2 are selected inthe signal region, while events with ntracks > 2 are rejected.705.5. Event ReconstructionPerformance of the Custom Displaced Vertex ConfigurationA summary plot of the signal efficiency increase observed with the custom vertex configurationis shown in fig. 5.15. This plot shows the ratio of the the number of signal events for the customto the default VSI configuration is shown for the four single-flavour mixing channels (µ−µµ,µ−µe, e−eµ and e−ee) as a function of lifetime. For most signal channels and lifetimes, thecustom configuration has larger signal yields, especially for 1 mm samples, where the e−eechannel has a factor of 3.8 increase in acceptance. Longer lifetime samples are minimallyimpacted by the additional selections applied to LRT tracks.Figure 5.15: Ratio of the number of selected signal events reconstructed with the customconfiguration to the default VSI configuration. Ratios are shown for the 10 GeV signal samplesin the µ−µµ, µ−µe, e−eµ and e−ee channels as a function of the proper decay length.To evaluate the vertex reconstruction efficiency for the signal, a matching procedure isused to determine if the simulated HNL decays are reconstructed as displaced vertices. Thismatching procedure follows the same definitions adopted in Ref. [78]. HNL decays are consid-ered to be reconstructed if the tracks associated to a displaced vertex are matched to particlesoriginating from the HNL. The matching of tracks to particles is based on a weighted scor-ing of shared detector hits between the track and particle trajectories. A track is consideredmatched to a particle if this score is greater than 0.5. For each pair of a reconstructed vertex715.5. Event Reconstructionposition, v, and the simulated decay vertex position, l, a matching score s is computed, whichuses the magnitude of the track pT as a weight. This score is given by:s(v, l) ≡∑i ∈ tracks in l( p(i)T |descendent of signal decay l)∑i ∈ tracks in vp(i)T(5.5)The total vertex efficiency can be broken up into several components including the ac-ceptance, the track selection efficiency and the core efficiency of the VSI algorithm. Theacceptance, seed and core efficiencies are defined as follows,• Acceptance (A): fraction of signal decays with at least two reconstructed tracks withpT > 1 GeV, a z-position of |z| < 2720 mm and a transverse distance from the origin ofLxy < 563 mm.• Seed efficiency (seed) : fraction of signal decays with at least two tracks passing theVSI track selection requirements.• Core efficiency (core) : fraction of signal decays with a reconstructed vertex that hasa matching score s(v, l) > 0.5.The total efficiency (tot) is then given by:tot = A · seed · core (5.6)These four efficiencies (A, seed, core and tot) are shown in fig. 5.16 as a function of radialdecay position, Lxy, for 10 GeV, 10 mm signal for the µ−µµ, µ−µe and e−ee channels. Thetotal efficiency peaks between 15-25% depending on the signal sample. The efficiency at verylow values of Lxy is suppressed due to the minimum |d0| of 1 mm and at high values of Lxydue to the requirements on the number of hits per track.Overall the total vertexing efficiency of the HNL signal is low compared to other long-livedDV signals because the HNL signature only has two tracks in the DV. If either of the tracks isnot reconstructed or the two reconstructed tracks do not form a good quality vertex, then thesignal is rejected. In contrast other long-lived displaced vertex signals can have many tracksand even if one track is missing, the signal vertex can still be reconstructed without this track.721−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (1−10 1 10 210LLP r [m ]00.20.40.60.811.21.4Acceptance µµeµµeeATLAS imulation I ternal= 13 TeVsVSI_LeptonsMod_LRT 3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [ m]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1011020Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffl d bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1010210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 0.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [m ]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, mm), 7182µµ-µSignal ( [mm]xyL(a) Acceptance, A1−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p010 210LLP r0.050.10.15.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal= 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 10 120) [GeV]lllTri-lepton mas (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10m ), 126.1µµ-µHNL (1−10 1 10 210LLP r [m ]00.20.40.60.811.21.4Acceptance µµeµµeeATL S imulation I ternal= 13 TeVsVSI_LeptonsMod_LRT 3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210L P r [mm]00.20.40.60.811.21.4seedε µ eµeATLAS Simulation Inter al = 13 TeVsVSI_LeptonsMod_LRT 3_1p0−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.2.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [m ]00.20.40.60.811.21.4coreε µµ eµµeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRT 3_1p01−10 1 10 210LL r [ ]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210L P r [m ]00.20.40.60.811.21.4Acceptance µeµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [m ]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]llTri-lepton mass (m3−102−101−1011020Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV syst matic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffl d bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1010210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 0.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [m ]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS ork in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [m ]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, mm), 7182µµ-µSignal ( [mm]xyL(b) Seed efficiency, seed1−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−1021−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (1−10 1 10 210LLP r [m ]00.20.40.60.811.21.4Acceptance µµeµµeeATLAS imulation I ternal= 13 TeVsVSI_LeptonsMod_LRT 3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]0.20.40.60.811.21.4seedε µµµ eµµeeeAT AS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.2.4.6.811.2.4Acceptance µµµeµµeeeAT AS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]0.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.81.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_L ptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]0. 50.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [ m]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1011020Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVse-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffl d bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1010210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 0.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [m ]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 ata-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, mm), 7182µµ-µSignal ( [mm]xyL(c) Core efficiency, core1−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLA Simulati n Inter al = 13 T VsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµµµeeeATLAS Simulation Inter al = 13 TeVsVSI_LeptonsM d_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.4.60.811.21.4seedε µµµ eµµeeeATL S Simulation Inter al = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATL S Simulation Inter al = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−111210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 T Vseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (1−10 1 10 210LLP r [m ]00.20.40.60.811.21.4Acceptance µµeµµeeATLAS imulati n I ternal= 13 TeVsVSI_LeptonsMod_LRT 3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulati n Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4Acceptance µµµeµµeeeATLAS Simulati n Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.20.40.60.811.21.4coreε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [ m]00.20.40.60.811.21.4seedε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p01−10 1 10 210LLP r [mm]00.050.10.150.20.250.30.350.40.450.5totalε µµµ eµµeeeATLAS Simulation Internal = 13 TeVsVSI_LeptonsMod_LRTR3_1p020 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−1011020Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffl d bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−101021Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 0.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [m ]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, 10mm), 7182µµ-µSignal ( [mm]xyL20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, , 10GeV, mm), 7182µµ-µSignal ( [mm]xyL(d) Total efficiency, totFigure 5.16: The three components of the vertex reconstruction efficiency and the total effi-ciency, measured as a function of radial decay position, Lxy, for µ−µµ, µ−ee and e− e signalswith mN=10 GeV and cτN =10 mm.735.5. Event Reconstruction5.5.3 Reconstructed HNL MassThe HNL mass (mHNL) can be obtained using energy-momentum conservation in the HNLproduction (W → Nl1) and decay (N → l2l3ν), where l1 is the prompt lepton and l2 andl3 are the charged leptons in the DV. The problem can be summarized with the followingequations. Four-momentum conservation in the N decay gives:pµN = pµ2 + pµ3 + pµν ≡ pµ23 + pµν (5.7)Four-momentum conservation in the W decay gives:pµW = pµ1 + pµN = pµ1 + pµ23 + pµν (5.8)It will also be useful to define:p223 = E223 − |~p23|2 = m223 (5.9)p‖23 ≡ ~p23 · vˆ (5.10)p⊥23 ≡ |~p23 − p‖23vˆ| (5.11)where m, E, and |~p| are the mass, energy, and momentum-vector magnitude of the particlesindicated by their subscript and vˆ is the flight direction of the HNL given by the vectorconnecting the PV and DV.The components of the neutrino momentum are not measured. Equivalently, due to eqs. (5.7)and (5.8), we could treat the components of pN or pW (respectively) as the unknowns. Eitherway, the HNL flight direction provides a constraint on the neutrino momentum componentsorthogonal to vˆ, leaving two remaining degrees of freedom. The simplest solution is to solvethe problem using the neutrino degrees of freedom (Eν and p‖ν) and computing the variousquantities in a reference frame that is rotated with respect to the lab frame.The solution to the HNL mass is presented in the coordinate system, k = (xˆ′, yˆ′, zˆ′), whichis rotated with respect to the ATLAS coordinate system (see section 3.2.1), such that theorigin of the k-frame is at the PV and the z′-axis points along the flight direction of the HNL.The definition of this coordinate system is:zˆ′ = vˆ, xˆ′ =~p23 × zˆ′|~p23 × zˆ′|, yˆ′ = zˆ′ × xˆ′ (5.12)Energy-momentum conservation in the W and N decays can be expressed in terms of pν ·vˆ = α745.5. Event Reconstructionusing:~p′23 ≡ ~q (5.13)E′23 =√q2 +m223 (5.14)~q = (0, |~p23 × zˆ′| ≡ q⊥, ~p23 · zˆ′ ≡ qz) (5.15)~pν = (0, −q⊥, α) (5.16)Eν =√q2⊥ + α2 (5.17)Equation (5.8) gives:m2W = m21 +m2ν +m223 + 2p′1 · (p′23 + p′ν) + 2p′23 · p′ν (5.18)where:p′1 · (p′23 + p′ν) = E′1(E′23 + E′ν)− p′1,z(qz + α) (5.19)p′23 · p′ν = E′23E′ν + q2⊥ − qzα (5.20)In the energy regime of interest, with particles that have GeV momenta, both the mass of theprompt lepton (m1) and the neutrino (mv) can be set to zero. Rearranging eq. (5.18) to solvefor Eν gives:E′ν = A+Bα (5.21)whereA =m2W−m2232 − E′1E′23 + p′1,zqz − q2⊥E′1 + E′23, B =p′1,z + qzE′1 + E′23(5.22)Subtracting eq. (5.21) from eq. (5.17) gives the following quadratic expression α:(B2 − 1)α2 + 2ABα+A2 − q2⊥ = 0 (5.23)Using the quadratic formula, the solution for α is:α =−AB ±√(B2 − 1)q2⊥ +A2(B2 − 1) (5.24)This gives two solutions for the z component of the neutrino momentum, α. Both solutionswere studied using simulated HNL events and it was observed that the solution with thesmaller | ~pN | typically led to a value for mHNL that was closer to the simulated HNL mass755.5. Event ReconstructionmN . This solution often corresponds to the forward emission of the neutrino with respect tothe HNL decay in the lab frame. Therefore, in the definition of the HNL mass used in theanalysis, the positive radical is chosen as the solution for α.From eq. (5.7) and the definitions in eqs. (5.13) to (5.17), the expression for the HNL massin terms of α is:m2HNL = m223 + 2p′ν · p′23 (5.25)= m223 + 2E′23√q2⊥ + α2 + 2q2⊥ − 2qzα (5.26)Substituting the expression for α in eq. (5.24) into eq. (5.26) gives the solution for the HNLmass.Picking the W massEquation (5.26) gives a solution for the HNL mass in terms of the known energies and momentaof the two charged particles in the HNL decay (E′23, ~p′23 ≡ ~q) and the component of theneutrino momentum in the z′ direction, α. Equation (5.24) provides an analytical solution forα, given the momenta of all three charged leptons and the mass of the W boson, mW .ATLAS has measured the W boson pole mass to be MW = 80.370± 0.019 GeV [79] andthis measurement is combined in Ref. [80] with results from LEP to provide a measurementfor the W boson width, ΓW = 2.195 ± 0.083 GeV. Since the W mass has a width, if mW isfixed to the pole mass in eq. (5.18), then it is possible mHNL has no real solution. Instead ofrejecting these events, mW is set equal to the median mW in the kinematically allowed regiondefined by the charged lepton kinematics. This ensures that α (and correspondingly mHNL)will always have a real solution. The difference in the HNL mass distribution between fixingthe mW to the pole mass and using the median mW in the kinematically allowed region canbe seen in fig. 5.17. Fixing the W mass results in events where the HNL mass has no realsolution. These are represented in fig. 5.17 by the entries at mHNL = −1.To define the kinematically allowed region, the minimum W mass that is consistent withthe charged lepton decay products (mW,min) is computed. From eq. (5.18), the mass of the Wboson is given by:m2W = m223 + 2(E′1E′23 + E′ν(E′1 + E′23)− p′1,zqz + q2⊥ − α(p′1,z + qz))(5.27)and mW,min occurs where:dm2W2dα= (E′1 + E′23)dEνdα− (p1,z + qz) = 0 (5.28)765.5. Event Reconstruction0 5 10 15 20 25 30HNL mass [GeV]510152025Eventsfix W pole massmedian allowed W mass-1 Ldt = 60 fb∫ = 13 TeV, sµµµchannel: VSI Leptons InternalATLAS20 40 60 80 100 120) [GeV]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (Figure 5.17: Two HNL mass distributions for a simulated µ−µµ with mN = 10 GeV andcτN = 10 mm. The mHNL is computed using mW fixed to the pole mass of 80.4 GeV (blue)and the median W mass in the allowed kinematic region (purple). Events where the HNLmass has no real solution are set to -1.Using dEνdα =d√q2⊥+α2dα =αEνin eq. (5.28), the value of α that gives the minimum mW is:dm2W2dα= (E′1 + E′23)αEν− (p′1,z + qz) = 0 (5.29)αEν=p′1,z + qzE′1 + E′23= B (same B as in eq. (5.23)) (5.30)α2E′2ν= B2 (5.31)α2 = B2E′2ν = B2(q2⊥ + α2) (5.32)α = ± q⊥B√1−B2 (5.33)Substituting α = q⊥B√1−B2 back into eq. (5.27), the minimum W boson mass is:m2W,min = m223 + 2E′1E′23 + (E′1 + E′23)√q2⊥ +q2⊥B21−B2 − p′1,zqz + q2⊥ − (p′1,z + qz) q⊥B√1−B2 (5.34)The cumulative probability for the W boson to have a mass greater than mW,min is used tofind the median of the remaining distribution. The probability density function (f) for mW isproportional to:f(m2W ) ∝1(m2W −M2W )2 +M2WΓ2W(5.35)775.6. Object DefinitionsTherefore, the cumulative distribution function (F) isF(m2W ) =1piarctan(m2W −M2WMWΓW)+12(5.36)The midpoint of the allowed kinematic region has a value ofFmed =1 + F(m2W,min)2(5.37)Rearranging eq. (5.36) for m2W givesm2W = M2W + ΓWMW tan(pi[F− 12])(5.38)Substituting F = Fmed, in eq. (5.38) gives an expression for the median W mass in thekinematically allowed regionm2W,med = M2W + ΓWMW tan(pi[1 + F(m2W,min)2− 12])(5.39)This value of mW,med is used in eq. (5.24) to solve for α.5.6 Object DefinitionsEvents in this search are selected using three types of physics objects: displaced vertices,muons and electrons. The definitions for each object are as follows:Displaced verticesDisplaced vertices are reconstructed from standard and large-radius tracks following the proce-dure described in section 4.2.3. A custom lepton-only displaced vertex configuration, describedin section 5.5.2, is used to perform the reconstruction. At the analysis level, only displacedvertices with exactly two tracks matched to displaced leptons (e/µ) are selected.Prompt muonsPrompt muons are reconstructed as described in section 4.1.4. The prompt muon in the eventis defined as the highest pT muon with |d0| < 3 mm and |z0 sin(θ)| < 0.5 mm that does notoverlap with any tracks in the displaced vertex. This muon is required to be a combined muonand pass the Medium quality working point. The muon is also required to have a pT > 3 GeV. Ifthe selected prompt muon overlaps with a prompt electron within ∆R =√∆η2 + ∆φ2 < 0.05,then the event is rejected.785.7. Event SelectionDisplaced muonsDisplaced muons are tracks in a displaced vertex that are matched to muon objects. Thematching of tracks to muon objects is described in section 4.1.4. A displaced muon must bematched to a combined muon that passes the Medium quality working point. The muon isalso required to have a pT > 3 GeV. If a displaced muon overlaps with an electron, and thematched muon passes at least the Loose quality working point, then the track is defined as amuon. If the track is not matched to a muon or an electron, then the vertex is rejected.Prompt electronsPrompt electrons are reconstructed as described in section 4.1.3. The prompt electron in theevent is defined as the highest pT electron with |d0| < 3 mm and |z0 sin(θ)| < 0.5 mm that doesnot overlap with any tracks in the displaced vertex. The prompt electron is required to passthe LHMedium quality working point. The electron is also required to have a pT > 4.5 GeV.If the selected prompt electron overlaps with a prompt muon within ∆R < 0.05, then theevent is rejected.Displaced electronsDisplaced electrons are tracks in a displaced vertex that are matched to electron objects. Thematching of tracks to electron objects is described in section 4.1.3. Displaced electrons arerequired to pass the custom VeryVeryLoose quality working point. The electron is also requiredto have a pT > 4.5 GeV and have a ∆pT/pT, track-only < 0.5, where ∆pT = pT, track-only −pT, calibrated electron. If a displaced electron overlaps with a muon and the matched muon doesnot pass the Loose quality working point, then the track is defined as an electron if thematched electron passes the VeryVeryLoose quality working point. If the track is not matchedto a muon or an electron, then the vertex is rejected.5.7 Event SelectionIn this search for displaced HNLs, a series of requirements are used to select events of interest.These selections are separated into a set of pre-selection requirements that are, for the mostpart, defined by properties of the displaced HNL signal or by the detector acceptance. Then,signal region (SR) selections are applied to maintain sensitivity to the signal, while alsoreducing the backgrounds (non-signal physics processes) as possible. Events that meet all thepre-selection and SR requirements are analyzed in the results shown in section 5.11.This section begins with a description of the main analysis framework that is used toselect data and simulated signal events (see section 5.7.1) and then describe the pre-selectionrequirements and SR selections in section 5.7.2 and section 5.7.3 respectively. Additional795.7. Event Selectionregions, described in section 5.7.4, are also defined to primarily study backgrounds in thedata.5.7.1 Analysis FrameworkSimulated signal and data events are processed through the analysis framework to select inter-esting events. The first steps in the framework, including the trigger, filter, reconstruction andderivation, all use analysis software that is written by collaboration members who are expertsin the areas of triggers and object reconstruction. These steps are designed to reconstruct thephysics objects of interest and reduce the number of events that need to be processed in theremaining steps to save time and computing resources. Generally speaking, these steps arecommon to most physics analyses and therefore, to streamline this process, they are usuallyrun by a central data processing team. The subsequent steps are usually shared by a fewanalysis teams and are customized to apply events selections for each analysis. Since thesesteps are custom to the analysis, analysis team members usually play a larger role in theprocessing of data from the derivation step to produce the final results.This search for displaced HNLs uses a special stream of data from the ATLAS experimentthat initially applies an event selection, known as a “filter”, to select events that are potentiallyinteresting for the analysis. This filter step is required in order to run the displaced trackingreconstruction described in section 4.2.1, since LRT cannot be run over all the full datasetbecause it is computationally expensive and requires a large amount of disk space to store allthe tracking information.The diagram in fig. 5.18 shows how simulated signal and data events are processed in theanalysis framework. The eight main steps in the framework are as follows,1. Trigger: It is impossible, in terms of data readout speed and storage, for ATLAS toprocess every proton-proton collision event. As a result, triggers are designed to selectevents of interest for further processing (see section 3.2.6 for more details about triggers).In this analysis, standard single muon and electron triggers are used to select data events.In the signal, it is usually the prompt lepton produced in the W boson decay that passesthe trigger requirements.2. Filter: A displaced HNL filter is used to select interesting data events that are thenreprocessed to reconstruct large-radius tracks. Only about 10% of the full dataset in theLHC Run 2 is selected by all the analysis filters included in this step. For more detailssee section 5.7.2.3. Reconstruction: Events that are selected by the filter are then reconstructed using thealgorithms described in chapter 4. In this step, DVs are reconstructed using the defaultVSI configurations discussed in section 5.5.1.805.7. Event Selection4. Derivation: A derivation step is used to skim away information that is not required forthe displaced HNL analysis. This reduces the size of the output files by 98% and alsoreduces the number of events that need to be reprocessed saving time and computingresources. This derivation step also re-runs the displaced vertex reconstruction using thecustom VSI configuration described in section 5.5.2. A basic event selection is applied inthis step that requires the event to have at least one DV reconstructed using the customVSI configuration.5. Filter Emulator: A filter emulator is run to estimate the impact of the data filter onsimulated signal events. See section 5.7.2 for more details.6. Ntuples: Events from the derivation step are processed and stored in ordered sets thatcontain n-elements. These data structures, known as “ntuples”, store the necessary infor-mation about each event, including the prompt lepton and displaced vertex information.This step stores the information in such a way that it is relatively fast to further processthe events to study the impact of the event selection in data and simulation.7. Histograms: After the ntuples are produced, a histogram-making step applies remain-ing events selections. This step also saves mini-ntuples that contain a smaller subset ofthe information only for selected events. These mini-ntuples are used as an input in thestatistical analysis framework.8. Statistical analysis: The final step in the analysis pipeline is the statistical analysis ofselected events in the signal and background. The details of this framework are describedin section 5.10.5.7.2 Pre-SelectionsAll data events are required to pass basic event cleaning and data quality requirements dis-cussed in section 5.4.1. In addition to this basic event cleaning, a series of pre-selection require-ments are defined to select events of interest in the HNL search. A full list of the pre-selectionrequirements can be found in table 5.8. These selections include:TriggerSingle muon and electron triggers are used to select events in this analysis. The list of triggersis shown in table 5.4. These triggers have a minimum pT requirement of 20-26 GeV (dependingon the year). The trigger efficiency for the HNL signal is ∼ 30−35%. Since the prompt leptonspectrum does not have a strong dependence on the HNL mass (see fig. 5.7), this triggerefficiency is fairly constant for all HNL mass and lifetime signal models.815.7. Event SelectionFilter Events (keep ~10% of data)Ntuple Maker CodeCustom Lepton-Only VertexingRun Large Radius Tracking & Secondary VertexingData EventsSimulated EventsTriggerFilterReconstructionNtuplesDerivationStatistical AnalysisHistograms (Mini-ntuples)Event Selection CodeLimit Setting CodeFilter EmulatorEmulation of the Filter Figure 5.18: The analysis framework pipeline that shows how data and simulated signal eventsare processed in the displaced HNL analysis.Table 5.4: Single muon and electron triggers from 2015-2018 that are used to select events ofinterest.Lepton Trigger name 2015–2016 2017 2018muonHLT mu20 iloose L1MU15 XHLT mu26 ivarmedium X X XelectronHLT e24 lhmedium L1EM20VH XHLT e26 lhtight nod0 ivarloose X X XFilterFour HNL filters are used to select events for the special data reprocessing that includes large-radius track and displaced vertex reconstruction. These filters require at least one promptand one displaced lepton. The filters are defined for the various combinations of prompt anddisplaced muons and electrons. Their requirements are listed in table 5.6.825.7. Event SelectionThe filter rate is defined as the number of data events that pass the filter selections dividedby the total number of events. The filter rate for the four HNL filters, as well as the overallrate that includes all analysis filters in the data reprocessing, is listed in table 5.5.Table 5.5: The HNL filter and overall filter rate for a set of test events in each of the fourdata taking years (2015-2018).Year HNL 4-filter rate Overall filter rate2015 0.61% 3.04%2016 2.09% 7.00%2017 3.77% 10.95%2018 2.38% 10.49%Table 5.6: Requirements of the four HNL analysis filters. Definitions of the lepton selections(e.g. ID or isolation requirements) used in the filter can be found in the descriptions of thelepton reconstruction algorithms in section 4.1.3 and section 4.1.4.Prompt µ Prompt e Prompt e Prompt µdisplaced µ displaced µ displaced e displaced efilter filter filter filterHLT Single muon Single electron Single muontrigger triggers triggers triggerspT > 28 GeVPrompt |η| < 2.5lepton Muon type Combined - CombinedElectron ID - LHLoose -Isolation∑p(0.3)T /pT < 0.05pT > 5 GeVDisplaced |η| < 2.5lepton Muon type Combined, standalone, -segment-taggedElectron ID - NoneIsolation∑p(0.3)T /pT < 1.0|d0| > 0.1 mm for combined muon > 1 mmwith χ2/dof < 5One unique feature about processing of the ATLAS data is that there is not an equivalentfilter step in the processing of simulated signal events. This can be seen visually in fig. 5.18where the simulated signal events only enter the analysis pipeline at the reconstruction step.As a result, a filter emulator selection is also applied using the same selections listed intable 5.6. However, while the selections used in the filter and filter emulator are the same,the objects, such as muons and electrons, have been re-fit using large radius tracks. As aresult, differences on the order of 3% are observed between data and simulated signal events.835.7. Event SelectionTherefore, a filter uncertainty is assigned to account for this difference in the event selection.More details about this uncertainty can be found in section 5.9.Displaced VertexEvents are required to include a displaced vertex that is reconstructed using the custom lepton-only vertex configuration described in section 5.5.2. The DV is required to have exactly twotracks matched to displaced leptons. The DV is also required to be within a fiducial volume of4 mm < Lxy < 300 mm. The definitions of displaced leptons (e/µ) can be found in section 5.6.Prompt LeptonSelected events are required to have one prompt lepton (either a muon or electron dependingon the channel). The definition of a prompt lepton can be found in section 5.6.Trigger MatchingThe trigger matching selection requires that at least one lepton in the event passes the singlelepton trigger requirements. This lepton is referred to as the “trigger-matched” lepton. About90% of the time, the prompt lepton is the trigger-matched lepton. However, there is alsoa small acceptance to signal events with where the displaced leptons fires the trigger. Thisrecovers some efficiency to events where the prompt lepton has pT below the trigger’s minimumpT thresholds. Thus, the trigger matching selection requires at least one prompt or displacedMedium (LHMedium) muon (electron) is trigger-matched and has pT > 27 GeV.5.7.3 Signal Region SelectionAfter applying the pre-selection requirements in section 5.7.2, additional selections are appliedthat further reduce the number of events in the SR. These selections can be divided up intoselections that are required by the HNL signature and selections that are applied to removesignal-like events from background processes. Selections defined by the HNL signature include:DV ChargeHNLs are neutral particles and will decay to particles whose charges sum to zero. Thus, inthe leptonic decay mode, the two charged tracks will have opposite charge. The DV chargeselection requires that the selected DV has exactly two opposite-sign (OS) tracks.DV TypeLeptons in the displaced vertex can have three different combinations of flavours dependingon the HNL decay channel. These combinations include two muons (µµ), two electrons (ee)845.7. Event Selectionor one muon and one electron (eµ). The DV type selection uses the displaced lepton objectdefinitions in section 5.6 to select DVs with tracks that are matched to the correspondinglepton flavours in each channel.Tri-Lepton MassThe tri-lepton mass (mlll) is the invariant mass of both the prompt lepton from the W bosondecay and the two displaced leptons in the vertex from the HNL decay. The tri-lepton massis reconstructed without the information about the kinematics of the neutrino in the HNLdecay. As a result, this variable underestimates the W boson mass for simulated signal events(see fig. 5.7). Due to the the minimum pT requirement in the trigger selection, the tri-leptonmass distribution starts to fall off around 40 GeV. Thus, the tri-lepton mass selection requires40 < mlll < 90 GeV.HNL MassThe reconstruction of the HNL mass (mHNL) is described in detail in section 5.5.3. The HNLmass selection requires that each event has mHNL < 20 GeV. HNL models that the LHC iscurrently sensitive to with mN > 20 GeV are prompt. Thus, this displaced analysis is notsensitive to models with HNL masses larger than 20 GeVPrompt and Same-Flavour Displaced Lepton ChargeFor HNL decays that conserve lepton number, the prompt lepton and the displaced leptonthat couples to the HNL must have opposite charges (see section 2.4). This analysis can onlyseparate LNC and LNV decays using an explicit charge requirement for the 1SFH model inthe µ−µe and e−eµ channels where the displaced leptons are experimentally distinguishable.In these channels for 1SFH models with only have LNC decays (e.g. in the “Dirac-limit”), anOS charge requirement between these leptons keeps 100% of the signal and removes approxi-mately half of the expected number of background events.In addition to the selections defined by the HNL signature, a series of selections are ap-plied to remove contributions from background processes. These selections include the cosmicmuon, heavy-flavour decay and Z mass vetoes discussed in section 5.8. These selections relyon a few additional variables including the DV mass (mDV), the DV radius (Lxy) and theinvariant mass of the prompt lepton plus one of the displaced leptons (mll). A summary ofthe selections applied in each channel can be found in table 5.7 and a list of all selections canbe found in table 5.8.85Table 5.7: Signal region selections that are applied in each channel.Selection e−ee µ−ee e−eµ µ−µe e−µµ µ−µµPre-selection:prompt µ x x xprompt e x x xDV charge x x x x x xPrompt + disp. l chargex x(single-flavour mixing with LNC decays)DV type:ee x xeµ x xµµ x xTri-lepton mass x x x x x xHNL mass x x x x x xCosmic muon veto x x x x x xMaterial veto x xHeavy-flavour decay veto:mDVcut x xmDV–Lxy cut x x x xZ mass veto x x x xTable 5.8: Description of the selection criteria used to defined the SR. All criteria are furtherexplained within this chapter.Level Selection ValuePre-selection Event cleaning Standard ATLAS event cleaningPrimary vertex At least one with pT > 500 MeVTrigger At least one single muonor electron triggerTrigger-matched lepton At least one Medium (µ)or LHMedium (e) lepton with pT > 27 GeVFilter At least one HNL filterPrompt lepton At least oneTrigger matched lepton At least oneDisplaced lepton-only vertex At least oneNumber of tracks in DV 2Fiducial volume 4 mm < Lxy < 300 mmSR selection DV charge Opposite-sign tracksPrompt + disp. l charge Opposite-sign leptons(For 1SFH models with only LNC decays)DV type ee, eµ or µµ vertexTri-lepton mass 40 GeV < mlll < 90 GeVHNL mass mHNL < 20 GeVCosmic muon veto√(Ση)2 + (pi −∆φ)2 > 0.05Material veto Applied for ee DVs onlyHeavy-flavour decay veto mDV > 5.5 GeV (µµ DVs) ormDV -Lxy cut (ee or eµ DVs)Z mass veto mll < 80 GeV or mll > 100 GeV,for same-flavour opposite-sign leptons865.7. Event Selection5.7.4 Additional RegionsATLAS searches are designed to be blind analyses in order to avoid biases when studying thedata. To perform a blind analysis, the data is analyzed in such a way that the final answeris not known until the complete analysis strategy is designed and approved by members ofthe collaboration. However, this does not mean that the data is never studied in the design ofthe analysis. Instead, additional regions are defined that have negligible contamination fromthe signal events to study the data. The regions in this search for HNLs include events withsame-sign vertices, a validation region and a control region.Same-Sign VerticesThe search for displaced HNLs requires a two-lepton DV to be reconstructed in the ID. Sincethis two-lepton vertex originates from a neutral particle, the signal requires that the chargesof the two leptons in the vertex have opposite signs. Therefore, selecting DVs with two same-sign (SS) leptons will have negligible signal contamination and this selection can be used tostudy contributions from background processes.Control RegionThe control region (CR) is defined using the same analysis selections described in table 5.8,except that the HNL mass selection is inverted to require that 20 < mHNL < 50 GeV. Thisregion is used to study OS and SS DVs in a region close to the SR. The number of observedOS events in the CR is also used to constrain background estimate in the HNL mass fit (seesection 5.10 for more details about the fit). In the region with mHNL > 20 GeV, the signalis not excluded, but its acceptance multiplied by its cross section with the current datasetyields significantly fewer than one signal event. Therefore, there is no signal contamination inthis inverted-HNL-mass CR.Validation RegionThe validation region (VR), also known as the inverted-prompt-lepton VR, is defined byvetoing events that contain a prompt electron or muon. HNL signal events produced from aW boson decay should always have a prompt lepton and thus, this region has a negligiblesignal contribution. The VR has higher statistics than the SR and is used to study backgroundphysics processes that produce OS displaced vertices. This region is also used to select acollection of DVs with two random crossing lepton-matched tracks that are used to estimatethe background (see section 5.8.6 for more details). The list of selections that define thevalidation region can be found in table 5.9.875.8. BackgroundsTable 5.9: Definition of the inverted-prompt-lepton VR. A prompt lepton is defined as anymuon or electron object with Loose or better quality that has |d0| < 3 mm and |z0 sin(θ)| <0.5 mm.Level Selection ValuePre-selection Event cleaning Standard ATLAS event cleaningPrimary vertex At least one with pT > 500 MeVFilter Pass any analysis filterNumber of prompt leptons 0DV selection Displaced lepton-only vertex At least oneCosmic veto√(Ση)2 + (pi −∆φ)2 > 0.05Number of track in vertex 2Fiducial volume 4 < Lxy < 300 mmDV type ee, eµ or µµ vertex5.8 BackgroundsBackgrounds are defined as physics processes that contribute to the selected events in the sig-nal region that are not from the production and decay of an HNL. Five sources of backgroundsare identified that produce two-lepton OS displaced vertices and satisfy the pre-selections de-fined in section 5.7.2. These sources include:1. Vertices from random track crossings (see section 5.8.1)2. Vertices from material interactions (see section 5.8.2)3. Decays from metastable particles, such as b-hadrons (see section 5.8.3)4. Z → ll decays (see section 5.8.4)5. Muons from cosmic-ray interactions (see section 5.8.5)The background estimation technique in this analysis uses a data-driven method to de-termine the contribution in the SR from random track crossings. This method is discussedin detail in section 5.8.6. This assumes that all other sources of backgrounds are negligiblecompared to the random track crossing background or have been removed by dedicated cutsin the event selection. In particular, backgrounds from metastable decays are rejected fromour signal region by DV mass and radius selections. Material interactions are either negligiblefor channels with displaced muons (e.g. eµ or µµ vertices) or rejected by a material veto(e.g ee vertices). Events from Z → ll decays are rejected by a Z mass veto cut and muonsfrom cosmic-ray interactions are rejected using a cosmic muon veto. Section 5.8.6 outlines thestudies that have been performed to validate these assumptions.885.8. Backgrounds5.8.1 Random Track CrossingsRandom track crossings occur when two uncorrelated tracks accidentally cross in the innerdetector sufficiently close to each other that the vertexing algorithm associates them to acommon displaced vertex. While the probability of a two-lepton random track crossing isrelatively low, this source of background is considered to be irreducible, since the DV mass isunconstrained.One way to estimate this background is to use the number of random crossings with twoSS tracks as an estimate for the number of random crossings with two OS tracks. This methodassumes that the probability for two tracks to form a random crossing vertex is independentof the charge of the two tracks. Hence it is equally likely that random crossings will form aSS or OS vertex and thus, the OS random crossing background can be estimated using SSdisplaced vertices. Validation of this charge assumption is described in section 5.8.6. Similartechniques are used to estimate accidental crossings of tracks in other ATLAS searches, suchas a super-symmetry search [81] and the 2019 ATLAS displaced HNL search [70]. However,this SS background estimation method is statistically limited and, as a result, it is not usedas the final background estimate in this analysis. Nonetheless, this method is used to studythe backgrounds and validate assumptions and event selections in the analysis.Instead of using the SS estimate, backgrounds from random crossings are estimated usinga novel data-driven approach that mixes prompt leptons and displaced vertices from differentevents. This method assumes that the prompt lepton is unrelated to the random crossingDV. Thus, events created from all possible pairs of prompt leptons and DVs can be used toincrease the statistics of the background estimate. This assumption has been validated usingthe prompt lepton shuffling technique and SS background estimate. For more details, see thevalidation studies in section 5.8.6.A full description of the data-driven estimate for random track crossings using the promptlepton shuffling method and the corresponding background uncertainties is found in sec-tion 5.8.6. The predicted number of background events in the signal and control regions fromrandom track crossings are listed in table 5.13.5.8.2 Material InteractionsInteractions with the inner detector material (both active layers and the support structures)can produce two-lepton vertices at some distance from the interaction point. This createsa source of displaced lepton vertices that is unrelated to the decay of an HNL. Materialinteractions are removed from the SR using DV mass cuts and a dedicated material map vetofor channels with displaced ee vertices.Many of the material interactions that produce ee displaced vertices have a reconstructeddisplaced vertex mass of mDV < 2 GeV. This can be seen in fig. 5.19 (c), which shows DV mass895.8. Backgroundsas a function of the DV radius for OS ee displaced vertices in the statistically enhanced VR(see section 5.7.4 for a description of the VR). Large clusters of events near the material layers(dashed grey lines) can be removed by requiring that the mDV is at least 2 GeV. Figure 5.19(b) and (c) shows that material effects for channels with displaced muons are not dominant.0 50 100 150 200 250 300 [mm]xyL012345678910 [GeV]DVm110210310Number of Opposite-Sign DVsMaterial LayersATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Regionee DVs(a) ee DVs0 50 100 150 200 250 300 [mm]xyL012345678910 [GeV]DVm110210310Number of Opposite-Sign DVsMaterial LayersATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Region DVsµµ(b) µµ DVs0 50 100 150 200 250 300 [mm]xyL012345678910 [GeV]DVm110210310Number of Opposite-Sign DVsMaterial LayersATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Region DVsµe(c) eµ DVsFigure 5.19: OS displaced vertices in the VR shown in bins of mDV versus Lxy. All verticesare required to pass the VR selections. Leptons in the selected DVs are also required to passVeryVeryLoose electron and Medium muon identification working points.However, it is also possible that material interactions can produce DVs with mDV > 2 GeV,which makes it difficult to distinguish between these material interactions and HNL signaldecays, even with the other vertex selections applied. Therefore, a material veto uses twothree-dimensional maps of the ID material to reject vertices that decay within the materiallayers. The first map, which extends in radius to Lxy < 150 mm, is constructed from low-mass vertices in the data (with selections to remove low-mass SM resonances) [82]. The secondmap, which extends in radius from 150 mm < Lxy < 300 mm, is reconstructed using verticesin simulation to create a more complete map than statistics will allow in data [82]. Bothmaps extend out to |z| = 300 mm and so the material veto also requires that the DV has905.8. Backgrounds|z| < 300 mm. The impact of the material veto for ee OS vertices in the VR is shown infig. 5.20 (a).0 50 100 150 200 250 300 [mm]xyL1−10110210310410510Vertices / 5 mm All, 33242 Pass material veto, 17953 Pass material and B-hadron veto, 190 Material LayersATLAS Internal = 13 TeVsValdiation RegionOS ee20 40 60 80 100 12) [GeVlllTri-lepton mass (m3−2−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m1−10110Vertices / 4 GeV Data-driven SS bkg, 6.0 Data-driven shuffled bkg, 6.0 DV systematic, 6.0 Prompt lepton systematic, 6.0 Data, 4.0 ATLAS Work in Progress= 13 TeVsChannel: e-eelid ti i(a) ee DVs0 50 100 150 200 250 300 [mm]xyL1−10110210310410510610Vertices / 5 mmAll, 59767 Pass B-hadron veto, 125 Material LayersATLAS Internal = 13 TeVsValdiation RegionµµOS 20 40 60 80 100 12) [GeV]lllTri-lepton mass (m32−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Wo k in Progress eµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m1−10110Vertices / 4 GeV Data-driven SS bkg, 6.0 Data-driven shuffled bkg, 6.0 DV systematic, 6.0 Prompt lepton systematic, 6.0 Data, 4.0 ATLAS Work in Progress= 13 TeVsChannel: -eeid(b) µµ DVs0 50 100 150 200 250 300 [mm]xyL1−10110210310410510Vertices / 5 mmAll, 34224 Pass B-hadron veto, 243 Material LayersATLAS Internal = 13 TeVsValdiation RegionµOS e20 40 60 80 100 12) [GeVlllTri-lepton mass (m32−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV syst matic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL (20 40 60 80 100 120) [GeV]lllTri-lepton mass (m1−10110Vertices / 4 GeV Data-driven SS bkg, 6.0 Data-driven shuffled bkg, 6.0 DV systematic, 6.0 Prompt lepton systematic, 6.0 Data, 4.0 ATLAS Work in Progress= 13 TeVsChannel: e-eelid i i(c) eµ DVsFigure 5.20: OS displaced vertices from data events using the VR selections as a function ofLxy. Displaced vertices are separated by flavour into three channels: ee, eµ and µµ. Distribu-tions labeled “All” (solid circles) have no additional selections applied. The distribution withopen circles in the ee channel has only the material veto applied and distributions with opensquares have the heavy-flavour decay veto applied.Peaks in the background for ee vertices can be seen, which correspond to regions thatare more material-dense. After applying the material veto, many of the material interactionsthat peak at the detector layers are gone. Due to imperfect detector modelling, the materialmap does not remove all the material interactions. However, the SR selections also includemDV cuts designed to remove vertices from metastable particle decays (see the heavy-flavourdecay veto in section 5.8.3). After applying the full analysis selections (including the heavy-flavour decay veto) the background from material interactions is considered to be negligible.Any uncertainty in this assumption is taken into account by a background DV systematicuncertainty that is derived for the nominal background estimate accounting for differences915.8. Backgroundsbetween SS and OS vertices (see section 5.8.6 for more details).Applying the material veto also removes any signal decays near material layers. Thisresults in roughly a 30 − 40% loss in signal efficiency. In fig. 5.20 (b) and (c) large peaksare not observed near the material layers in the VR for µµ and eµ displaced vertices and,therefore, the material veto is not applied for channels with at least one displaced muon.5.8.3 Metastable Particle DecaysSM particles produced in proton-proton collisions at the LHC with lifetimes near the displacedHNL signal region, and potentially result in two-lepton vertices with a DV radius between 4and 300 mm, are charm, bottom and strange hadrons, as well as the tau lepton.• Hadrons with b quarks, also called b-hadrons, can have decay lengths of a few mm whenthey are highly boosted and/or in the tail in the exponential decay distribution. Theseparticles have masses of the order of 5 to 6 GeV, thus encroaching on the signal region.Double-semi-leptonic decays b→ c+W (→ l + ν) followed by c→ d+W (→ l + ν) canalso produce contributions to all three DV types (eµ, µµ and ee).• J/Ψ mesons have masses of 3.1 GeV and can decay to pairs of same-flavour OS leptons(µ+µ− or e+e−). These decays can be displaced if the J/Ψs are produced by otherheavy-flavour particles. These would mostly come from b-hadron decays in order to bedisplaced enough to contaminate the signal region. They are separated here from otherb-hadron decays because their DV mass would be narrowly peaked at the J/Ψ mass.• Strange baryons and the tau lepton have lifetimes near the signal region, however theyhave smaller masses, between 1 and 2 GeV. Moreover, strange baryons almost alwaysdecay into hadrons, thus almost never produce vertices containing leptons. As such, theydo not contribute to the background in this search.• The Υ meson is another relatively massive (9.5 GeV) particle, which can decay into alepton pair. Its production cross section is small and its lifetime is very short. Since theΥ meson is not produced in b-hadron decays, one would not expect it to give rise todisplaced vertices.Contributions from metastable decays are studied in the VR and separated according to theDV type (µµ, eµ or ee). In particular, when looking at the DV mass distribution of theselected events in fig. 5.21, a heavy-flavour continuum spectrum is observed that falls offaround 5.5 GeV and a narrow contribution from J/Ψ events is observed in the same flavourchannels (ee and µµ). The background estimation method described in section 5.8.6 assumesthat only random crossings contribute to backgrounds in the SR. Therefore, analysis selectionsare designed to remove additional OS contributions from metastable decays from the SR.925.8. Backgrounds0 2 4 6 8 10 12 14 16 18 20DV mass [GeV]0.511.522.533.5610×Vertices / 0.25 GeV0 2 4 6 8 10 12 14 16 18 20DV mass [GeV]110210310410510610Vertices / 0.25 GeV0 2 4 6 8 0 2 4 6 2DV mass [GeV]2−024ratioOS ee 17953SS ee 1058ATLAS Internal-1 = 13 TeV, 139.0 fbsValidation Region2 40 60 80 100 120) [G ]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((a) ee DVs0 2 4 6 8 10 12 14 16 18 20DV mass [GeV]0.020.040.060.080.10.120.140.160.180.20.22910×Vertices / 0.25 GeV0 2 4 6 8 10 12 14 16 18 20DV mass [GeV]11210310410510610710810Vertices / 0.25 GeV0 2 4 6 8 0 2 4 6 2DV mass [GeV]2−024ratio 59767µµOS 687512µµSS ATLAS Internal-1 = 13 TeV, 139.0 fbsValidation Region2 40 60 80 100 1) [G ]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Wo k in Progress eµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((b) µµ DVs0 2 4 6 8 10 12 14 16 18 20DV mass [GeV]0.20.40.60.81610×Vertices / 0.25 GeV0 2 4 6 8 10 12 14 16 18 20DV mass [GeV]110210310410510610Vertices / 0.25 GeV0 2 4 6 8 0 2 4 6 2DV mass [GeV]2−024ratio 34224µOS e 1850µSS eATLAS Internal-1 = 13 TeV, 139.0 fbsValidation Region2 40 60 80 100 120) [Ge ]lllTri-lepton mass (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, Data-driven bkg., 43.5, 10 GeV, 10mm), 126.1µµ-µHNL ((c) eµ DVsFigure 5.21: OS and SS displaced vertices in the Validation Region as a function of the DVmass. Leptons in the DVs are required to pass the Medium (VeryVeryLoose) quality workingpoints for muons (electrons). The material map veto is also applied for the ee channel. Theratio of OS to SS vertices is shown in the bottom ratio plot.The correlation between mDV and Lxy in fig. 5.19 shows that OS DVs from metastable de-cays typically occur at smaller radii. Based on the distributions in fig. 5.19, an mDV > 5.5 GeVselection would reject the metastable decays. However, this completely removes sensitivity toHNL decays with mDV < 5.5 GeV and significantly impacts the sensitivity to models with5.5 GeV < mN < 10 GeV.12 Instead, a selection that removes events with DVs that havesmall mDV and Lxy would remove metastable decays while maintaining some sensitivity tolong-lived HNL signals with mN < 5.5 GeV.To exploit the correlation between mDV and Lxy in the background, a diagonal cut in themDV–Lxy plane is optimized using the difference between OS and SS vertices as a measure of12The displaced vertex mass is reconstructed from the two charged leptons from the HNL decay (i.e. the neu-trino is not reconstructed) and, thus, the displaced vertex mass in signal always underestimates the simulatedHNL mass (see fig. 5.9).935.8. Backgroundshow different the two distributions are. Based on the properties of random crossings, if thereis good agreement between SS and OS vertices, then this implies that only random crossingsremain. Therefore, regions of phase space where there is a large difference between OS and SSvertices have contributions from non-random processes, while regions with small differencesare dominated by random track crossings. The result of the optimization study is shown infig. 5.22.0 50 100 150 200 250 300 [mm]DVr012345678910 [GeV]DVm051015202530Opposite-sign minus same-sign DVsHeavy-Flavor DecayBackground VetoATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Region DVsµµ(a) µµ DVs0 50 100 150 200 250 300 [mm]DVr012345678910 [GeV]DVm051015202530Opposite-sign minus same-sign DVsHeavy-Flavor DecayBackground VetoATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Region DVsµe(b) eµ DVs0 50 100 150 200 250 300 [mm]DVr012345678910 [GeV]DVm051015202530Opposite-sign minus same-sign DVsHeavy-Flavor DecayBackground VetoATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Regionee DVs(c) ee DVsFigure 5.22: Correlation plot of DV mass (mDV) versus radius (Lxy = rDV) for the differencebetween OS and SS vertices in the three DV type channels. The data events studied in theseplots are selected from events in the VR. The heavy-flavour decay veto applied in each channelis shown by the solid red line. The z-axis maximum in the plots is saturated at 30 in order toprovide a colour scale that can distinguish regions with small negative entries (more SS thanOS DVs) from those with small positive entries (more OS than SS DVs).In the eµ channel, a diagonal cut with mDV > 7 GeV(1 − Lxy150 mm) for vertices with mDVbetween 2 and 5.5 GeV (red line in fig. 5.22 (b)) is sufficient to remove the OS events in thesmall mDV/Lxy region. Below 2 GeV, there is still an excess of OS events at large radii andabove 5.5 GeV, b-hadron decays are not expected to contribute. This same diagonal cut is also945.8. Backgroundssufficient to remove contributions from metastable decays in the ee channel. However, in theµµ channel (fig. 5.22 (a)), the diagonal cut fails to remove contributions from resonant J/Ψdecays. Changing the slope of the diagonal cut further reduces the additional phase space thatis gained by including this cut. The signal efficiency increase for channels with µµ DVs usinga modified diagonal cut was not sufficient to significantly increase the analysis sensitivity toµµ decays. Therefore, the channels with µµ DVs have a flat mDV > 5.5 GeV selection applied.After applying the heavy-flavour decay veto, DVs from data events in the validation regionare compared to check the agreement between the SS and OS distributions. Good agreementbetween OS and SS DVs (a ratio of 1) in fig. 5.23, indicates that random track crossingsdominate. With the heavy-flavour decay veto applied, the background from metastable decaysis considered to be negligible. Any uncertainty in this assumption is taken into account by theDV background systematic described in section 5.8.6. A summary of the heavy-flavour decayveto applied in the SR can be found in table 5.10.0 10 20 30 40 50 60 70 80 90 100 [GeV]DVm2040Events / 4 GeV0 10 20 30 40 50 60 70 80 90 100 [GeV]DVm2040Events / 4 GeV0 10 20 30 40 50 60 70 80 90 100 [GeDVm2−024OS/SSOpposite-sign (OS)Same-sign (SS)ATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Region DVsµµ(a) µµ DVs0 10 20 30 40 50 60 70 80 90 100 [GeV]DVm2040Events / 4 GeV0 10 20 30 40 50 60 70 80 90 100 [GeV]DVm2040Events / 4 GeV0 10 20 30 40 50 60 70 80 90 100 [GeDVm2−024OS/SSOpposite-sign (OS)Same-sign (SS)ATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Region DVsµe(b) eµ DVs0 10 20 30 40 50 60 70 80 90 100 [GeV]DVm10203040Events / 4 GeV0 10 20 30 40 50 60 70 80 90 100 [GeV]DVm10203040Events / 4 GeV0 10 20 30 40 50 60 70 80 90 100 [GeDVm2−024OS/SSOpposite-sign (OS)Same-sign (SS)ATLAS Work in Progress-1 = 13 TeV, 139 fbsValidation Regionee DVs(c) ee DVsFigure 5.23: OS and SS displaced vertices with the heavy-flavour decay veto applied for dataevents in the VR. The material veto is also applied for displaced ee vertices.955.8. BackgroundsTable 5.10: Description of the heavy-flavour decay veto.DV type Selectionµµ mDV > 5.5 GeVee or eµ mDV >5.5 GeV, if Lxy ≤ 225/7 mm7 GeV(1− Lxy150 mm), if 225/7 mm < Lxy < 750/7 mm2 GeV, if Lxy ≥ 750/7 mm5.8.4 Leptonic Z Boson DecaysLeptonic decays of Z bosons contribute to the background if one of the leptons from the decayis identified as the prompt lepton and the other lepton forms a vertex with a third lepton.This third lepton could be from a random crossing or an asymmetric photon conversionwhere only one of the leptons is reconstructed. The random crossing background estimate,described in section 5.8.6, assumes that the prompt lepton is unrelated to the leptons in thedisplaced vertex. This assumption is not true for Z decays where the prompt lepton and oneof the leptons in the vertex are produced by a Z boson decay and, therefore, these events areremoved from the signal region with a dedicated Z mass veto. The Z decay background isonly present in channels where the prompt lepton and at least one of the displaced leptonshave the same flavour (i.e. µ−µµ, e−ee, µ−µe and e−eµ). The Z mass veto is not applied tochannels where the prompt and displaced leptons have different flavours (i.e µ−ee and e−µµ).To study this background, Z → ll events are selected in data using the pre-selectionrequirements and the heavy-flavour decay veto (described in section 5.8.3). Selected eventsmust have a two-lepton SS vertex. The prompt and same-flavour lepton in the displaced vertexmust also have opposite charges. Events that do not meet the last charge requirement cannotbe produced in a neutral Z boson decay. The mass between this pair of leptons (mll) in theselected data events is shown in fig. 5.24. Z decays are identified as events with mll near theZ boson mass of 91 GeV. For channels with indistinguishable displaced leptons (e.g. µ−µµand e−ee), the displaced lepton with the highest pT is paired with the prompt lepton toreconstruct the di-lepton mass, mll. It is assumed that the displaced lepton with the highestpT is more likely to come from the Z decay. This assumption was validated using data eventsto show that the highest pT displaced lepton usually comes from the Z decay.The Z mass veto selection is summarized in table 5.11. Events from Z decays are removedusing a mll cut in a window around the Z mass. This selection has a negligible impact on oursignal acceptance because, in signal, the same-flavour lepton pair originated from a W bosondecay and typically has a di-lepton less than 80 GeV.965.8. Backgrounds0 20 40 60 80 100 120 140 160 180 200Mass of prompt + disp. Muon (OS) [GeV]1234567Vertices / 4 GeVSS bkg, 19.0 Z massATLAS Internal = 13 TeVsVSI_LeptonsModµµµv5 EXOT29, 20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−10−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µ-µChannel: 20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, µµ-µChannel: 2 40 60 80 100 1) [ ]llMass of prompt + ame-flavour i . lepton (m3−102−101−10Vertices / 4 GeV Data-driven S bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 r i rogress -l: (a) µ−µµ0 20 40 60 80 100 120 140 160 180 200Mass of prompt + disp. Electron (OS) [GeV]2468101214Vertices / 4 GeVSS bkg, 49.0 Z massATLAS Internal = 13 TeVsVSI_LeptonsModµv5 EXOT29, ee20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, µµ-µChannel: 100 120) [ ]llMass f rompt + same-flavour disp. l pton (3−12−11−12Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 kg DV systematic, 2.5 kg plep systematic, 2.5 ata, 10.0 TL S ork in rogress = 13 TeVs-, -l: 20 40 60 80 100 120) [GeV]llMass of prompt + same-flavour disp. lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8,µChannel: -e(b) e−eµ0 20 40 60 80 100 120 140 160 180 200Mass of prompt + disp. Muon (OS) [GeV]246810121416Vertices / 4 GeVSS bkg, 67.0 Z massATLAS Internal = 13 TeVsVSI_LeptonsModeµµv5 EXOT29, 20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Wo k in Progress eµ-µv8, µµ-µChannel: 20 6 80 0 12) [GeV]llMass of prompt + same-flavour disp. lepton (3−102−11−12Vertices / 4 GeV ata-driven SS bkg, 4.0 ata-driven shuffled bkg, 2.5 kg DV systematic, 2.5 kg plep systematic, 2.5 ata, 10.0 TL S i r r = 13 TeVs, 20 40 60 80 100 120) [GeV]llMass of prompt + same-flavour disp. lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8,eµ-µChannel: (c) µ−µe0 20 40 60 80 100 120 140 160 180 200Mass of prompt + disp. Electron (OS) [GeV]1020304050Vertices / 4 GeVSS bkg, 100.0 Z massATLAS Internal = 13 TeVsVSI_LeptonsModv5 EXOT29, eee20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Wo k in Progress eµ-µv8, µµ-µChannel: 100 120) [GeV]llMass f rompt + same-flavour disp. l pton (3−12−11−12Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 kg DV systematic, 2.5 kg plep systematic, 2.5 ata, 10.0 TL ork in rogress = 13 Tes-, -l: 20 40 60 80 100 120) [GeV]llMass of prompt + same-flavour disp. lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 ATLAS Work in Progress = 13 TeVseµ-µv8, Channel: -ee(d) e−eeFigure 5.24: The invariant mass between the prompt lepton and same-flavour displaced lepton(mll) for selected VR data events in the Z mass veto study. Events around the Z mass with80 GeV < mll < 100 GeV are identified as Z decays and are removed from the SR.Table 5.11: Description of the Z mass veto.Channel Selectionµ−µµµ−µe mll < 80 GeV ormll > 100 GeVe−eµ if prompt and same-flavour leptons have opposite charges.e−eee−µµNo veto applied.µ−ee5.8.5 Muons from Cosmic-Ray InteractionsMuons from cosmic-ray interactions in the atmosphere can penetrate through the earth andinteract with the ATLAS detectors. When cosmic muons enter the magnetic field in the ID,they bend in the φ direction. If a vertex is reconstructed from two segments of a muon thattraverses the detector from the top down, then it can be reconstructed as an opposite-sign975.8. Backgroundsvertex. These cosmic ray muon interactions can occur at any distance from the interactionpoint and therefore produce a background source of OS displaced vertices. However, sincethese two tracks come from the same energetic muon, they should be almost perfectly back-to-back in η− φ space. This means that ∆φ− pi and ∑ η of the two tracks should be close tozero.A minimum separation between the tracks in the displaced vertex is required to removeback-to-back muons from cosmic ray interactions. The cosmic veto stipulates that the twoleptons within the displaced vertex have a separation,√(Ση)2 + (pi −∆φ)2 > 0.05. Thisselection is based on a study of cosmic-ray muon interactions that was performed in thecontext of another ATLAS displaced vertex search [83]. A similar selection was also used inthe 2019 ATLAS displaced HNL search that analyzed pp data from 2016 [70]. This selectionis 100% efficient in signal and is therefore applied to all channels.5.8.6 Data-Driven Estimate of Random Track Crossings Using a PromptLepton Shuffling MethodThe main drawback of the data-driven SS background estimate for random crossings (de-scribed in section 5.8.1) is that it is statistically limited. The probability of two leptonsaccidentally crossing and forming a displaced vertex is very small and, in addition to thevertex being reconstructed, the random crossing DV also needs to be paired with a “goodquality” prompt lepton that passes all the pre-selection requirements. Given that the signaldistribution for the HNL mass (see section 5.5.3) peaks at the simulated mass, it would beideal to have a background estimate with a smooth distribution as a function of this vari-able to provide a strong discriminant between signal and background. To do this requires anincrease in the statistics of the random track crossing background estimation method.The data-driven SS background estimate provides one prompt lepton for every two-leptonSS vertex. However, if we assume that the prompt lepton is unrelated to the DV, then wecan pair each two-lepton vertex with a prompt lepton from a different event and re-calculatethe HNL and tri-lepton masses. The validation of the assumption that the prompt lepton isunrelated to the random crossing DV is described in section 5.8.6. Once it is established thatthe pairing of the prompt lepton and displaced vertex is random, pairing leptons with verticesfrom different events can be used to form a larger collection of events to increase the statisticsof the background estimate.The increase in statistics achieved with this method is limited by the number of selectedprompt leptons and the number of selected random crossing DVs. To address the first limita-tion, a “loose” collection of prompt leptons is selected from data events using the pre-selectionrequirements and the presence of a SS DV with the same DV type (i.e. µµ, eµ, ee) that hasno lepton identification or DV mass requirements. The prompt leptons selected using this985.8. Backgroundsmethod were found to have similar kinematics (e.g. pT, η, φ) to prompt leptons in the SR andthus, this selection does not bias the shuffling estimate. The second limitation is addressedby selecting random crossing DVs from data events in the VR. Events in this region do notcontain prompt leptons and therefore have a statistically enhanced number of random crossingDVs from real data events.The nominal background estimate shuffles OS vertices selected in the VR with the “loose”collection of prompt leptons. Combining each OS DV with each lepton, the shuffled lepton(SL) sample has at least 2000 times the number of events in the original event sample for eachchannel, resulting in a high-statistics background model. The SL sample is initially normalizedto the number of events from the SS background estimate, such that:NBSR = NSLSR ×NSSSR +NSSCRNSLSR +NSLCR(5.40)NBCR = NSLCR ×NSSSR +NSSCRNSLSR +NSLCR(5.41)where NBSR (NBCR) is the background prediction in the signal (control) region, NSSSR (NSSCR)is the number of same-sign DV events in the signal (control) region and NSLSR (NSLCR) is thenumber of shuffled lepton events in the signal (control) region. In the statistical fit describedin section 5.10, this normalization is unconstrained, so this choice simply provides an initialstarting point for background estimate. Distributions of the shuffled background estimate areshown in fig. 5.25 as a function of the HNL mass. The SR selection applied in these plots islisted in section 5.7.3, except that the mHNL < 50 GeV. In this way, the signal and controlregions can be studied together.Uncertainties in the Background EstimateTwo sources of systematic uncertainties are identified in the prompt lepton shuffling back-ground estimation method. The dominant uncertainty comes from the assumption that theselected DVs used in the shuffling method are from random track crossings. If the selected DVsare not from random crossings, then this provides a source of bias in the estimate. Randomtrack crossings should have uncorrelated tracks and the distributions from random crossingevents should be independent of track charge. Therefore, the difference between SS and OSdistributions can be used as a measure of the uncertainty on the background prediction. SSvertices from the VR are also selected and shuffled with the “loose” collection of promptleptons to produce the DV systematic distributions shown in fig. 5.25.The difference between the nominal and DV systematic distributions is used as a shapeuncertainty on the background estimate. The better the shape agreement is between the two995.8. Backgroundsdistributions, the smaller the systematic uncertainty is. The shape agreement is the worst inchannels with µµ DVs and is limited by the number of DVs in the VR. This results in thelargest DV systematic uncertainty in the µ−µµ and e−µµ channels.0 10 20 30 40 50 [GeV]HNLm3−102−101−10110210Events / 2.5 GeVSR CRBackgroundDV systematicPrompt lepton systematicSS DataOS DataATLAS Work in Progress-1 = 13 TeV, 139 fbse-ee(a) e−ee0 10 20 30 40 50 [GeV]HNLm3−102−101−10110Events / 2.5 GeVSR CRBackgroundDV systematicPrompt lepton systematicSS DataOS DataATLAS Work in Progress-1 = 13 TeV, 139 fbs-eeµ(b) µ−ee0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CRBackgroundDV systematicPrompt lepton systematicSS DataOS DataATLAS Work in Progress-1 = 13 TeV, 139 fbsµe-e(c) e−eµ0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CRBackgroundDV systematicPrompt lepton systematicSS DataOS DataATLAS Work in Progress-1 = 13 TeV, 139 fbseµ-µ(d) µ−µe0 10 20 30 40 50 [GeV]HNLm2−101−10110Events / 2.5 GeVSR CRBackgroundDV systematicPrompt lepton systematicSS DataOS DataATLAS Work in Progress-1 = 13 TeV, 139 fbsµµe-(e) e−µµ0 10 20 30 40 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CRBackgroundDV systematicPrompt lepton systematicSS DataOS DataATLAS Work in Progress-1 = 13 TeV, 139 fbsµµ-µ(f) µ−µµFigure 5.25: The HNL mass (mHNL) shapes for the background estimate (shaded purple), DVsystematic (solid blue line), prompt lepton systematic (dashed blue line), observed SS events(grey triangles) and observed OS events (black circles) for the six different channels.1005.8. BackgroundsThe second source of systematic uncertainty is due to the finite number of prompt lep-tons used in the shuffling method. A prompt lepton uncertainty is derived using a differentcollection of prompt leptons and comparing the shapes between the nominal and systematicdistributions. In the nominal method, a “loose” collection of prompt leptons is selected usingevents with a SS DV of the same DV type (e.g. in the µ−µµ background estimate, eventswith SS µµ vertices are used to select prompt muons). To account for differences in the HNLmass shape due to the finite number of prompt leptons, the OS vertices are also shuffled withprompt leptons from SS events with a different DV type (e.g. in the µ−µµ prompt leptonsystematic, events with SS eµ vertices are used to select prompt muons). The prompt leptonsystematic distributions are also shown fig. 5.25 and are also used as a shape uncertainty onthe background estimate.The impact of the background systematics in the SR are summarized in table 5.12. For eachchannel, the difference between the nominal and systematic uncertainty predictions dividedby the nominal prediction is shown for the DV and prompt lepton uncertainties.Table 5.12: The relative systematic uncertainties on the background estimate, estimated bycreating shuffled events from SS DVs or from prompt leptons taken from events with differentDV channels. The total uncertainty is the quadrature sum of the two contributions. Theuncertainties are treated as uncorrelated among the different channels.ChannelRelative Uncertainty (%)DV Prompt l Totale−ee 35 <1 35µ−ee 27 <1 27e−eµ 2 1 2µ−µe 5 5 7e−µµ 70 2 70µ−µµ 79 3 79Background PredictionsThe nominal background and systematic uncertainty distributions are shown for mHNL infig. 5.25. For reference, the observed SS and OS data events are also shown in these plots.The shuffled background estimate is fairly smooth as a function of the HNL and tri-leptonmass. Assuming that the random crossing events do not have a particular shape in the mHNLdistribution, other than those introduced by the kinematic cuts, the upper tails of the recon-structed mass distribution are used to validate that the background modeling matches whatis observed in data. The CR defined in section 5.7.4, with mHNL between 20 and 50 GeV,is used to provide additional constraints on the background prediction. This region was alsoused to validate the background estimation method by comparing OS and SS events prior to1015.8. Backgroundslooking at the OS events in the SR.The background predictions prior to the fit, as well as the observed number of SS andOS events, are shown in table 5.13. The shuffled background predictions are listed with thecombined statistical and systematic uncertainty, while the observed number of backgroundevents (SS and OS) are shown with statistical uncertainties only.Table 5.13: Estimated background predictions with statistical and systematic uncertainties inthe signal region and the control region. The observed yields are shown for OS DVs and SSDVs.ChannelSignal region Control regionBackground Observed yield Background Observed yieldPrediction SS OS Prediction SS OSe−ee 0.6 ± 0.2 1 2 5.4 ± 0.2 5 2µ−ee 0.3 ± 0.1 0 1 3.7 ± 0.1 4 1e−eµ 2.3 ± 0.1 0 0 10.7 ± 0.1 13 5µ−µe 0.9 ± 0.1 0 2 4.1 ± 0.1 5 13e−µµ 1.5 ± 1.1 1 1 2.5 ± 1.1 3 3µ−µµ 2.4 ± 1.4 0 2 3.6 ± 1.8 6 9Background Estimate ValidationBoth the SS and shuffled lepton background estimate assumes that the background events inthe SR are dominated by random track crossings combined with the association of a promptlepton. The shuffled lepton estimate also assumes that the association of a prompt lepton to ashuffled vertex is random. In the SS estimate, the displaced vertex is already associated witha prompt lepton in the same event and no assumptions need to be made. This section willdiscuss the studies performed to validate these assumptions.Assumption 1: there is no dependence on track charge in the creation of random crossingvertices.• Under the assumption that only random crossings survive after applying the heavy-flavour decay veto (and material veto for ee DVs), SS events in the VR should not haveany charge asymmetry between ++ and −− DVs. In fig. 5.26, no significant asymmetryis observed between ++ and −− DVs in the eµ and ee channels. Although the availablestatistics in the µµ channel is limited, there is no physics motivated reason why µµvertices should behave differently compared to the other two channels.• A custom track algorithm, described in appendix A, is used to randomly shuffle tracks1025.8. Backgroundsfrom different events and produce displaced vertices. This algorithm randomly pairsleptons from different events to create a set of fake events. Thus, vertices reconstructedusing this method form a pure sample of random track crossings. The track shufflingstudies in appendix A (in particular fig. A.4) demonstrate that SS and OS distributionsmatch at better than 20%, including key kinematic variables.• Conclusion: random track crossings are independent of track charge. If the backgroundin our signal region consists only of random crossings, then SS distribution is a goodestimate of the OS background.0 20 40 60 80 100 120DV mass [GeV]0.511.522.5310×Vertices / 5 GeV0 20 40 60 80 100 120DV mass [GeV]110210310Vertices / 5 GeV0 20 40 60 0 1 0 1 0DV mass [GeV]2−02ratio 34µµSS ++ 28µµSS -- ATLAS Internal = 13 TeVsValidation Region20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, µµ-µChannel: (a) µµ DVs0 20 40 60 80 100 120DV mass [GeV]123456789310×Vertices / 5 GeV0 20 40 60 80 100 120DV mass [GeV]110210310Vertices / 5 GeV0 20 40 60 0 1 0 1 0DV mass [GeV]2−02ratio 202µSS ++ e 170µSS -- eATLAS Internal = 13 TeVsValidation Region20 40 60 80 100 120) [ eV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress 13 eseµ-µv8, µµ-µChannel: (b) eµ DVs0 20 40 60 80 100 120DV mass [GeV]24681012310×Vertices / 5 GeV0 20 40 60 80 100 120DV mass [GeV]110210310410Vertices / 5 GeV0 20 40 60 0 1 0 1 0DV mass [GeV]2−02ratioSS ++ ee 286SS -- ee 231ATLAS Internal = 13 TeVsValidation Region20 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffl d bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress seµ-µv8, µµ-µChannel: (c) ee DVsFigure 5.26: SS displaced vertices in the VR with the heavy-flavour decay veto applied. Thematerial veto for ee DVs is also applied. SS DVs are separated by track charge into verticeswith two positively charged tracks (SS ++) and two negatively charged tracks (SS −−). Thisstudy does not include the ∆pT/pT cut for displaced electrons described in section 5.6.Assumption 2: backgrounds are dominated by random crossings, except in the low mDVregion (below 5.5 GeV) where heavy-flavour decays dominate.• Using the fact that random crossings are independent of track charge, good agree-ment between SS and OS distributions indicates that only random crossings remain. In1035.8. Backgroundsfig. 5.21, no significant differences between SS and OS distributions are observed abovemDV ∼ 5.5 GeV. Below 5.5 GeV, heavy-flavour decays dominate, leading to an excess ofOS displaced vertices. After applying the heavy-flavour decay veto described in fig. 5.23,good agreement is obtained (within the available statistics).• The number of SS and OS events are also compared in the CR (see table 5.13) and nosignificant difference between the two types of events is observed.• An inverted tri-lepton mass validation region is used to study data event in the tailsof the mlll distribution (i.e. mlll < 40 or mlll > 90 GeV). This region has a signalto background ratio of less than 5%, which makes it possible to study the data eventswithout significant signal contamination. Although this region has low statistics due tothe limited number of events that are selected by the filter discussed in section 5.7, nosignificant differences are observed between SS and OS DVs.• Conclusion: OS and SS distributions show good agreement in the VR and CR, whichimplies that the background is dominated by random crossings. The DV systematic,described in section 5.8.6, takes into account any uncertainties from this assumption.Assumption 3: the pairing of a prompt lepton with a displaced vertex from accidental trackcrossings is random.• The shuffling background method relies on artificially creating fake shuffled events andrandomly pairing a shuffled displaced vertex with a prompt lepton. Using this method,SS vertices are shuffled with prompt leptons and the shape of the resulting distributionis compared to the shape of the SS background estimate. This comparison is performedin a looser signal region that does not have the heavy-flavour decay veto applied in orderto increase the statistics in the shape comparison. Events are selected using a minimum2 GeV DV mass cut and the pre-selection requirements. The results are shown for themHNL and mlll variables in fig. 5.27 and fig. 5.28 respectively. The shuffling factor, f ,which is defined as the ratio of the number of shuffled events to number of SS backgroundevents, is also included in the plots.• A Kolmogorov-Smirnov (KS) goodness-of-fit test [84] is performed to quantify the shapeagreement between the two distributions. Table 5.14 shows the resulting KS probabil-ities. Two distributions are considered incompatible if the KS probability is much lessthan one. The results of the KS test indicate that the shuffled and SS backgroundestimate have compatible mHNL and mlll shapes.• Conclusion: good shape agreement between the shuffled and SS background estimatesindicates that the pairing of a prompt lepton with an accidental crossing two leptondisplaced vertex is random.1040 10 20 30 40 50HNL mass [GeV]1−10110210310Vertices / 2 GeV0 10 20 30 40 50HNL mass [GeV]012ratiorandom plep 57orig. plep 57ATLAS Internal = 13 TeVsVSI_LeptonsModµµ-µchannel: shuffling factor f=5720 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, -µChannel: (a) µ−µµ0 10 20 30 40 50HNL mass [GeV]1−10110210310410Vertices / 2 GeV0 10 20 30 40 50HNL mass [GeV]012ratiorandom plep 128orig. plep 128ATLAS Internal = 13 TeVsVSI_LeptonsModµchannel: e-eshuffling factor f=12820 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µ-µChannel: (b) e−eµ0 10 20 30 40 50HNL mass [GeV]1−10110210310410Vertices / 2 GeV0 10 20 30 40 50HNL mass [GeV]012ratiorandom plep 187orig. plep 187ATLAS Internal = 13 TeVsVSI_LeptonsModeµ-µchannel: shuffling factor f=18720 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µ-Chann l: (c) µ−µe0 10 20 30 40 50HNL mass [GeV]1−10110210310Vertices / 2 GeV0 10 20 30 40 50HNL mass [GeV]012ratiorandom plep 59orig. plep 59ATLAS Internal = 13 TeVsVSI_LeptonsModchannel: e-eeshuffling factor f=5920 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, µµ-µChannel: (d) e−ee0 10 20 30 40 50HNL mass [GeV]1−10110210310Vertices / 2 GeV0 10 20 30 40 50HNL mass [GeV]012ratiorandom plep 40orig. plep 40ATLAS Internal = 13 TeVsVSI_LeptonsMod-eeµchannel: shuffling factor f=5920 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µµ-µChannel: (e) µ−ee0 10 20 30 40 50HNL mass [GeV]1−10110210310Vertices / 2 GeV0 10 20 30 40 50HNL mass [GeV]012ratiorandom plep 36orig. plep 36ATLAS Internal = 13 TeVsVSI_LeptonsModµµchannel: e-shuffling factor f=5920 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−101210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µ-µChannel: (f) e−µµFigure 5.27: HNL mass distribution for the SS background estimate (orig. plep) and forthe shuffled background estimate (random plep), where plep is an abbreviation for “promptlepton”. The shuffling factor, f , which is defined as the ratio of the number of shuffled eventsto number of original SS background events, is shown on the plots for each channel.1050 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]1−10110210310Vertices / 8 GeV0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]012ratiorandom plep 57orig. plep 57ATLAS Internal = 13 TeVsVSI_LeptonsModµµ-µchannel: shuffling factor f=5720 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, -Ch l: (a) µ−µµ0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]1−10110210310Vertices / 8 GeV0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]012ratiorandom plep 128orig. plep 128ATLAS Internal = 13 TeVsVSI_LeptonsModµchannel: e-eshuffling factor f=12820 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µ-µChannel: (b) e−eµ0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]1−10110210310Vertices / 8 GeV0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]012ratiorandom plep 187orig. plep 187ATLAS Internal = 13 TeVsVSI_LeptonsModeµ-µchannel: shuffling factor f=18720 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, µ-Chan l: (c) µ−µe0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]1−10110210310Vertices / 8 GeV0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]012ratiorandom plep 59orig. plep 59ATLAS Internal = 13 TeVsVSI_LeptonsModchannel: e-eeshuffling factor f=5920 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−101210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, µµ-µChannel: (d) e−ee0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]1−10110210310Vertices / 8 GeV0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]012ratiorandom plep 40orig. plep 40ATLAS Internal = 13 TeVsVSI_LeptonsMod-eeµchannel: shuffling factor f=5920 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−10110210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progresseµ-µv8, µµ-µChannel: (e) µ−ee0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]1−10110210310Vertices / 8 GeV0 20 40 60 80 100 120 140 160 180 200Tri-lepton mass [GeV]012ratiorandom plep 36orig. plep 36ATLAS Internal = 13 TeVsVSI_LeptonsModµµchannel: e-shuffling factor f=5920 40 60 80 100 120) [GeV]llMass of prompt + same flavour displaced lepton (m3−102−101−101210Vertices / 4 GeV Data-driven SS bkg, 4.0 Data-driven shuffled bkg, 2.5 Bkg DV systematic, 2.5 Bkg plep systematic, 2.5 Data, 10.0 Work in Progress eµ-µv8, µµ-µChannel: (f) e−µµFigure 5.28: Tri-lepton mass distribution for the SS background estimate (orig. plep) and forthe shuffled background estimate in colours (random plep), where plep is an abbreviationfor “prompt lepton”. The shuffling factor, f , which is defined as the ratio of the number ofshuffled events to number of original SS background events, is shown on the plots for eachchannel.1065.9. Signal Systematic UncertaintiesTable 5.14: The KS test probabilities obtained when comparing the shuffled and SS back-ground estimate HNL mass (mHNL) and tri-lepton mass (mlll) distributions. The KS test isdone separately for each channel. Two distributions are considered incompatible if the KSprobability is much less than one.KS probabilityµ−µµ µ−µe µ−ee e−eµ e−ee e−µµmHNL 0.43 0.99 0.94 0.80 0.99 0.99mlll 0.20 0.23 0.73 0.62 0.89 0.455.9 Signal Systematic UncertaintiesThis section focuses on systematic uncertainties in the signal prediction from both exper-imental and theoretical effects. Both up and down variations (±1σ) are modeled for mostof the uncertainties. The sources of systematic uncertainties in the background estimate arediscussed in section 5.8.6.Many of the experimental systematics are well understood and can be evaluated withcentral tools developed by CP groups. Examples of such systematics include lepton trigger,reconstruction and identification uncertainties. However, due to the non-standard displacednature of the signal, other uncertainties must be evaluated separately. A summary of the sys-tematic uncertainties and their contributions to the overall uncertainty of the signal selectionefficiency are listed in table 5.15. Each uncertainty in the table is briefly discussed below.Table 5.15: Table summarizing the systematic uncertainties that impact the signal prediction.Systematic uncertainties in this table are the impacts on the signal yields in the SR.Type SourceMaximum Selection Efficiency Uncertainty [%]µ−µµ µ−µe µ−ee e−ee e−eµ e−µµExperimental Integrated luminosity 2Pileup 3Filter 3Tracking 3Displaced vertexing 11 21 19 20 28 9Displaced lepton identification 5 7 7 7 6 4Trigger < 1 1 < 1 < 1 < 1 < 1Lepton reconstruction4 9 12 17 15 2and identificationW cross section and modelling 3Theoretical HNL branching ratio 5Total 8 – 341075.9. Signal Systematic UncertaintiesDisplaced VertexingThe displaced vertex reconstruction efficiency can vary between data and simulation. Theimpact of this uncertainty is evaluated using displaced kaon decays. Kaons are produced inrelative abundance at the LHC and have relatively long mean lifetimes of cτ = 26.84 mm.This provides a way to measure the difference in the vertex reconstruction efficiency for theHNL signal samples with cτN = 1, 10, 100 mm).The ratio of the number of selected Ks displaced vertices in data to simulated eventsis calculated as a function of the displaced vertex pT and radius. These distributions arenormalized such that the data to simulation ratio is equal to one in the first bin with thesmallest radius. This assumes that the tracking and displaced vertex reconstruction is well-understood close to the interaction point. Any uncertainty in this low-radius bin is taken intoaccount by the track reconstruction uncertainty. The difference between the data to simulationratio and one is symmetrized and reported as the ±1σ DV reconstruction uncertainty. Themaximum size of this uncertainty varies as a function of the DV pT and radius for eachmass-lifetime signal between 9 and 28%.Track ReconstructionEvaluation of the track reconstruction efficiency is performed using a “track-dropping” method.The probability of reconstructing a track is determined as a function of pT and η. Next, HNLdecays are selected using the SR selections and this nominal selection efficiency is comparedto the efficiency obtained with a certain fraction of tracks removed (dropped) from the event.When a displaced track is removed from the vertex, the event no longer passes the two-trackvertex selection and, thus, the event is not selected. The overall difference between the nominaland “track-dropping” selection efficiencies is symmetrized and reported as a 3% uncertainty.Displaced Lepton IdentificationPrompt lepton reconstruction and identification uncertainties are well-understood. However,the displaced nature of the leptons in the HNL decay introduces an additional uncertainty thatis not captured in the standard uncertainties. In particular, the lepton identification efficienciesbecome smaller as the |d0| of the lepton-matched track becomes larger. This effect is studiedin simulation because there is no good source of displaced leptons in the data to model thisbehaviour. To quantify the impact, distributions of signal events are studied with and withoutthe lepton identification criteria applied (Medium for muons and VeryVeryLoose for electrons)as a function of the lepton-matched track |d0|. The two distributions are normalized so thatthe ratio is equal to one for events with 0 < |d0| < 3 mm. For leptons with |d0| < 3 mm,the standard identification uncertainties should be sufficient. This choice of normalizationquantifies the uncertainty of the identification for leptons with larger |d0|. The majority of1085.9. Signal Systematic UncertaintiesHNL signal events have small |d0| and therefore this |d0| extrapolation uncertainty is usuallysmall. However, for signals with lower masses and longer lifetimes, the uncertainty can be aslarge as 7%.FilterA filter is used to select data events prior to the displaced track and vertex reconstruction(see section 5.7.2). To evaluate the impact of the filter on simulated events, a filter emulatoris used. However, there is a mismatch in the signal efficiency due to the different physicsobjects used by the data and emulated filters. The impact of this uncertainty is evaluatedusing simulated events that are reconstructed with and without the large-radius tracks. A 3%uncertainty is applied to account for this discrepancy.PileupWhile pileup is modeled in simulation, the simulated collision conditions are not identical tothose experienced during the data collection. A centrally managed tool is used to re-weightsignal events and take into account the impact of pileup during the various data periods. Thisuncertainty is reported to be 3%.Integrated LuminosityThe uncertainty in the combined integrated luminosity for the data collected between 2015and 2018 is 2% [85]. This value is obtained using a dedicated luminosity detector [86].Prompt Lepton Trigger, Reconstruction and IdentificationThe systematic uncertainties associated with the lepton calibration, identification, reconstruc-tion and trigger efficiencies are implemented using the central analysis tools. These uncertain-ties are estimated using Z → ll and J/Ψ → ll events for high-pT (20-1000 GeV) and low-pT(3/4.5-20 GeV13) leptons respectively. The analysis selection requires one trigger-matchedlepton (either prompt or displaced) and the trigger uncertainty is a calculated for the trigger-matched lepton in the event. Standard reconstruction, calibration and identification uncer-tainties are also applied to each of the three leptons in the event, based on the definition ofeach object in chapter 4.HNL Cross SectionTwo uncertainties are assigned to the HNL cross section calculation in eq. (2.7). The first is a3% experimental uncertainty on the ATLAS measurement of the W → lν cross section. The13The minimum low-pT threshold is 3 GeV for muons and 4.5 GeV for electrons.1095.10. Statistical Analysissecond is a 5% theoretical uncertainty on the HNL branching ratio. Previous HNL searchesused a parameterization of the mass, mixing angle and lifetime relationship described in Ref.[27] to compute the N → llν branching ratio. However, this parameterization is estimated todiffer by up to 30% from the most precise calculations to date. In this analysis, branching ratiosare analytically computed for each mass and lifetime sample, taking into account perturbativehigher-order corrections. These calculations, before including the corrections, are within 1% ofthe values generated by Madgraph. After including higher-order corrections, the differencesbetween the analytic computations and Madgraph vary between 3 and 8% for HNLs withmasses between 2.5 and 20 GeV. It is known that Madgraph neglects these higher-ordercorrections and is consequently wrong. Nevertheless, a conservative 5% systematic uncertaintyis assigned to the HNL branching fraction, BR(N → llν).5.10 Statistical AnalysisA global fit for the signal strength µ is performed using the CLs prescription [87] and im-plemented using a statistics package called TRExFitter [88]. A likelihood function, L(α) =P (x|α), is used to define a probability function for a hypothesis α given an observation x.In this analysis, the probability of observing of n events is tested using a signal plus back-ground hypothesis, µS+µbB, where µ is the strength of the signal and µb is the unconstrainedbackground normalization. The likelihood function is:L(n|µ, µb, ~θ) =∏i∈binsP(ni|µS(~θ) + µbB(~θ))·∏j∈NPG(θj)︸ ︷︷ ︸systematics(5.42)In this expression, the likelihood of observing n events given an expected number of µSsignal plus µbB background events is given by a Poisson distribution P . Here, a signal strengthof µ = 0 corresponds to a background-only hypothesis, while µ = 1 corresponds to the nomi-nal signal hypothesis. The expected number of signal events is computed using the simulatedsamples discussed in section 5.4.2 and the predicted background shape is given by the eventshuffling method described in section 5.8.6. The systematic uncertainties described in sec-tions 5.8.6 and 5.9 are accounted for by introducing nuisance parameters ~θ into the likelihood.This method uses Gaussian probability density functions to constrain the expected numberof events and take into account fluctuations that occur due to systematic errors. In addition,the background model includes a normalization factor µb that controls the overall strength ofthe background B. The background prediction for each channel has an independent µb whosevalue is determined in the global fit.The distribution of the main observable, mHNL, is split into two bins: a CR bin with20 < mHNL < 50 GeV and an SR bin with mHNL < 20 GeV. Including the CR bin in the1105.10. Statistical Analysislikelihood directly constrains the background prediction in the SR, which is allowed to floatfreely in the fit. The likelihood is maximized to determine the best-fit value for the globalsignal strength µ, which is shared across all channels that contribute to the signal model.In the statistical analysis, the profile likelihood ratio is used as the test statistic qµ. Out ofconvenience, the negative log of the profile likelihood ratio is used to allow for a minimizationinstead of a maximization prompt and multiplied by two by convention:qµ = −2 lnλ(µ) (5.43)The profile likelihood ratio is defined as:λ(µ) =L(µ, ˆˆθµ)L(µˆ, θˆµ)(5.44)where L is the likelihood, µ is the signal strength, µˆ and θˆ are estimators for the signal strengthand nuisance parameters that maximize the likelihood andˆˆθµ is a conditional maximum-likelihood estimator for the nuisance parameters given a specific µ. This profile likelihoodratio can take on values between zero and one, where larger values indicate more disagree-ment between the data and the signal-plus-background hypothesis. The probability of thebackground fluctuating such that it is equal or larger than the observed number of dataevents is given by the p-value p0, such that:p0 =∫ ∞qobsf(q0|0, θˆ0)dq0 (5.45)where f(q0|0, θˆ0) is the probability distribution function in the background-only hypothesisq0 with µ = 0 and qobs is the observed test statistic. A similar p-value for the signal-plus-background hypothesis qµ is defined as:pµ =∫ ∞qobsf(qµ|µ, θˆµ)dqµ (5.46)Instead of using the p-value pµ to exclude the signal hypothesis, the CLs method [87]is used. This method is a conservative frequentist approach that avoids excluding signalswhere the experiment lacks sensitivity. For example, if the expected number of signal eventsis very small compared to the background prediction, and the observed number of eventshas a downward fluctuation, then the signal-plus-background hypothesis can be excluded.This effect is mitigated in the CLs method by deriving a test statistic from the ratio of thesignal-plus-background to the background-only hypothesis. This test statistic equals:CLs =pµp0(5.47)1115.11. ResultsIf the signal-plus-background and background-only hypotheses are well separated (i.e. theexperiment has good sensitivity), then p0 pµ and the exclusion will be very similar to theexclusion computed with pµ only. However, if the two distributions are similar, then the CLsis approximately one, which reduces the probability of excluding the signal. The 95% CL onthe signal strength can be found by varying µLimit until CLs(µLimit) = 0.05. Signal modelsare excluded if µLimit < 1.To test each signal hypothesis, the TRExFitter software package is used to generate tenthousand pseudo-experiments for each value of µ with µˆ constrained between 0 and 100 tocreate signal-plus-background (f(qµ|µ, θˆµ)) and background-only (f(q0|0, θˆ0)) distributions.From these toy experiments, the p-values p0 and pµ are calculated and µLimit is computedfor each of the generated mass and lifetime samples discussed in section 5.4.2. Based on thesignal samples that are excluded, limits on |U |2 as a function of mN can be extracted forthe various scenarios listed in table 5.1. A cubic spline interpolation method is used to createsmooth contours with ±1σ and ±2σ bands in the |U |2 versus mN plane.5.11 ResultsThis section discusses the results of the statistical analysis described in section 5.10. Fig-ure 5.29 shows the signal and background yields before (pre-fit) and after (post-fit) the globalfit is performed for the 2QDH model with inverted-hierarchy mixing. Good agreement is ob-served between the background prediction and the observed data events. This true for allsignal models. The pre-fit and post-fit plots for the rest of the models are shown in figs. 5.30and 5.31 respectively. No significant excess is found in the data and the best-fit for the signalstrength µ is consistent with zero in all scenarios. The fit also has no significant deviationsfrom zero for the fitted values of the nuisance parameters. The systematic uncertainties onthe shuffled background estimate are the only nuisance parameters that are pulled from theirnominal value, but they are all within one standard deviation of the expected value.In fig. 5.32, the mHNL distribution for the post-fit background and the expected signalnormalized to the pre-fit signal strength and the observed events are shown. The pre-fit signalstrength normalization is used because, after the global fit is performed, the signal strengthis zero and the signal distributions would not be visible.The post-fit background predictions and the background scale factors µb are listed intable 5.16 for the 2QDH model with IH mixing in the “Majorana-limit”. Due to the negligiblesignal yield found by the fit, the background predictions are essentially identical for thedifferent signal hypotheses. Table 5.16 also shows the background prediction and observedevent-yield in the single-muon (single-electron) mixing scenarios for the µ−µe (e−eµ) channel.These two channels are shown in the “Dirac-limit” with the additional LNC configuration:l±α − l∓α l±γ . For more details about this LNC configuration see section 5.7.3.112Table 5.16: Post-fit background predictions, observed event-yields and scale factors µb withstatistical and systematic uncertainties in the control and signal regions. The results are shownfor the 2QDH model with inverted-hierarchy mixing in the “Majorana-limit”. The results arealso shown for all final states and for the 1SFH Dirac-limit, LNC configuration l±α − l∓α l±γ .Model ChannelSignal region Control regionµbBackground Observed Background Observede−ee 0.4± 0.3 2 3.6± 1.8 2 0.7±0.40.3µ−ee 0.2± 0.14 1 1.8± 1.3 1 0.5±0.40.32QDH e−eµ 0.9± 0.4 0 4.1± 1.9 5 0.4±0.20.2(Majorana-limit) µ−µe 2.8± 0.8 2 12.3± 3.2 13 3.0±0.90.7e−µµ 1.2± 0.9 1 2.8± 1.6 3 1.0±0.60.4µ−µµ 2.2± 1.5 2 8.7± 2.9 9 1.9±0.60.51SFH e± − e∓µ± 0.6± 0.3 0 2.4± 1.4 3 0.5±0.30.2(Dirac-limit) µ± − µ∓e± 1.9± 0.6 0 8.1± 2.6 10 2.9±1.00.8(a) (b)(c) (d)Figure 5.29: Pre-fit (a-b) and post-fit (c-d) plots for the 2QDH model with inverted-hierarchy(IH) mixing in the “Dirac-limit” (left column) and “Majorana-limit” (right column). Thesignal region (SR) includes events with mHNL < 20 GeV and the control region (CR) includesevents with 20 < mHNL < 50 GeV.113(a) (b)(c) (d)(e) (f)Figure 5.30: Pre-fit plots for the 1SFH model with muon-only mixing (a-b), electron-onlymixing (c-d) and the 2QDH model with normal hierarchy (NH) mixing (e-f) in the “Dirac-limit” (left column) and “Majorana-limit” (right column). The signal region (SR) includesevents with mHNL < 20 GeV and the control region (CR) includes events with 20 < mHNL <50 GeV.114(a) (b)(c) (d)(e) (f)Figure 5.31: Post-fit plots for the 1SFH model with muon-only mixing (a-b), electron-onlymixing (c-d) and the 2QDH model with normal hierarchy (NH) mixing (e-f) in the “Dirac-limit” (left column) and “Majorana-limit” (right column). The signal region (SR) includesevents with mHNL < 20 GeV and the control region (CR) includes events with 20 < mHNL <50 GeV.1150 5 10 15 20 25 30 35 40 45 50 [GeV]HNLm3−102−101−10110210310Events / 2.5 GeVSR CRBackgroundUncertaintyDataHNL (5 GeV)HNL (10 GeV)HNL (15 GeV)ATLAS Work in Progress-1 = 13 TeV, 139 fbs=10 mmNτe-ee, c(a) e−ee0 5 10 15 20 25 30 35 40 45 50 [GeV]HNLm3−102−101−10110210310Events / 2.5 GeVSR CRBackgroundUncertaintyDataHNL (5 GeV)HNL (10 GeV)HNL (15 GeV)ATLAS Work in Progress-1 = 13 TeV, 139 fbs=10 mmNτ-ee, cµ(b) µ−ee0 5 10 15 20 25 30 35 40 45 50 [GeV]HNLm2−101−10110210310Events / 2.5 GeVSR CRBackgroundUncertaintyDataHNL (5 GeV)HNL (10 GeV)HNL (15 GeV)ATLAS Work in Progress-1 = 13 TeV, 139 fbs=10 mmNτ, cµe-e(c) e−eµ0 5 10 15 20 25 30 35 40 45 50 [GeV]HNLm2−101−10110210310Events / 2.5 GeVSR CRBackgroundUncertaintyDataHNL (5 GeV)HNL (10 GeV)HNL (15 GeV)ATLAS Work in Progress-1 = 13 TeV, 139 fbs=10 mmNτe, cµ-µ(d) µ−µe0 5 10 15 20 25 30 35 40 45 50 [GeV]HNLm2−101−10110210Events / 2.5 GeVSR CRBackgroundUncertaintyDataHNL (7.5 GeV)HNL (10 GeV)HNL (15 GeV)ATLAS Work in Progress-1 = 13 TeV, 139 fbs=10 mmNτ, cµµe-(e) e−µµ0 5 10 15 20 25 30 35 40 45 50 [GeV]HNLm2−101−10110210310Events / 2.5 GeVSR CRBackgroundUncertaintyDataHNL (7.5 GeV)HNL (10 GeV)HNL (15 GeV)ATLAS Work in Progress-1 = 13 TeV, 139 fbs=10 mmNτ, cµµ-µ(f) µ−µµFigure 5.32: The mHNL distribution in the SR and CR for the observed data and the post-fitbackground for the 2QDH model with inverted-hierarchy mixing in the “Majorana-limit”.Simulated signal samples with three different mass points are also shown normalized to thepre-fit signal strength. After the global fit is performed, the signal strength is zero.1165.11. ResultsThe signal strength is found to be zero after the global fit is performed. Therefore, limits areset on the mixing angles squared |U |2 in various HNL scenarios for masses in the approximaterange of 3 < mN < 15 GeV. The observed limits are within the ±1σ band of the expectedlimits for all models.The observed and expected limits with ±1σ and ±2σ uncertainty bands for the 1SFHmodel with muon-only and electron-only mixing in the ”Dirac-limit” are shown in fig. 5.33.Summary plots of the observed 95% CL contours for the four models in the ”Dirac-limit” and”Majorana-limit” are also shown in fig. 5.33. The observed and expected limits for the restmodels are shown in fig. 5.34. The strongest limits are observed for the 2QDH model with IHmulti-flavour mixing. This scenario has equal mixing strength between all neutrino flavoursand thus, the combination of all six channels leads to the strongest exclusion limits.(a) (b)(c) (d)Figure 5.33: The expected (dashed line) and observed (solid line) 95% confidence level (CL)contours for the 1SFH model with muon-only (a) and electron-only (b) mixing in the “Dirac-limit” and the observed 95% CL contours for the four HNL models listed in table 5.1 in the“Dirac-limit” (c) and “Majorana limit” (d). The limits are shown for the mixing angle (|U |2)as a function of the HNL mass (mN ). The regions enclosed by the contours are excluded. Theobserved contours for the 1SFH models are also shown for the 1997 DELPHI [68] and the2019 ATLAS [70] results.1175.11. ResultsThe unusual shape of the limit contour is related to the relationship between the mixingangle, lifetime and mass described in eq. (2.8). The analysis is sensitive to models with cτNbetween 1 and 100 mm. For models with 3 < mN < 5 GeV, this lifetime range correspondto mixing angles between 10−3 and 10−5. For longer lifetimes models (with smaller mixingangles), there are not enough decays in the detector volume for the analysis to have sensitivity.As the mass increases, models that the search is sensitive to are too short-lived and fail theminimum Lxy requirements, resulting in a limit in the sensitivity beyond ∼ 15 GeV. The dipin the contour around 5 GeV is a result of the Lxy-dependent mDV selection in the heavy-flavour decay veto (see section 5.8.3), which removes events with small mDV and Lxy. Thisselection is required to remove decays from metastable particles, but also limits the availablephase space for models with short lifetimes and 2 < mN < 5 GeV. This selection was notused in the statistically limited 2019 ATLAS analysis, which explains the shape differencebetween the two ATLAS results. Regardless, this region of phase space is well-covered by the1997 DELPHI results, as shown in fig. 5.33 (a).Observed limits on the square of the HNL to νµ mixing angle |Uµ|2 for the 1SFH modelexceed the limits previously set by ATLAS in both the low-mass (∼ 1 GeV improvement) andhigh-mass (∼ 4 GeV improvement) region. The results also extend the limits to mixing anglesthat are approximately three times smaller than the 2019 ATLAS limits. The limits on thesquare of the HNL to νe mixing angle |Ue|2 are set for the first time by ATLAS for a long-livedHNL. The CMS collaboration submitted their first displaced HNL results for single-flavourmixing scenarios [89]. This analysis uses 138 fb−1 of data collected by the CMS experimentbetween 2015 and 2018. The CMS and ATLAS limits are comparable in the muon-only singleflavour mixing scenarios, except at large values of |Uµ|2 where CMS excludes a larger region ofphase space. One major difference between the two searches is that CMS has a different trackreconstruction workflow, which does not require a minimum Lxy selection. This means thatCMS can search for prompt and displaced HNL signatures in the same analysis. This trackingworkflow also makes it easier to study the heavy-flavour decay background in simulation. TheCMS analysis uses simulated MC samples to estimate the heavy-flavour decay backgroundcontribution between 0 and 4 cm [90]. The ATLAS analysis instead has a minimum Lxyselection of 4 mm and uses an Lxy-dependent mDV selection to remove the heavy-flavour decaybackground, which impacts the signal sensitivity at larger |Uµ|2 (shorter cτN ). However, thisregion of phase space is well-covered by the DELPHI experiment exclusion limits (see fig. 5.2).In the electron-only mixing scenarios, CMS also excludes a similar region at larger values of|Ue|2 that also overlaps with the DELPHI limits. However, at smaller values of |Ue|2, theATLAS |Ue|2 limits exceed the CMS limits by about a factor of two for 5 < mN < 14 GeV.The 139 fb−1 ATLAS results also include a new interpretation for realistic 2QDH models withmulti-flavour mixing scenarios that assume inverted and normal neutrino-mass hierarchies. Todate, this is the first experiment that has directly explored 2QDH models.118(a) (b)(c) (d)(e) (f)Figure 5.34: The expected (dashed line) and observed (solid line) 95% CL contours for themixing angle, |U |2, in the 1SFH model with muon-only (a) and electron-only (b) mixing in the“Majorana-limit” and the contours for the 2QDH model with NH (c-d) and IH (e-f) mixingin the “Dirac-limit” and “Majorana-limit” as a function of the HNL mass, mN . The greenand yellow bands indicate the ranges of expected limits obtained within ±1 and ±2 standarddeviations of the median limit reflecting uncertainties in the signal and background yields.The regions enclosed by the contours are excluded.119Chapter 6ATLAS Inner Tracker Upgrade6.1 ATLAS Inner TrackerThe LHC is undergoing a series of upgrades in order to produce ten times its current lumi-nosity. For more information about the High-Luminosity LHC (HL-LHC), see section 3.1.5.In order to meet the requirements of this challenging new environment, an all-silicon trackingsystem, called the Inner Tracker (ITk), will be installed inside the ATLAS solenoid magnetand replace the current inner detector (pixel + SCT + TRT). Figure 6.1 shows a sketch ofthe ITk. More details about the ITk can be found in Ref. [91].3.3 Material Description within the SimulationFigure 3.6: A visualisation of the ITk as implemented in the simulation frameworkinactive elements of the detector were implemented in the simulation framework, whichdescribes their size, position, and material composition. A visualisation of the simulateddetector, including all material elements, is shown in Figure 3.6. The material descriptionis based on the technical design of the detector as discussed in the following chapters.For each pixel layout candidate simulation model, the relevant physical design was de-tailed by the ITk pixel mechanics groups. All pixel sensors are modelled as 100 µm thicksilicon for the innermost two layers and as 150 µm elsewhere, and front-end chips are mod-elled as silicon with extra elements added as appropriate, corresponding to additional chipcomponents such as metal layers. This approach provides a conservative estimate of thematerial. For pixel barrel services, the cable material included varies as a function of z toaccurately reflect the number of cables that will be required for the modules at that position.For pixel end-caps, the masses and materials of both the support structure and services aremodelled according to mechanical descriptions. For the Inclined design, the individualinclined-sensor supports are individually modelled as carbon foam wedges.The strip barrel detector models eachmaterial contribution separately, withmasses andma-terial compositions reflecting themechanical designs. For the strip end-caps somematerialsare merged: materials/objects that sit next to each other are not individually modelled, butinstead one homogeneous block of material is included, adjusted to have the correct radi-ation length as calculated based on the engineering designs.For the Strip Detector global supports, the barrel and end-caps are modelled in detail, in-cluding the stave cooling pipes, carbon-foam, face-sheets, cable bus, hybrids, and front-end ASICs. In the end-caps, the silicon sensors are described individually, but the remain-31Figure 6.1: A longitudinal view of the active regions of the ITk detector. The pixel detector isshown in the inner region (smaller radius) and is surrounded by the strip detector. The stripend-cap disks can be seen on either side of the barrel region, coloured with blue and greenstripes. Figure taken from [91].The ITk will consist of a pixel detector near the beam line that is roughly twice the radiusand four times the length of the current pixel detector. The ITk-Pixel detector has five barrellayers an five layers of inclined or vertical rings that will provide coverage in the forwardregion. This will be surrounded by a segmented strip tracking detector covering over threetimes the silicon area of the current SCT detector. The ITk-Strip detector consists of four1206.1. ATLAS Inner Trackerlayers in the barrel region and six disks in the end-cap. The work presented in this dissertationfocuses on detector quality assurance and the readout for the ITk-Strip detector.6.1.1 Inner Tracker Strip DetectorThe ITk-Strip detector is segmented into four barrel layers with one end-cap region on eachside of the barrel containing six end-cap disks. The barrel extends from -1400 to 1400 mmalong the z-axis and consists of silicon sensors with 24.1 mm short strips with a pitch of75.5 µm. In the end-caps, the strip pitch can vary from 70-80 µm. Module pairs are combinedto implement stereo angles of 52 mrad in the barrel and 40 mrad in the end-caps [91]. The basicunit of the ITk-Strip detector is a module shown in fig. 6.2. A module consists of a sensor andone or two electrical circuit boards, called hybrids, that house the front-end applied specificintegrated circuits (ASICs) called ABCStar and HCCStar. These front-end chips are discussedin more detail in section 6.3. Modules are constructed by gluing the hybrid on the sensors andconnecting wire bonds that are 25 µm in diameter between the read-out chips and the siliconstrips on the sensors. A power board also sits on the hybrid to supply power to the front-endchips.5 ITk Silicon Strip Detector OutlineFigure 5.3: Exploded view of a short-strip barrel module with all relevant components. Long-stripmodules and end-cap modules feature the same component groups.barrel, two strip lengths are used: long strips are suitable in the lower occupancy region atlarger radii (layers L2 and L3), whereas further subdivision with shorter strips is requiredat lower radii (layers L0 and L1). Therefore two different module types are required forthe barrel section: the so-called short-strip and long-strip barrel modules where "short" and"long" refers to the strip length.The short-strip barrel modules contain two hybrids, each with ten ABCStar read-out ASICsand long-strip modules contain one hybrid with ten ABCStar. Each petal has nine mod-ules on each side organised in six subsegments referred to as rings (R0-R5) (see Figure 5.2);e.g. all R0 sensors of 32 petals in one disk will represent a ring around the beam axis inthe Rf plane. The three inner rings (R0-R2) at the lowest radii from the beam axis haveone module each with one or two hybrids, while the outer three rings (R3-R5) have twomodules butted side-by-side, each with one hybrid spanning over the two neighbouringmodules. Covering such a complex geometry over a large area requires six different sensorgeometries and thirteen individual hybrids. The details of the modules for the barrel andthe end-caps are described in the three following chapters: in Chapter 6 the various activecomponents to form a silicon strip module including the silicon strip sensor and the ASICsare described. The layout of the hybrids and the power boards required for the modulesand the production steps to build modules including the planned quality assurance meas-ures are summarised in Chapter 7. The results of electrical characterisations and test beamstudies of prototype modules are shown in Chapter 8.As the final prototype chips ABCStar and HCCStar were not available at the prototype94Figure 6.2: An expanded view of a strip module in the barrel. Petal modules consist of thesame basic components, but with different hybrid and sensor geometries. Figure take from[91].The work in this dissertation focuses on strip detectors in the end-cap region. An end-cap disk is made up of 32 petal-shaped wedges. Each petal consists of nine sensors, with six1216.2. Quality Assurance for ITk-Strip Petalsdifferent geometries labelled R0-R5 that are mounted on each side of a petal core structure.The petal core structure consists of a carbon fibre structural base containing cooling channels,kapton bus-tape that provides electrical connections and silicon modules. A full sketch of thepetal is shown in fig. 6.3.9 Local Supports: Staves and PetalsFigure 9.4: Schematic view of a petal. (Top) Full petal sketch showing petal core and siliconmodules.The blue sensors are glued directly on the co-cured facing, here indicated in light brown. (Bottom)Internal structure of a petal core showing the cooling pipe routing. The red lines indicate the ti-tanium pipe; the yellow region shows the carbon-foam enclosing the pipes. The light blue area isfilled with the honeycomb filling material.9.2.4 Estimated Radiation LengthTable 9.4 shows estimates for the radiation length of a single short-strip barrel stave aswell as for a petal. These numbers represent best estimates based upon stave and petalprototyping and extrapolation to the use of expected lower-mass components (e.g. ABC130hybrids and titanium cooling pipes). For comparison, the current SCT radiation lengthexcluding barrel or disk support is 2.48% for the barrels and 3.28% for the end-caps [86].The lower expected radiation lengths can be achieved as a result of the high degree ofsharing of support, power and services in the upgrade designs.9.3 Electrical ConceptIn this section, the details of the system-level components common to both stave and petallocal supports are described. The detailed designs of these components differ only through194R5 R4 R3 R2 R1 R0Figure 6.3: A full sketch of a strip petal and the modules labelled R0-R5. The sensors, in blue,are glued onto the core surface shown in yellow. Light green and yellow chips are housed onthe green hybrids and glued onto the sensors. The power boards are shown in orange. Figuremodified from [91].6.2 Quality Assurance for ITk-Strip PetalsThe ITk-Strip detector needs to operate reliably for ten to fifteen years. Therefore, reliabilitytesting of all the various detector components is an essential part of the detector design andconstruction program. Quality Assurance (QA) tests study the performance and reliabilityof components during the research and development phase and during production. In par-ticular, during pre-production, large-scale, multi-module prototypes of ITk-Strip componentshelp demonstrate that the construction of all components meet certain quality thresholds.QA tests are generally “destructive” in nature, which means they involve more extreme stresstesting of the components than what would typically be experienced during detector opera-tion. Examples of stress tests include operating at elevated or lowered temperatures, rapidthermocycl and operating at elevated voltages [91]. For the purposes of this dissertation,only the thermocycling QA tests for the petal will be discussed.Thermocycling is a type of stress test that repeatedly elevates and lowers the temperaturein a controlled environment. The goal of thermocycling the petal is to repeatably stress thevarious components and study whether they fail. Examples of failures for the petal wouldbe object movement (e.g. movement of the sensors or hybrids) or failure of components (e.g.1226.2. Quality Assurance for ITk-Strip Petalsbroken wire bonds or glue failures).A thermocycling QA program was designed to thermocycle a loaded petal in a climatechamber and measure features, such as sensor bow, sensor positions etc., before and after thethermocycling, to determine their stability. Thermocycling tests are performed in a controlledenvironment known as a climate chamber. For this test, the climate chamber needed to ac-commodate the entire petal structure, which is approximately 800 mm in length. Part of thedesign of this QA program was to procure and test a new climate chamber suited to the needsof the ITk petal production at TRIUMF, Canada’s particle accelerator centre. The details ofthe climate chamber testing can be found in section 6.2.1.The thermocycling program was initially designed with a smaller prototype version of thepetal called a petalet. The petalet is made out of the same materials as a full-sized petal, butonly has room for one sensor, called the R0 sensor, on either side of the structure. The designand assembly of the petalet, as well as the thermocycling tests are discussed in section 6.2.2.Once a full-size prototype petal structure was built, the petal was also subjected to the samethermocycling tests. These tests are discussed in section 6.2.3.6.2.1 Thermocycling ProgramDuring thermocycling, it is important to maintain a dry environment so that there is no riskof water condensing on the detector. For this reason, it was extremely important to find amachine that included a dry air system. Careful validation of the thermocycling program andmonitoring of the moisture levels in the chamber was done to ensure the safety of the petalwhen undergoing temperature cycling tests. This validation included a monitoring system setup to measure the temperature, dew point and relative humidity in the chamber. A sensormeasured the internal air temperature of the chamber and the relative humidity (RH) of theair, which is defined as the ratio of the amount of moisture present in the system relative tothe amount of moisture that would be present if the air was completely saturated. Since thelatter amount is dependent on the temperature of the system, it is more useful to considerthe dew point of the system. The dew point (DP) is the temperature below which, given themoisture in the chamber, water droplets will start to form. Given the temperature (T) andrelative humidity (RH), the dew point temperature in the chamber can be calculated usingthe Magnus formula shown in eq. (6.1). For the temperature range from 45◦C to 60◦C, theMagnus parameters are given by β = 17.62 and λ =243.12◦C [92].DP (T,RH) =λ(ln(RH100 ) +βTλ+T )β − (ln(RH100 ) + βTλ+T )(6.1)In addition to the sensor inside the chamber, a second sensor was used to measure thepressure differential between the inside and the outside of the chamber (∆P = Pin − Pout),1236.2. Quality Assurance for ITk-Strip Petalsas well as the temperature and RH outside of the chamber. This external monitoring systemwas used to record any changes in the external temperature/humidity that might influencethe internal chamber environment. The pressure monitoring was also used to see if there werepoints in the thermocycling program where the pressure differential changed from positive tonegative. This change in pressure could result in moist air from the outside being sucked intothe system, so we wanted to see if there were places in the thermocycling program that weresusceptible to these types of pressure changes.(a)(b)Figure 6.4: The final validated thermocycling program (a) with a ramp rate of 1.33◦C/minand soak times of 15 hours and 30 min at 21◦C and ±40◦C respectively. This plot showsthe temperature and RH for the full 46-hour program. The red curves show the measuredtemperature inside the climate chamber and the blue curves show the RH inside the chamber.The temperature and RH curves (b) for the first thermocycle where the RH spike is thelargest. The plot in (b) also indicates the dew point inside the chamber (dashed red line) andthe measured pressure differential (green line), which is defined as ∆P = Pin − Pout.1246.2. Quality Assurance for ITk-Strip PetalsWhen testing the thermocycling program, the soak time (how long the system sits at thesame temperature), and temperature ramp time (how quickly you change the temperature ofthe system) had the most impact on the dryness of the system. In order to prevent conden-sation from forming on and damaging the detector, it was decided to find a program thatwould maintain a dew point at least 10◦C below the air temperature inside the chamber.Before finalizing the thermocycling program, it was important to optimize the soak and ramptimes to achieve a program that met the dew point criterion and took a reasonable amountof time to complete 10 cycles between ±40◦C. The 46-hour program, shown in fig. 6.4), wasestablished to meet the thermal cycling test and detector safety requirements.6.2.2 Thermocycling the PetaletThe petalet is a prototype version of the petal structure that was designed for initial testing.The overall size of the petalet is 15 × 18 cm. The petalet has the same components as thepetal and consists of a carbon fibre base, a kapton bus-tape, and space for two R0 modules.However, due to the limited availability of components at the time, the prototype version wetested, only had one module mounted on side A. Stable reference markers were also gluedonto the structure to define a global coordinate system on the petalet. The location of thereference markers are shown in fig. 6.5.Figure 6.5: The location of the stable markers glued directly to the carbon surface labeled1-5.1256.2. Quality Assurance for ITk-Strip PetalsFigure 6.6: The petalet hanging in the climate chamber right before thermocycling.To investigate the stability of the structures over time, various measurements of the loca-tions of the components and properties of the sensor were recorded. Features on the sensorand hybrids are sometimes referenced to as fiducial markers since they are used by imagingmachines to locate the objects when loading them on the petal. Measurement scans were doneusing a coordinate measuring machine (CMM) to locate features on the sensor, hybrid andbus-tape. Next, the petalet was placed in the climate chamber and the thermocycling program(described in section 6.2.1) was run. For the test with the petalet, the structure was hungfrom the wire rack in the climate chamber using copper beryllium alloy wire with a thicknessof 180 µm (see fig. 6.6). After the program was finished, the measurements were repeated andthe results were examined to study any changes that occurred during thermocycling.Measurements of the sensor flatness and bow are shown in table 6.1. The flatness ismeasured by scanning across the surface of the sensor and taking x, y, z measurements ateach point. The flatness is then reported by the CMM as the width of a zone bounded bytwo parallel planes that contains all the measured data points of the surface. The sensor bow,given by eq. (6.2), is also a measure of how flat a sensor is.bow =14(∑cornersz)− centrez (6.2)Scans of the surface on side A and B before and after thermocycling are shown in fig. 6.7.These plots show how the surface shape of the sensor changed before and after thermocycling.The flatness and bow measurements (for the R0 sensor on side A) are also recorded in thetext on the right-hand side of these plots, along with additional sensor measurements, suchas the sensor length, radius etc. We observed that the flatness on both sides and sensor bowon Side A are the same before and after thermocycling.1266.2. Quality Assurance for ITk-Strip PetalsTable 6.1: Measurement results for flatness of Side A and B, as well as the bow for the sensoron side A.Measurement Type Before (µm) After (µm)Flatness (Side A) 131 ± 3.78 131 ± 3.78Sensor Bow (Side A) 37.2 ± 0.54 37.6 ± 0.54Flatness (Side B) 390 ± 3.78 389 ± 3.78Figure 6.7: Plots of the surface scans of the sensor on side A and the bus-tape surface of sideB before and after thermocycling. The flatness, bow and other sensor measurements are alsoshown in the text on the right-hand side of the plots.The locations of the features on the petalet are measured using the coordinate systemdefined by the stable reference markers. Defining a vector from the origin of the coordinatesystem to each feature as ~R, we measure ∆~R = (~x′−~x, ~y′−~y), where unprimed coordinates aremeasured before thermocycling and the primed coordinates are measured after. To visualizethe displacement, a plot the displacement vectors (∆R) is shown in fig. 6.8. In this visualizationwe are looking to see if the displacements of the features have a common direction that mightarise, for example, from gravity pulling uniformly on the module during thermocycling. Themagnitudes of the displacements were on the order of a few µm with no common directionand consistent with no movement within the measurement uncertainty of around 3 µm. Basedon our analysis of the results all components on the petalet passed the thermocycling stresstest.1276.2. Quality Assurance for ITk-Strip Petalssensor fiducials hybrid fiducials bus-tape fiducials origin of coordinate systemFigure 6.8: Plot of the displacement vectors (∆~R) for the features on side A, including thetwo hybrids in purple, the sensor in blue and the bus-tape in brown. The vector magnitudesare uniformly scaled by a factor of 2000 to visually examine if there is a common directionfor the displacements.6.2.3 Thermocycling the Semi-Electrical PetalWhile the petalet was a useful structure to design and test the thermocycling program becauseit was a small-scale object that was more readily available, the goal of the thermocyclingprogram was to stress test large-scale objects that are as similar as possible to the finalproduction design. The structure used in the full-size petal tests is known as the first semi-electrical petal (see picture in fig. 6.9). The semi-electrical petal is fully loaded on both sidesand consists of the following modules:• R5: Dummy sensors that include lithography, reference markers and bond pads• R4: Dummy sensors with no lithography or reference markers; module was built withcracked dummy sensors• R1-R3: Dummy sensors that include lithography, reference markers and bond pads• R0: Fully electrical sensors1286.2. Quality Assurance for ITk-Strip PetalsFigure 6.9: A photo of the first semi-electrical petal. This petal was the prototype used inthe thermocycling tests discussed in this section. This photo was taken by the TRIUMFcommunications team.Petal measurements before and after thermocycling were performed using the CMM in adedicated measurement frame. This frame is constructed out of aluminum and consists of aflat surface where three petal locators rest. These locators are found on the outer left andright edges the petal and on the inner edge of the petal. During assembly, these locators arewhat will hold the petals to the assembly structure to construct the end-cap disks. The threepetal locators are then secured in the measurement frame using 3D printed locking pins. A1296.2. Quality Assurance for ITk-Strip Petalscoordinate system is set up using the petal locators and the two petal fiducial markers on theinner and one of the outer petal locators. The petal fiducials are tiny circles in the carbonfibre structure that are used during loading to construct a coordinate system that can be usedto precisely place the modules on the carbon fibre structure. The x- and y-axes are definedusing the petal fiducials and the x-y plane is defined as the surface of the petal locators. Theorigin is set to be the inner petal fiducial. A sketch of the coordinate system used for the petalmeasurements is found in fig. 6.10.y-axisx-axisz-axisorigin (x0,y0)x-y planex-y planeSide A Side Bxyzpetal locatorsFigure 6.10: The petal coordinate system. The x- and y-axes are defined using the two petalfiducials on the inner and outer petal locators. The origin is defined as the inner fiducial andthe x-y plane is defined as the flat surface of the petal locators.The CMM manual tool is used to measure different markers on the sensors, hybrid and bus-tape on both sides of the petal. There are nine sensors per side and a total of five measurementsare taken per sensor, with one in each corner, as well as a point in the centre of the sensor tobe used for bow measurements. On each side the petal, there are a total of 13 hybrids withfour measurements taken per hybrid. Finally, eight points on the kapton bus-tape are also1306.2. Quality Assurance for ITk-Strip Petalsmeasured. In total, 210 measurements are record. Pictures of the different features that weremeasured on the petal are shown in fig. 6.11.(a) electrical sensor F (b) dummy sensor F(c) hybrid F (d) hybrid circle F(e) bus-tape circle FFigure 6.11: Pictures of the different fiducial markers on the sensors, hybrids and bus-tape.These markers are measured by the CMM to determine the position of the various componentson the semi-electrical petal.It should also be noted that while measurements were taken on each of the modules, R2 inparticular had some fiducials obscured and others that were difficult for the CMM to measure.The R4 modules also have dummy mechanical sensors that did not have any fiducial markersand therefore these sensors could not be measured. As a result, these modules are ignored1316.2. Quality Assurance for ITk-Strip Petalsand so not all 210 measurements are included in the analysis.The sources of measurement uncertainty include the CMM measurement uncertainty formanual tool and circle fitting and the petal inner fiducial position (x0, y0) that is used toestablish the coordinate system. The measurement uncertainty for each feature is estimatedas the standard deviation (σ) from ten repeated measurements of the x-y position. The CMMmeasurement uncertainties and the petal fiducial uncertainty can be found in table 6.2. Thefiducial markers on the dummy sensors where not as well defined as the other sensors so thesensor fiducial markers are recorded as two different uncertainties.Table 6.2: Measurement uncertainties for the features on the semi-electrical petal.Feature Type σx (µm) σy (µm)F on hybrid 1.53 1.37Circle on hybrid 2.73 1.89F on sensor 1.53 1.11F on dummy sensor 3.48 3.06Circles on bus-tape 3.97 3.81Petal fiducial 0.4 0.8(a) Support bar (b) 3D locking pinsFigure 6.12: The support bar in the vertical orientation in the climate chamber. The threeattachment points on the bar are where the three petal locators are attached and secured tohang the petal in the chamber.1326.2. Quality Assurance for ITk-Strip PetalsSince the petal is heavier than the petalet structure, the beryllium alloy wire used tohang the petalet in the climate chamber did not support the weight of the full-sized petal.Instead, a metal bar was built to hang the petal in the climate chamber. This bar can behung horizontally or vertically to allow the petal to hang in different orientations. 3D printedlocking pins (similar to the pins used in the measurement frame) were used to fix the petalto the support bar (see fig. 6.12). Pictures of the semi-electrical petal hanging in the climatechange before and during the thermocycling test can be found in fig. 6.13.(a) Before thermocycling (b) During thermocyclingFigure 6.13: The petal hanging in the climate chamber before and during thermocycling.Immediately after thermocycling, the petal was brought back to the clean room and placedin the measurement frame to measure the location of the features. Initially, the analysis ofthe measurements taken before and after showed worrying 3σ ∆R displacements that wereconsistent with movement due to gravity. This can be seen in the arrow plot of one of theR5 sensors on side A in fig. 6.14. The arrows indicate the direction of motion of the fiducialmarker marker, while the magnitudes of the displacements are shown in the coloured boxes.A statistical analysis of the roughly 100 different points on each side of the petal was alsodone. The “pull” of two measurements is defined as (x1−x2)/σx, where σx is the uncertaintyon the two measurements. For a set of measurements that are consistent with no movement,the pull plots should have a Gaussian distribution centred at zero with width one. These pullplots for the x and y measurements of the features on the petal are shown in fig. 6.15.133R5S0 Side A4231 hybrid movement sensor movement sensor fiducials hybrid fiducials ΔR (μm)Figure 6.14: Arrow plot and ∆R displacements of the four sensor fiducials (in blue) and thefour fiducials on the hybrid (in purple) for one of the R5 sensors on side A. The arrows in theplot are magnified by a factor of 2000 to visually see the direction of motion. The magnitudesand uncertainties of the displacements are shown in the boxes.20− 15− 10− 5− 0 5 10 15 20yσ y / Δ051015202530Number of MeasurementsATLAS InternalEntries: 98Mean: -1.165Std. Dev.: 1.58Side A(a) y-pull immediately after thermo-cycling20− 15− 10− 5− 0 5 10 15 20yσ y / Δ05101520253035Number of MeasurementsATLAS InternalEntries: 98Mean: -0.816Std. Dev.: 1.74Side A(b) y-pull 48-hours later20− 15− 10− 5− 0 5 10 15 20yσ y / Δ051015202530Number of MeasurementsATLAS InternalEntries: 98Mean: -0.068Std. Dev.: 1.59Side A(c) y-pull four weeks later20− 15− 10− 5− 0 5 10 15 20xσ x / Δ05101520253035Number of MeasurementsATLAS InternalEntries: 98Mean: 0.35Std. Dev.: 1.27Side A(d) x-pull immediately after thermo-cycling20− 15− 10− 5− 0 5 10 15 20xσ x / Δ051015202530Number of MeasurementsATLAS InternalEntries: 98Mean: 0.226Std. Dev.: 1.4Side A(e) x-pull 4-hours later20− 15− 10− 5− 0 5 10 15 20xσ x / Δ051015202530Number of MeasurementsATLAS InternalEntries: 98Mean: -0.153Std. Dev.: 1.45Side A(f) x-pull four weeks laterFigure 6.15: Statistical analysis of the roughly 100 different points measured on Side A ofthe petal. The pull in the y-direction (∆y/σy) and the pull x-direction (∆x/σx) are shownimmediately after thermocycling and the measurements are repeated 48 hours and four weekslater. After 48 hours, the mean of the pull is closer to zero, which indicates that after sometime the structures relax and are more consistent with no movement after thermocycling.1346.2. Quality Assurance for ITk-Strip PetalsImmediately after thermocycling, the mean of the y-pull was negative, which indicatesthat, on average, the measurements were trending down in the y-direction. This motion wasespecially worrying since it was consistent with the direction of gravity when the petal washanging in the climate chamber during thermocycling. However, the measurements were re-peated 48 hours later and the mean of the pull in the y-direction was closer to zero indicatingthat the structures seemed to be relaxing back into the position that they occupied prior tothermocycling. The measurements were repeated four weeks later and the distributions werefound to be more consistent with zero movement.We concluded that moisture effects were the cause of the displacements observed imme-diately after thermocycling. In the climate chamber, the petal is kept in very dry storage.Dry air is constantly pumped into the chamber to maintain a low dew point and preventmoisture buildup on the detector (see discussion of dew point in section 6.2.1). This removalof moisture from the environment can cause structures on the petal to shrink. However, uponreturn to the clean room environment, where the measurements are done with the CMM, thestructures re-expand and return to their original positions.This moisture effect theory was further confirmed with tests performed with the petal in ahorizontal orientation in the climate chamber. Similar order of magnitude displacements alongthe long axis of the petal were observed immediately after thermocycling. Since the petal washanging horizontally, these displacements were no longer consistent with movement due togravity. The conclusion from these tests is that nothing untoward happened to the petal after10 thermal cycles and while stressing the petal, we observed a well-known phenomenon thatdrying out the petal can result in small displacements of the various structures.As mentioned at the start of this section, QA tests are designed to stress the structuresbeyond what would typically be experienced during detector operation. Since the structuresrelaxed back to their original position, and no permanent damage occurred, even after beingsubjected to a much drier environment than we expect to operate the detector in, this testwas considered a success.100 Thermocycles TestThe goal of these tests is to thermally stress the petal to determine the reliability of its designand construction. Since the petal passed the initial 10 thermal cycles stress test, a subsequenttest was run where the climate chamber program was set to run 100 thermal cycles insteadof 10. After 100 thermal cycles, visual inspection of the petal showed that one of the hybridson the R4 modules has bowed significantly. The glue under this hybrid had failed, causingthe structure to bow and a crack to developed on the right-hand side of the R4 sensor (seefig. 6.16).1356.2. Quality Assurance for ITk-Strip PetalsThe analysis of the measurements taken before and after the 100 cycles test was consistentwith this crack and bowing occurring during the test. Figure 6.16 shows the arrow plots forthis sensor and the large ∆R and ∆z displacements that occurred during thermocycling. Thepull plots in fig. 6.18 show that the rest of the measured features, not permanently damagedby the bowing and cracking, exhibited the previously observed contraction after removing thepetal from the dry climate chamber. After two weeks the structures relaxed back to theiroriginal positions and distributions were consistent with no movement, indicating that allstructures (except for R4) passed the long-term stress test. The outliers in the pull plots wereverified to be measurements from the R4 hybrid where the failures (cracking and bowing)occurred. A similar crack also occurred on side B on another R4 module.Although the 100 thermal cycles test observed two failures of the R4 modules, thesemodules were always “compromised”. They were built using dummy sensors that were crackedeven before the semi-electrical petal underwent the thermocycling stress tests. This result isnot all that surprising, since these R4 modules were not built using the final productionsensors.We concluded from this test that all modules that did not use dummy sensors (i.e. allmodules except R4) passed the long-term stress test. However, this test also demonstratedthat it would be useful to perform a long-term stress test (similar to this 100 thermocycletest) on a fully electrical petal with no dummy/cracked sensors.Figure 6.16: The crack on the R4 sensor and the bowing of a hybrid on the same module.Photos are taken immediately after thermocycling the semi-electrical petal 100 times.136R4H0 Side A2143Δz[μm]ΔR[μm]hybrid fiducials Figure 6.17: Arrow plot and displacements (∆R and ∆z) of the four fiducials (in purple) forone of the hybrids on side A. The arrows in the plot are scaled by a factor of 2000 to visuallysee the direction of motion. The magnitudes and uncertainties of the displacements are shownin the boxes.20− 15− 10− 5− 0 5 10 15 20yσ y / Δ024681012141618Number of MeasurementsATLAS InternalEntries: 96Mean: -3.564Std. Dev.: 2.89Side A(a) y-pull immediately after thermocycling20− 15− 10− 5− 0 5 10 15 20yσ y / Δ05101520253035Number of MeasurementsATLAS InternalEntries: 96Mean: -1.542Std. Dev.: 2.35Side A(b) y-pull two weeks later20− 15− 10− 5− 0 5 10 15 20xσ x / Δ0510152025Number of MeasurementsATLAS InternalEntries: 96Mean: 2.221Std. Dev.: 1.71Side A(c) x-pull immediately after thermocycling20− 15− 10− 5− 0 5 10 15 20xσ x / Δ05101520253035Number of MeasurementsATLAS InternalEntries: 96Mean: 0.552Std. Dev.: 3.09Side A(d) x-pull two weeks laterFigure 6.18: Statistical analysis of the roughly 100 different points measured on Side A of thepetal. The pull in the y-direction (∆y/σy) and the pull x-direction (∆x/σx) are shown imme-diately after thermocycling and two weeks later. After two weeks, the central distribution ismore consistent with zero, except for outliers with large pulls that are from the measurementsof the hybrid on the module where the failure occurred.1376.3. ITk-Strip Readout6.3 ITk-Strip ReadoutThe ITk-Strip detector will consist of approximately 60 million channels that need to beread out at a frequency of 1 MHz [91]. This provides a challenging readout requirement onthe order of 1013 channels per second. The current inner tracker has readout rate of roughly1010 channels per second. This added complexity required a re-design of the ATLAS dataacquisition system (DAQ). The current ATLAS DAQ (fig. 6.19 (a)) consists of front-end elec-tronics and downstream readout systems that are custom to each detector in ATLAS. Thenew DAQ system (fig. 6.19 (b)) will remove some of the dependency on custom electronics andreplace them with a single board common to each detector that uses commercially availablefield-programmable gate arrays (FPGAs). These so-called Front-End Link Exchange (FE-LIX) cards are advantageous because they are detector independent and provide a scalablearchitecture suited to a large complicated DAQ system.networknetworknetworkData Processing Data Processing(a) Current ATLAS DAQnetworknetworknetworkData Processing Data Processing(b) HL-LHC Era DAQFigure 6.19: Current and HL-LHC era DAQ systems for the ATLAS experiment. The FELIXcards will replace the current readout drivers (RODs) and readout systems (ROSs) used inthe current DAQ system. Figure adapted from [93].In addition to the FELIX cards, the ITk-Strip readout also includes front-end ASICs thatare designed specifically for the detector. There are three main ASICs housed on the siliconmodules. They include the ABCStar, the HCCStar and the AMAC. Only two of the three(the HCCStar and AMAC) chips are required to communicate with the FELIX cards. Theirfunctionality and production chip names are summarized in table 6.3. Depending on the layoutof the detector, between nine and eleven ABCStar chips are connected to a single HCCStarchip. The HCCStar packages the data and sends the information downstream. The HCCStaris the only communication link between the ABCStars and the software system and thereforethe HCCStar is also responsible for configuring registers and reporting back the status of theABCStar chips to the central DAQ system.Information from many HCCStar chips on a single structure, such as a petal, is merged1386.3. ITk-Strip Readouttogether on an end-of-structure (EoS) card and converted to an optical signal. The EoS cardalso contains other chips (lpGBT and VL+) that convert the data into a custom data protocoland into an optical signal. The diagram in fig. 6.20 focuses on the upstream path where thedata from the silicon sensor is buffered and read out by FELIX. However, in reality, there arealso streams of data which flow in the other direction and pass information from the DAQsystem through FELIX to the front-end chips. The data lines connecting the AMAC andFELIX are also not represented in this diagram.Table 6.3: Overview of the custom made ASICs for the ITk Strip Detector [91].Acronym Full Name Basic Functionality Production ChipABC ATLAS Binary Chip Converts incoming charge signal into ABCStarhit information.HCC Hybrid Controller Chip Interface between ABC and bus-tape. HCCStarAMAC Autonomous Monitor Provides monitoring and interrupt AMAC-IIand Control Chip functionality.Figure 6.20: A diagram of the ITk-Strip readout showing how all the custom ASICs (ABCStar,HCCStar and AMAC) are connected to each other and merged in the end-of-structure (EoS)card before being converted to an optical signal and sent to FELIX.6.3.1 HCCStar EmulatorAlthough the final ITk-Strip detector will consist of 60 million channels, this number ofworking readout channels will not be ready until close to the detector installation date. Tounderstand how all the information will be integrated together, various demonstrators havebeen built to test the front-end electronics. Using these systems, we can gain a better under-standing of the ITk-Strip readout and prepare for the eventual operation of the detector. Togain experience with a large-scale ITk-Strip readout system, a firmware emulator was designedto mimic both the detector and the front-end chips.The logic for the HCCStar emulator was designed and tested in a simulation and then1396.3. ITk-Strip Readoutintegrated into an FPGA. The emulator generates ITk-Strip-like data packets that are sentthrough optical fibres to a FELIX card. With the FPGA resources on the current card usedto built the emulator, up to 120 HCCStar chips can be emulated, which is equivalent toapproximately 300,000 channels. With more cards, this firmware can be used to emulate thenumber of channels on the order of the whole ITk-Strip detector.The HCCStar emulator was designed to mimic the physics data-taking mode of the realHCCStar chips. In physics mode, the primary function of the HCCStar is to transmit thedata collected by the silicon sensors when a trigger command is received. During detectoroperation, this trigger command is sent to the front-ends from the central DAQ system whenthe decision has been made that a specific collision event should be saved for further analysis(see section 3.2.6 for more details about the ATLAS trigger system). This means the emulatorneeds to respond and send back data, in the same format as a real HCCStar chip, when itreceives a trigger command.8b/10bEncoderPacket FormatterEvent BuilderHit GeneratorHCCStar EmulatorsFIFOGBTRXTXGBTLoopbackFIFO4b from E-link40 MHz clockL0aTagBCRGBT RXFrame SyncL0aTagBCRLCB Wrapper240 MHz clockE-link Mux2 3 4 51BRAMData from PCIeFELIG Lane WrapperFrom FELIXTo FELIXRX pathTX pathControl and TriggerFrame Sync DecoderFIFOFIFO8b/10b Enc.8b/10b Enc.8b/10b Enc.8b/10b Enc.Figure 6.21: A sketch of the HCCStar emulator and LCB wrapper integrated into the FELIGdata generation structure.A schematic of the main firmware blocks used in the HCCStar emulator can be found infig. 6.21. The blocks specific to ITk-Strip data structures are integrated into an existing datageneration infrastructure that converts the emulated data into optical signals. This firmwareis called the front-end link generator (FELIG) and was designed to test the functionality ofthe FELIX cards. The main unit of the firmware is called the FELIG lane wrapper. The logiccontained inside this wrapper is duplicated up-to 24 times on separate optical channels. The1406.3. ITk-Strip Readoutdata in and out of the lane wrapper are sent though a GBT14 block. This block converts acustom CERN data protocol into bits of information that are passed to the rest of the datageneration logic. This block is also responsible for encoding the data into the GBT protocolto send back to FELIX.There are two main blocks of firmware that are specific to the data format used in theITk-Strip DAQ system. The first is the LCB (L0a, Control and BCR) wrapper. This firmwarefunctionality is also contained in the real HCCStar ASIC and is responsible for receivingtriggers and commands sent via FELIX and decoding them into a format that the HCCStarunderstands. In physics mode, the three main pieces of required information are the L0atrigger, tag and BCR. The L0a trigger is analogous to the L-1 trigger used in the current DAQsystem and is the name of the hardware-based trigger that will be used in ATLAS during theoperation of the HL-LHC. The tag is a data event identifier that is used to uniquely locateevent data in a buffer. The tag is passed to the front-ends by the central DAQ system to tellthe front-ends which data event to send back. This tag is then packed and sent along withthe data to ensure that the correct collision event is received. The BCR is the bunch counterreset. The LHC is filled with bunches of protons that collide every 25 ns (see section 3.1.1for more details about the LHC filling scheme). Every detector in ATLAS is sent a global 40MHz clock that is synchronized with these bunch crossings. The front-ends use this clock tocount the bunch crossings. This associates each bunch crossing with a number and enablesthe front-ends to unique identify events. However, these counters are not infinite, so a BCRsignal is sent to reset all these counters to align them with the LHC orbit.The second ITk-Strip specific firmware is the HCCStar emulator block. This firmware waswritten to mimic the data transmission of a real HCCStar ASIC. This block receives the L0a,tag and BCR from the LCB wrapper and builds data events. A block memory (BRAM) isused to store emulated detector hit information that is loaded into memory by the software.Once the data packets have been built, they are encoded and sent back to FELIX.The HCCStar emulator has been successfully operated using ITk software. The softwareis able to send triggers and receive data back from the emulator. Custom data packets can beloaded into the BRAM to test various aspects of the DAQ system. Since the data generator isscalable, the emulator can be used to mimic multiple HCCStars in one demonstrator system.This setup can be used to perform large-scale tests of the ITk-Strip DAQ system and preparethe system for the eventual operation.14GigaBit Transceiver (GBT) architecture is a data protocol developed at CERN to be used in data trans-mission for experiments that require high data rate links and electronic components capable of sustaining highradiation doses. [94]141Chapter 7ConclusionThe SM is a highly successful theory that describes fundamental particles and their inter-actions. With the discovery of the Higgs boson at the LHC in 2012, the final piece of theSM was found [95]. However, experimental evidence suggests that the SM is not a completedescription of our universe. For example, it does not predict the existence of dark matter,nor does it explain the observations of neutrino flavour oscillations. Since the detection of theHiggs boson, no new fundamental particles have been discovered. Searches for BSM particlesare therefore essential to the LHC physics program.This dissertation presented a search for a new particle that provides a mechanism whichcould explain the very light neutrino masses. This search for displaced HNLs was performedusing 139 fb−1 of proton-proton collision data collected with the ATLAS detector. No signif-icant excess of events were observed. Constraints on the mixing angles between HNLs andSM neutrinos were placed in the challenging long-lived region of phase space. Models withmixing angles between 10−3 − 10−7 were excluded in different HNL scenarios for masses inthe approximate range of 3 < mN < 15 GeV. These results extended the reach of previouslypublished ATLAS results on HNL mixing with muon neutrinos and placed the first ATLASconstraints on the mixing with electron neutrinos for a long-lived HNL. New interpretationsof the results were also included for realistic multi-flavour mixing scenarios that are consistentwith neutrino flavour oscillations.In the next LHC data taking period (Run 3), ATLAS LLP searches will benefit from therecent optimization of the LRT software. Until now, the reconstruction of displaced tracksrequired significant computing resources and an extensive amount of disk space to record allthe track information. The LRT software has now been optimized to ensure that displacedtracks can be reconstructed using the available computing resources. For the design pileup inRun 3, the computer processing time has been reduced by a factor of two [96]. This means thatall ATLAS data will now be available for LLP searches to analyze. This software optimizationwill enable searches to significantly improve their signal to background ratios and to designbetter validation and control regions. This new workflow will also enable analysis designs thatcan bridge the gap between prompt and displaced searches.For the displaced HNL search, this will simplify the study of the backgrounds. This opensthe possibility of estimating heavy-flavour decay backgrounds using MC simulations and im-proving the sensitivity to low-mass HNLs with shorter lifetimes. Future searches can also be142Chapter 7. Conclusionextended by considering semi-leptonic HNL decay channels. Thus, the combination of Run 3data with the existing dataset has the potential to extend ATLAS’s sensitivity to displacedHNLs.However, if HNLs weakly interact with SM neutrinos, their observation will require sig-nificantly more data. Thus, the quest for new physics will heavily rely on the successfuloperation and upgrades of the accelerator and detectors. This dissertation also presented de-tector performance and readout research for the ATLAS ITk. Installing new detectors withenhanced tracking performance will enable ATLAS to take full advantage of the LHC luminos-ity upgrades. A test was developed to study the dimensional stability of the ITk silicon stripdetectors. A large-scale object (petal) underwent temperature cycling to stress the detectorcomponents. These tests showed that the petal did not have any points of failure, such asmovement of the silicon sensors with respect to the support structures. The primary functionof the ITk is to reconstruct tracks in dense environments during the operation of the HL-LHC.The dimensional stability of the detector components is therefore crucial to its design.The ITk-Strip detector will have approximately 60 million channels that need to be readout at a rate on the order of 1013 channels per second. 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Technical report, May 2021.151Appendix AData-driven Estimate of RandomTrack Crossings Using a TrackShuffling MethodThis method uses the number of random crossings from tracks in different events as an estimatefor the number of random crossings from tracks in the same events in the signal region. Thismethod assumes that the probability for two tracks to form a random crossing vertex isindependent of whether the tracks come from the same event or from different events. Thus,the number of background events from random track crossings can be estimated by combiningtracks from different data events and producing fake vertices from them.Displaced vertices reconstructed from accidental track crossings is an inherently randomprocess and, due to the relatively small number of lepton-matched tracks (on average twoper event) that pass the VSI track selection in each data event, the accidental crossing of twolepton tracks is very rare. Thus, the track shuffling method can artificially enhance the numberof random crossing DVs and can be used to provide a background estimate. Additionally, thismethod also serves as a useful tool to study the properties of random track crossings becausethis method randomly pairs tracks from different events creating a pure sample of randomcrossing events.To estimate the number of two-lepton random crossing DVs in the signal region, fourregions are defined that are labelled A through D. In this method, a SR is defined (region A)and the background is estimated by counting the number background events in three otherregions (regions: BCD) where there is no expected signal contamination. These regions arelisted in table A.1.This estimation method, known as the “ABCD method”, assumes that the distributionin the two axes (AB vs. CD and AC vs. BD) is uncorrelated and that all the sources ofbackground listed in section 5.8, except for random track crossings, are negligible. Then, thenumber of events in the signal region A is computed as,NANB=NCND⇒ NA = NCND·NB (A.1)where Nα is the number of events in region α.152A.1. Shuffling Analysis FrameworkTable A.1: The different regions used in the random track crossing background estimation.Signal Region Validation Region(Prompt lepton) (Prompt lepton veto)OS DV SS DV OS DV SS DVTracks fromA B A’ B’same eventTracks fromC D C’ D’different eventsA shuffling factor is also defined as the ratio between shuffled and not shuffled events, asf = ND/NB and provides a metric of how many more random crossing DVs can be producedvia this track shuffling method. Larger shuffling factors would result in smaller statisticaluncertainties in the background estimate.A.1 Shuffling Analysis FrameworkThe shuffling analysis framework uses a custom shuffling algorithm to create a list of tracksthat are shuffled together from different data events. It also makes use of the HNL analysisframework (described in section 5.7.1) to create and analyze displaced vertices from a list ofshuffled tracks. The shuffling analysis framework can be divided into four steps (see fig. A.1):1. Make ntuples: This step uses the filtered data event with displaced reconstruction asan input and applies track selections to save a list of lepton-matched track in an ntuple.In this step, information about the lepton objects matched to each track, includinglepton identification criteria and lepton type (electron or muon), is also saved in thentuple. Information about the run number and event number for each track is alsoincluded.2. Make CFF files: The shuffling algorithm creates a common-file format (CFF) file thatcontains a list of lepton-matched tracks (selected in the previous step) and a list ofshuffling instructions that maps various combinations of tracks into unique fake events.The main requirement in this shuffling step is to maximize the number of fake eventsproduced, while also ensuring that any pair of leptons is used in at most one fake event(For more details, see appendix A.2).3. Derivation: This step is similar to the derivation step in the main analysis framework.A collection of tracks is constructed using the list of tracks saved in the CFF file. Thiscollection of tracks is used as an input to the VSI vertexing algorithm, which reconstructsdisplaced vertices using the shuffled tracks. The rest of the information about the event(e.g. the primary vertex, additional non-lepton tracks etc.) is retrieved from a so-called153A.2. Track Shuffling Problem“host-event” that is supplied by an auxiliary data file. At this point, a fake event hasbeen created with displaced vertices that consist of lepton-matched tracks from differentoriginal events.4. Make ntuples and histograms: Once fake events have been reconstructed, they areanalyzed and saved in ntuples and mini-ntuples using the same steps as the main-analysisframework.Ntuple Maker CodeDataReconstructionNtuples (Lepton-matched tracks)CFF Files (Tracks + shuffling instructions)Event Selection CodeShuffling Algorithm Custom Lepton-Only VertexingDerivationReconstructionNtuplesHistograms (Mini-ntuples)Ntuple Maker CodeFigure A.1: An illustration of the main steps of the shuffling analysis framework that demon-strated the types of files are needed as inputs to each step.A.2 Track Shuffling ProblemTo produce fake events with accidental crossings of two lepton tracks, a map of the vari-ous combinations of tracks into unique fake events must be produced. This problem can besummarized as follows,The final requirement is the key to the shuffling problem. This ensures that the sameaccidental crossing of two tracks is not created in multiple fake events. In practice, computa-tional constraints prevent all of the lepton-matched tracks from being shuffled simultaneously.Instead, the lepton-matched tracks are divided into chunks of tracks with P < N leptons per154A.3. Validation of the Track Shuffling MethodGiven a collection of N leptonsand given k, a desired number of tracks per fake event,maximize the number of fake events from the N leptonsrequiring that any pair of leptons is used in at most one fake event.chunk. These chunks of P leptons are shuffled independently. Uniquely shuffling a set of Nobjects is a conceptually straightforward combinatorics problem, but due to the constraintthat “any pair of leptons is used at most one fake event”, it is very challenging to solvemathematically.The solution employed in the shuffling algorithm is to solve this “shuffling problem” inadvance for a set of P leptons and create a so-called shuffling basis that pre-determineswhich leptons should be used in each fake event. One key aspect of this shuffling basis isthat it uses information about the number of electrons and muons in each event to createa set of instructions to produce a list of shuffled lepton-matched tracks with a distributionthat matches the input lepton distribution. The shuffling algorithm then chunks the selectedlepton-matched tracks into groups of size P and uses the shuffling basis to create a set ofinstructions that determines which leptons will be used in each fake event.A.3 Validation of the Track Shuffling MethodTo validate the shuffling analysis framework, a “do-nothing” configuration is implementedto bypasses the random shuffling part of the framework and create instructions that produceevents with the same lepton-matched tracks as the original events. Thus, when the collection oftracks is created in the derivation step, it consists of the exact same tracks that were originallyselected by the vertexing algorithm in the original data events. The vertexing algorithm isdeterministic and, if the same event information and input tracks are used, then the samevertices should be reconstructed. However, there are a few key differences in this “do-nothing”configuration that can slightly alter the collection of reconstructed displaced vertices. Whilethe selected tracks are the same in the real and “fake” events, the rest of the informationabout the event, including the primary vertex and the non-selected tracks used the VSI trackattachment step, is retrieved from a random auxiliary “host-event”. Careful study of thedependence of the vertex collection on the primary vertex and non-lepton tracks is thereforerequired.The VSI algorithm has two checks that depend on the primary vertices in the event. First,in the two-track vertex forming step, there is primary vertex compatibility condition for eachtrack. This will reject the vertex if either of the tracks is determined to be compatible with theprimary vertex. Second, in the track attachment step, if the reconstructed lepton-only vertexis < 0.5 mm from the hard-scatter or any pileup vertex, then the track attachment procedure155A.3. Validation of the Track Shuffling Methodis skipped. This second check has a negligible impact on vertices in the fiducial volume of4 mm< Lxy < 300 mm. The original primary vertices are passed along in the “do-nothing”configuration and so this dependence on the primary vertices can cause small differences inthe vertex reconstruction.To study the impact of selecting a different primary vertices, events created using the “do-nothing” configuration are compared to the original data events in fig. A.2. Small differenceson the order of 10-20% can be observed mainly at low DV radius where there is a strongerdependence on the location of the primary vertex.0 50 100 150 200 250 300 [mm]xyL0.050.10.150.20.250.30.350.40.45610×Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL110210310410510Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL0.811.2ratioMaterial Layersoriginal DAOD 13711donothing, orig. hadrons 12954ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B, all 2-lep SS DVs0 10 20 30 40 50DV mass [GeV]0.20.40.60.811.21.41.6610×Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]110210310410510610Vertices / 1 GeV0 10 20 0 5DV mass [GeV]0.811.2ratiooriginal DAOD 13711donothing, orig. hadrons 12954ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B, all 2-lep SS DVs0 10 20 30 40 [GeV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8ATLAS Work in Progress = 13 Tes, 10 GeV, 10 mmµµ-µLNC, (a) DV mass0 50 100 150 200 250 300 [mm]xyL0.050.10.150.20.250.30.350.40.45610×Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL110210310410510Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL0.811.2ratioMaterial Layersoriginal DAOD 13711donothing, orig. hadrons 12954ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B, all 2-lep SS DVs0 10 20 30 40 5D mass [GeV]0.20.40.60.811.21.41.6610×Vertices / 1 GeV10 20 30 40 5DV mass [GeV]110210310410510610Vertices / 1 GeV0 10 20 0 5DV mass [GeV]0.811.2ratiooriginal DAOD 13711donothing, orig. hadrons 12954ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B, all 2-lep SS DVs1 20 30 40 5 [GeV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8 Work in Progress , 10 GeV, 10 mmµµ-µLNC, (b) DV radiusFigure A.2: Displaced vertices as a function of DV mass and radius for events produced usingthe “do-nothing” configuration (in purple) and the original data events (in blue). In the “‘do-nothing” configuration, the original non-selected tracks are also saved such that, the onlydifference between each event is the primary vertex. Differences at low Lxy can be observed,from the locations of the primary vertices.In the custom VSI configuration, the track attachment of non-selected tracks (mainlyhadrons) is used in the vertexing algorithm to reduce the number of two-lepton displacedvertices. The dependence on the non-selected tracks is checked using the “do-nothing” con-figuration where tracks are taken from a random host-event or from the original data event.Comparing the distributions in fig. A.3 shows that there are some missing correlations be-tween the non-selected tracks and the selected lepton-matched tracks that results in a 10-20%difference for vertices with mDV > 5 GeV.156A.4. Small-Scale Test of the Track Shuffling Method0 10 20 30 40 50DV mass [GeV]0.20.40.60.811.21.41.61.822.2610×Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]110210310410510610Vertices / 1 GeV0 10 20 0 5DV mass [GeV]00.511.5ratiodonothing, orig. hadrons 12954donothing, host hadrons 18402ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B0 50 100 150 200 250 300 [mm]xyL0.10.20.30.40.5610×Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL110210310410510Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL00.511.5ratioMaterial Layersdonothing, orig. hadrons 12954donothing, host hadrons 18402ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B10 20 30 40 50 [ eV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8 Work in Progress , 10 GeV, 10 mmµµ-µLNC, (a) DV mass10 20 30 40 50DV mass [GeV]0.20.40.60.811.21.41.61.822.2610×Vertices / 1 GeV10 20 30 40 50DV mass [GeV]110210310410510610Vertices / 1 GeV10 20 0 5DV mass [GeV]00.511.5ratioonothing, orig. hadrons 12954onothing, host hadrons 18402ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B0 50 100 150 200 250 300 [mm]xyL0.10.20.30.40.5610×Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL110210310410510Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL00.511.5ratioMaterial Layersonothing, orig. hadrons 12954onothing, host hadrons 18402ATLAS Internal = 13 TeVsVSI_LeptonsModRegion B0 10 20 30 40 50 [GeV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8 Work in Progress TeV, 10 GeV, 10 mmµµ-µLNC, (b) DV radiusFigure A.3: Displaced vertices as a function of DV mass and radius (Lxy) for events producedusing the “do-nothing” configuration with the original non-selected tracks (in purple) andnon-selected tracks from host data events (in pink). Differences between the distributionsshow that using hadrons from a random host-event misses some correlations between thenon-selected tracks in the original event and the lepton-only displaced vertices.A.4 Small-Scale Test of the Track Shuffling MethodThe data-driven estimate of random track crossings using a track shuffling method was testedusing one data run from 2016. In this small-scale test, events were selected in the VR andprocessed with the “do-nothing” and shuffled configurations to produce both same-event anddifferent-event collections respectively. SS and OS vertices for the shuffled and non-shuffledevents are separated in the A’B’C’D’ regions as defined in table A.1. In this test run, a totalof 3.703 × 105 original events were processed and 6.967 × 106 shuffled events were created,which gives a shuffling factor of f = 18.8. The results from the small-scale shuffling test areshown in fig. A.4. The ratio between the shuffled and not shuffled events has a good agreementwith the expected shuffling factor (see ratio plots in fig. A.4). Shuffled vertices form a purerandom crossing sample and, in fig. A.4 (d), excellent agreement between SS and OS verticesis observed. This also demonstrates that random crossings are independent of track charge.While this small scale test was considered a success, numerous challenges arose whentrying to scale up the system that mainly stemmed from having to process large amountsof data (on the order of hundreds of terrabytes) in a non-standard way. ATLAS’s main dataprocessing framework is designed to efficiently run over large data files to analyze collisionevents. However, in the framework described in fig. A.1, the large data files are used as anauxiliary input and the main event information in stored in the custom CFF files.157A.4. Small-Scale Test of the Track Shuffling Method0 10 20 30 40 50DV mass [GeV]0.020.040.060.080.10.12610×Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]1−10110210310410510Vertices / 1 GeV0 10 20 0 5DV mass [GeV]0102030ratioshuffled, C' 4265donothing, A' 166ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS ee DVs > 4DVWith mat. veto, m0 50 100 150 200 250 300 [mm]xyL0.20.40.60.81610×Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL1−10110210310410510610Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL0102030ratioMaterial Layersshuffled, C' 4265donothing, A' 166ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS ee DVs > 4DVWith mat. veto, m0 10 20 30 40 50DV mass [GeV]510152025303540Fraction of Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]4−103−102−101−10110Fraction of Vertices / 1 GeV0 10 20 0 5DV mass [GeV]00.511.52ratioshuffled, C' 1donothing, A' 1ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS ee DVs > 4DVWith mat. veto, m0 50 100 150 200 250 300 [mm]xyL50100150200250Fraction of Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL4−103−102−101−10110210Fraction of Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL00.511.52ratioMaterial Layersshuffled, C' 1donothing, A' 1ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS ee DVs > 4DVWith mat. veto, m0 10 20 30 40 50 [GeV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8 Work in Progress , 10 GeV, 10 mmµµ-µLNC, 0 50 100 150 200 250 300 [mm]xyL012345678910DV mass [GeV]5−051015202530M terial LayersDiagonal Cut> 5.5 GeV CutDVmATLAS Internal = 13 TeVs DVsµµV OS-SS (a) OS DVs0 10 20 30 40 50DV mass [GeV]1020304050310×Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]1−10110210310410Vertices / 1 GeV0 10 20 0 5DV mass [GeV]0102030ratioshuffled, D' 4179donothing, B' 172ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, SS ee DVs > 4DVWith mat. veto, m0 50 100 150 200 250 300 [mm]xyL0.050.10.150.20.250.30.350.4610×Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL1−10110210310410510Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL0102030ratioMaterial Layersshuffled, D' 4179donothing, B' 172ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, SS ee DVs > 4DVWith mat. veto, m0 10 20 30 40 50DV mass [GeV]1020304050Fraction of Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]4−103−102−101−10110Fraction of Vertices / 1 GeV0 10 20 0 5DV mass [GeV]00.511.52ratioshuffled, D' 1donothing, B' 1ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, SS ee DVs > 4DVWith mat. veto, m0 50 100 150 200 250 300 [mm]xyL50100150200250Fraction of Vertices / 10 mm0 50 100 150 200 250 300 [mm]xyL4−103−102−101−10110210Fraction of Vertices / 10 mm0 50 10 50 00 2 0 3 [mm]xyL00.511.52ratioMaterial Layersshuffled, D' 1donothing, B' 1ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, SS ee DVs > 4DVWith mat. veto, m0 10 20 30 40 50 [Ge ]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8TL Work in Progress = 13 Tes, 10 GeV, 10 mmµµ-µLNC, 0 50 100 150 200 250 300 [mm]xyL012345678910DV mass [GeV]5−051015202530Ma erial LayersDiagonal Cut> 5.5 GeV CutDVmATLAS Internal = 13 TeVs DVsµµV OS-SS (b) SS DVs0 10 20 30 40 50DV mass [GeV]0.020.040.060.080.10.120.14610×Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]1−1011210310410510Vertices / 1 GeV0 10 20 0 5DV mass [GeV]00.511.52ratioshuffled, C' 4265shuffled, D' 4179ATLAS Internal = 13 TeVsVSI_L ptonsModCR Region, OS vs SS ee DVs > 4DVWith mat. veto, m0 10 20 30 40 50DV mass [GeV]123456789310×Vertices / 1 GeV0 10 20 30 40 50DV mass [GeV]1−10110210310Vertices / 1 GeV0 10 20 0 5DV mass [GeV]00.511.52ratiodonothing, A' 166donothing, B' 172ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS vs SS ee DVs > 4DVWith mat. veto, m10 20 30 40 50 [ eV]TTruth Leading Disp. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8 Work in Progre s e, 10 GeV, 10 mmµµ-µLNC, 0 50 100 150 200 250 300 [mm]xyL012345678910DV mass [GeV]5−051015202530M erial LayersDiagonal Cut> 5.5 GeV CutDVmATLAS Int rnal = 13 TeVs DVsµµV OS-SS (c) “do-nothing” DVs10 20 30 40 50DV mass [GeV]0.020.040. 60.08.10.120.14610×Vertices / 1 GeV10 20 30 40 50DV mass [GeV]1−101121031045Vertices / 1 GeV1 2 0 5DV mass [GeV]00.511.52ratioshuffled, C' 4265shuffled, D' 4179ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS vs SS ee DVs > 4DVWith mat. veto, m10 20 30 40 50D mass [GeV]123456789310×Vertices / 1 GeV10 20 30 40 50DV mass [GeV]1−10110210310Vertices / 1 GeV1 2 0 5DV mass [GeV]00.511.52ratiodonothing, A' 166donothing, B' 172ATLAS Internal = 13 TeVsVSI_LeptonsModCR Region, OS vs SS ee DVs > 4DVWith mat. veto, m10 20 30 40 50 [ eV]TTruth Leading Di p. Lepton p3−102−101−101Fraction of Events / 2 GeVMadGraphweighted Pythia8un-weighted Pythia8 Work in Progress 13 TeVs, 10 GeV, 10 mmµµ-µLNC, 0 50 100 150 200 250 300 [mm]xyL012345678910DV mass [GeV]5−051015202530M terial LayersDiagonal Cut> 5.5 GeV CutDVmATLAS Internal = 13 TeVs DVsµµV OS- S (d) shuffled DVsFigure A.4: DV mass distribution for shuffled and “do-nothing” events for SS and OS displacedvertices. The ratio between shuffled and not shuffled events is the shuffling factor. For thistest, with only one collision run from 2016, the expected shuffling factor of 18.8 is the dashedblack line in the ratio plot. OS and SS vertices are directly compared in (c) and (d) for thenot shuffled and shuffled events respectively.During the small-scale test of the track shuffling method, this non-standard way of pro-cessing the data caused large surges in data transfer volume on the worldwide LHC computinggrid. The two large spikes in fig. A.5 are attributed to data being transferred for the trackshuffling estimate. This unique way of processing the data single-handedly helped computingexperts commission protocols to prevent these types of surges, which can cause major inter-ruptions in the central computing network. Due to the difficulties faced when scaling up thesystem, this background estimate was not pursued for the final background estimate in theanalysis. Nonetheless this track shuffling method shows promising results for the estimationof random two-track crossing backgrounds.158Figure A.5: Data transfer volume on the worldwide LHC computing network as a function oftime. The two large spikes is this plot can be attributed to the large amounts of data beingtransferred for this track shuffling estimate. Figure obtained from the computing monitoringsystems.159
Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Gay, Colin
Lister, Alison
Displaced vertex search for heavy neutral leptons using the ATLAS detector
Text