Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Newhouse, Robin
Doctor of Philosophy - PhD
University of British Columbia
The Standard Model of particle physics is a powerful theory of nature, yet it does not account for all physical observations. Notably, the nonzero masses of the three neutrino flavours and their transformations into one another suggest the need for an extension of the Standard Model. One such extension postulates the existence of Heavy Neutral Leptons (HNLs, 𝑁) — right-handed neutrino states that do not interact with other particles except through mixing with Standard Model neutrinos. HNLs may generate light neutrino masses through the so-called “seesaw mechanism.” This dissertation presents a direct search for long-lived HNLs using 139 fb⁻¹ of √s=13 TeV pp collision data collected by the ATLAS detector at the Large Hadron Collider. In this search, the 𝑁 is produced via W → 𝑁 μ or W → 𝑁 e and decays into a neutrino and two charged leptons, which form a displaced vertex in the inner detector. No signal is observed, and limits are set on the squared mixing angles of the 𝑁 with the Standard Model neutrinos in the mass range 3 GeV < m𝘕 < 15 GeV. For the first time in a collider search, results are presented in the context of realistic HNL mixing models consistent with neutrino oscillation data. Such a displaced vertex search relies heavily upon nonstandard reconstruction algorithms. An additional pass of the track reconstruction algorithm with relaxed collision vertex pointing requirements is executed on a subset of the recorded data to improve sensitivity to long-lived particles in the inner detector. This Large-Radius Tracking (LRT) configuration is effective yet computationally expensive due to the reconstruction of many “fake” tracks not formed from individual charged particles. This algorithm was optimized in preparation for the Run 3 data-taking period, which began in July 2022. Fake LRT tracks are reduced by 95%, drastically improving the purity and reducing the computational load such that LRT is now run in the default reconstruction pipeline. This optimization is expected to substantially improve the sensitivity and reduce the complexity of long-lived particle analyses in ATLAS, including future HNL searches.
Using displaced tracks to search forsterile neutrinos in the ATLAS detectorbyRobin NewhouseB.Sc., The University of British Columbia, 2015A THESIS 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)December 2022© Robin Newhouse 2022The following individuals certify that they have read, and recommend to the Faculty of Graduate andPostdoctoral Studies for acceptance, the thesis entitled:Using displaced tracks to search for sterile neutrinos in the ATLAS detectorsubmitted by Robin Newhouse in partial fulfillment of the requirements for the degree of Doctor ofPhilosophy in Physics.Examining Committee:Alison Lister, Associate Professor, Physics & Astronomy, UBCSupervisorJeremy Heyl, Professor, Physics & Astronomy, UBCSupervisory Committee MemberMichael Hasinoff, Professor, Physics & Astronomy, UBCUniversity ExaminerMichiel van de Panne, Professor, Computer Science, UBCUniversity ExaminerTodd Adams, Professor, Physics, Florida State UniversityExternal ExaminerAdditional Supervisory Committee:Colin Gay, Professor, Physics & Astronomy, UBCSupervisory Committee MemberAriel Zhitnitsky, Professor, Physics & Astronomy, UBCSupervisory Committee MemberiiAbstractThe Standard Model of particle physics is a powerful theory of nature, yet it does not account for all physicalobservations. Notably, the nonzero masses of the three neutrino flavours and their transformations into oneanother suggest the need for an extension of the StandardModel. One such extension postulates the existenceof Heavy Neutral Leptons (HNLs,N ) — right-handed neutrino states that do not interact with other particlesexcept through mixing with Standard Model neutrinos. HNLs may generate light neutrino masses throughthe so-called “seesaw mechanism.”This dissertation presents a direct search for long-lived HNLs using 139 fb−1 of√푠 = 13 TeV 푝푝 collisiondata collected by the ATLAS detector at the Large Hadron Collider. In this search, the N is produced via푊 → N휇 or푊 → N푒 and decays into a neutrino and two charged leptons, which form a displaced vertex inthe inner detector. No signal is observed, and limits are set on the squared mixing angles of the N with theStandard Model neutrinos in the mass range 3 GeV < 푚N < 15 GeV. For the first time in a collider search,results are presented in the context of realistic HNL mixing models consistent with neutrino oscillation data.Such a displaced vertex search relies heavily upon nonstandard reconstruction algorithms. An additionalpass of the track reconstruction algorithm with relaxed collision vertex pointing requirements is executed ona subset of the recorded data to improve sensitivity to long-lived particles in the inner detector. This Large-Radius Tracking (LRT) configuration is effective yet computationally expensive due to the reconstructionof many “fake” tracks not formed from individual charged particles. This algorithm was optimized inpreparation for the Run 3 data-taking period, which began in July 2022. Fake LRT tracks are reduced by95%, drastically improving the purity and reducing the computational load such that LRT is now run in thedefault reconstruction pipeline. This optimization is expected to substantially improve the sensitivity andreduce the complexity of long-lived particle analyses in ATLAS, including future HNL searches.iiiLay SummaryThe ATLAS detector at the Large Hadron Collider (LHC) tests the Standard Model of particle physics (SM)and searches for evidence of new phenomena by smashing protons together at record energies. A growingarea of interest in particle physics involves searching for long-lived particles (LLPs), predicted by severaltheories, which travel a small but macroscopic distance in collider experiments. Detecting such hypotheticalparticles in ATLAS requires specialized algorithms. This dissertation explains how a “displaced tracking”algorithm was optimized to enable such searches for LLPs. The physics analysis presented here searches forone of these LLPs called a “Heavy Neutral Lepton” (HNL) using data collected by ATLAS. If discovered,the HNL would help explain the mysterious masses of neutrinos — elusive fundamental particles with smallbut nonzero masses. Unfortunately, no evidence of a new particle is found, but new limits are set, which willhelp guide future experiments.ivPrefaceThe research presented in this dissertation is based on data collected by the ATLAS experiment. The ATLAScollaboration’s ongoing success is made possible by more than 5500 members (nearly 3000 authors) from245 institutes in 42 countries, including graduate students, postdoctoral researchers, and professors. Thesescientists develop simulation and reconstruction software, design and commission new detector technologies,monitor data-taking operations, and publish analyses of the recorded data. These activities are done withhelp from the broader scientific community, not the least of which is the successful operation of the LargeHadron Collider, without which none of this work would be possible.I wrote this dissertation’s text with some phrases and definitions taken from ATLAS publications andunpublished internal documentation, clearly attributed in each case. The captions in some figures areattributed to the source if they have minor or no alterations. Figures with no reference in the caption wereproduced by me or in collaboration with other ATLAS researchers.ATLAS submits final results to peer-reviewed journals and publishes preliminary results not subjectto external peer review. In both cases, the figures are subject to formal internal review. Figures labelled“ATLAS”, “ATLAS Preliminary”, “ATLAS Simulation”, “ATLAS Simulation Preliminary”, or “ATLASOnline” are public results which use ATLAS simulation or data and are internally reviewed by the collab-oration. “ATLAS Internal” or “ATLAS Simulation Internal” figures are not reviewed by the collaborationand do not indicate approval from all members.Chapters 2 and 3 present the theoretical background knowledge necessary to understand and motivatethe HNL analysis. The presentation of this subject matter is inspired by well-known textbooks cited inthe bibliography. Chapters 4 and 5 summarize the experimental apparatus (the LHC and ATLAS) and thestandard ATLAS reconstruction algorithms. Those chapters are drawn from several ATLAS design reportsand performance studies. Chapters 6 and 7 contain my original work, with detailed contributions andacknowledgements listed below.Chapter 6 describes my work in optimizing the large-radius tracking (LRT) algorithm for its inclusion inthe default Run 3 reconstruction pipeline. The work was done with other members of the LRT optimizationteam: Jackson Burzynski, Matthias Danninger, Giuliano Gustavino, Bingxuan Liu, Amber Roepe, and JohnStupak. Each of these individuals contributed significantly to the performance studies, algorithm tuning,software development, and presenting and gathering feedback from physics groups. Matthias Danninger ledthe project, coordinating with ATLAS management and other stakeholders to ensure the effort’s success.Jackson Burzynski and Bingxuan Liu produced many of the Run 3 performance figures in this dissertation.We received support from the tracking performance group. The following summarizes my contributions tothis optimization effort:vPreface• I developed and computed performancemetrics to determine the degree of impact for each optimization.• I performed a study on pileup effects to demonstrate the robustness of the algorithm as a function oftrack multiplicity.• I led the design, development, training, testing, and deployment of the DNN discriminant.• I wrote the necessary code to execute an additional tracking pass and include the LRT collection inthe ATLAS EDM.• I presented several progress updates in internal ATLAS group meetings and workshops.• I conducted a review of systematic uncertainties associated with LRT tracks, helping lay the foundationfor ongoing uncertainty studies.The campaign to include LRT in the default reconstruction was a major success. Physics and computingsub-groups were initially skeptical of the introduction of a new strategy which had the potential to negativelyimpact physics analyses. The perseverance of this small team and the continually demonstrated progresspaid off. The LRT algorithm will now be applied to every event recorded by ATLAS in Run 3 and was alsorun in the reprocessing of existing Run 2 data. Our team was distinguished with an ATLAS OutstandingAchievement Award. This award, presented every two years to roughly eight groups or individuals, recognizesexceptional technical contributions to the collaboration. An ATLAS PUB Note (public technical documentwithout external review) is currently being drafted, which will document the details and performance ofthe optimization. The LRT configuration and procedure described in section 6.2 are used in the analysispresented in chapter 7.Chapter 7 presents a search for Heavy Neutral Leptons (HNLs) with a displaced signature. At the time ofthis writing, the analysis has been accepted by Physical Review Letters. Fifteen team members contributedto this analysis at various levels, and I was one of the three principal data analyzers, along with DominiqueTrischuk and Christian Appelt. Dominique Trischuk led a significant portion of this analysis, includingthe development of the background estimation technique, the 푚HNL discriminant, the custom vertexingconfiguration and its inclusion in a custom derivation. She also conducted studies on spin correlations,coordinated signal sample production, and developed control and validation regions. Christian Appeltcarried out the statistical interpretation, including implementing the TRExFitter workspace, executing toyMC experiments, and interpolating the exclusion limit contours. Susumu Oda developed and studied theDRAW filters to preselect data. Alison Lister, Matthias Danninger, Abi Soffer, and Heiko Lacker definedthe analysis strategy and provided support throughout, with Matthias Danninger and Margaret Lutz as theanalysis contacts. Two Short Term Associates (external collaborators brought on for temporary authorship ofan ATLAS publication) who contributed to this analysis are Oleg Ruchayskiy and Jean-Loup Tastet. Theirsubstantial knowledge of HNL theory and phenomenology was crucial in producing the realistic modelinterpretations which set this analysis apart. The following summarizes my contributions to the analysis:• I was the lead developer of the main analysis software, DHNLAlgorithm, with features implementedby Dominique Trischuk and Jackson Burzynski.viPreface• I co-developed the event selection software, DHNLNtupleAnalysis, with Dominique Trischuk.• I coordinated andmonitored the relevant data processing on the LHC computing grid and our institute’slocal computing cluster.• I implemented and validated the signal systematic uncertainties, both standard and nonstandard,including those related to displaced tracking and vertexing, displaced lepton identification, and filteremulation.• I prepared the public electronic repository of our results on HEPdata along with Christian Appelt.• I regularly presented updates at internal ATLAS meetings and provided guidance to other analyses.• I wrote relevant portions of the internal documentation.In addition to drawing from the published analysis [1], this chapter contains text and figures drawn from theanalysis’s unpublished internal documentation. Margaret Lutz, Christian Appelt, Dominique Trischuk, andI wrote a majority of the internal documentation. Abi Soffer and Margaret Lutz were the contact editorsresponsible for writing the paper and guiding it through publication.To become an ATLAS author one must contribute at least 80 days of technical work to one of thecollaboration’s high-priority activities. My qualification task involved developing a machine-learning-basedscore to be used in the ambiguity solver of the standard track reconstruction algorithm. I created, trained,and implemented a DNN-based score which used various track trajectory and quality parameters as inputs.It was successful and robust, but failed to outperform the existing metric to a degree that could persuade thetracking group to adopt the new procedure. However, this work directly led to the insights and tools used todevelop the DNN discriminant in the LRT optimization.I was also part of a team that published an analysis comparing several algorithms used to distinguishbetween flavours of boosted jets [2]. In this analysis I conducted several background data studies with helpfromOliverMajersky. In theATLAS reconstruction software, I implemented aDNN-based top quark taggingalgorithm developed by Jannicke Pearkes and Wojtek Fedorko. This “TopoDNN” score was compared toother identification algorithms in the publication and performed well.I presented my work at several forums including international and national conferences, ATLAS-wideworkshops, and internal collaboration meetings.• R. Newhouse. Proposed CMOS-based Sensors for the ATLAS Detector: CHESS-2. 54th WinterNuclear Particle Physics Conference. Banff, Canada, 2017.• R. Newhouse, E. Khoda, S. Sen. Machine Learning in Dense Tracking Environments. ATLASTracking & Flavour Tagging Workshop. Hamburg, Germany. 2019.• R. Newhouse, M. Danninger, G. Gustavino, J. Stupak, A. Roepe, B. Liu. Re-optimization of large-radius tracking for Run 3. ATLAS Exotics + SUSY Workshop 2020. Online. 2020.• R. Newhouse. Jet Substructure + Correlations in Hadronic Final States from ATLAS. 9th Edition ofthe Large Hadron Collider Physics Conference. Online. 2021.viiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 The Standard Model of Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2 Particle content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.3 Standard Model Lagrangian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.4 Strong force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.5 Electroweak force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.6 Electroweak symmetry breaking and the Higgs mass mechanism . . . . . . . . . . . . . . . 82.7 Successes and limitations of the Standard Model . . . . . . . . . . . . . . . . . . . . . . . 102.7.1 Successes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.7.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Neutrino masses and heavy neutral leptons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1 Neutrino oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.1 A brief history of detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.2 Neutrino oscillation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Mass and weak eigenstates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2.1 Two-neutrino system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16viiiTable of Contents3.2.2 Three-neutrino system and the PMNS matrix . . . . . . . . . . . . . . . . . . . . . 173.3 Mass mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.1 Dirac mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3.2 Majorana mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3.3 Type-I seesaw mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.3.4 Searches for Majorana fermions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3.5 The Weinberg operator and other types of seesaw . . . . . . . . . . . . . . . . . . . 213.3.6 Are heavy neutral leptons beyond the Standard Model? . . . . . . . . . . . . . . . 233.4 Motivation for HNL searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.4.1 GeV-scale HNLs and displaced vertices . . . . . . . . . . . . . . . . . . . . . . . . 244 Experimental apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.1 Accelerator and injection chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.1.2 Beam characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.1.3 Run 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2 The ATLAS detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2.1 Coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2.2 Inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2.3 Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.2.4 Muon spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.2.5 Magnet system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384.2.6 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385 Object reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1 Tracks and Vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.1.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.1.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.1.3 Primary vertex reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475.2 Electrons and photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.2.3 Isolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.2.4 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3.2 Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.4 Hadronic jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.4.1 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52ixTable of Contents6 Large-radius tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536.2 Run 2 LRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.2.1 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 556.3 Improvements for Run 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.3.1 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566.3.2 Selection criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.3.3 DNN discriminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.4 Performance study on simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.4.1 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.4.2 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626.4.3 Fake rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.4.4 Vertexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.4.5 Pileup robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.5 Comparison to data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.6 Performance study on computing resources . . . . . . . . . . . . . . . . . . . . . . . . . . 676.7 Impact on analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696.8 Inclusion in Run 3 and Run 2 reprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . 697 Heavy neutral lepton analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717.2 Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727.2.1 Monte Carlo samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727.2.2 Data samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767.2.3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.2.4 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 777.3 Reconstruction and object definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787.3.1 Muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.3.2 Electrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 797.3.3 Displaced vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.3.4 HNL mass and DV mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817.4 Analysis design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.4.1 Analysis framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827.4.2 Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 857.4.3 Signal region selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 867.4.4 Data blinding strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.5 Backgrounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.5.1 Material interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.5.2 Metastable SM particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.5.3 푍 → ℓℓ decays with a random crossing . . . . . . . . . . . . . . . . . . . . . . . . 91xTable of Contents7.5.4 Cosmic ray muons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.5.5 Random track crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.5.6 Data-driven estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927.5.7 Background estimate validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 947.6 Signal systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.6.1 Standard systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.6.2 Theory and signal modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.6.3 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987.6.4 Displaced track and DV reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 997.6.5 Filter emulation efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.6.6 Lepton 푑0 extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.7 Background systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.8 Statistical methods and results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.8.1 Statistical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.8.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1118 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113xiList of Tables5.1 This set of minimum requirements is imposed on each track candidate used in the inside-outtracking pass. A hole is defined as an intersection of the track trajectory that contains asensitive detector element but does not contain a cluster. Quantities with si. refer to silicon— the combined pixel and SCT detectors. 푑퐵퐿0 is the transverse impact parameter calculatedwith respect to the measured beam-line position. 푧퐵퐿0 is the longitudinal impact parametermeasured from the primary vertex, and 휃 is the polar angle of the track [104]. . . . . . . . . 456.1 Important selections that differ between the standard and the LRT setups in the Run 2configuration [129]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546.2 Differences introduced for Run 3 optimization of LRT. The following changes drasticallyreduce the fake rate while maintaining high reconstruction efficiency of displaced tracks. . . 597.1 A summary of the eight models that are used in the interpretation of the analysis results.Models are defined according to the number of HNLs (one or two), the fraction of LNC andLNV decays, and the relative strength of the mixing between the lepton generations. Theinverted (IH) and normal (NH) hierarchy benchmarks are used for 2QDHmodels, while onlythe 1SFH model is used for the single-flavour mixing interpretation. . . . . . . . . . . . . . 737.2 The cross section for LNC and LNV decays for one HNL model in the Dirac or Majoranacases, a quasi-degenerate HNL pair in the Majorana case and a quasi-degenerate HNL pairin the Dirac case. The total cross section is the sum of the LNC and LNV contributions. . . . 757.3 Single 휇 and single 푒 triggers from 2015–2018 are used to collect signal region data.mu20 and mu26 signify that the trigger requires a ≥20GeV muon and a ≥26GeV muon,respectively. Similarly, e24 and e26 correspond to a ≥24GeV and a ≥26GeV electron. . . . 777.4 The four HNL filters included in the DRAW filter in the DRAW_RPVLL data stream. . . . . . . 787.5 Description of the selection criteria used in the signal region. The lepton quality selectionLHMedium for prompt electrons is defined in reference [116] and Medium for muons isdefined in reference [167]. TheDisplaced lepton quality requirement for displaced electronsis described in reference [128]. In the 푍 mass veto, 훼 and 훽 refer to flavours of the promptand one of the two displaced leptons, respectively. . . . . . . . . . . . . . . . . . . . . . . 867.6 Definition of the VR event selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897.7 Definition of the metastable particle veto. . . . . . . . . . . . . . . . . . . . . . . . . . . . 91xiiList of Tables7.8 Table summarizing systematic uncertainties impacting reconstruction efficiencies. The val-ues shown in the table refer to the impacts on the signal yields for each channel. The totaluncertainty is the sum in quadrature of all systematic components (the root of the sum of thesquares). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977.9 The relative systematic uncertainties on the background estimate, estimated by creatingshuffled events from SS DVs or from prompt leptons taken from events with different DVchannels [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.10 Yields of estimated post-fit background events and of observed events in the signal and controlregions for all final states. The background yield uncertainties include both systematic andstatistical uncertainties. The last two rows show the 1SFH Dirac-limit, LNC configurationℓ±훼–ℓ∓훼ℓ±훾 [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108xiiiList of Figures2.1 This diagram represents the particle content of the SM and the forces by which each particleinteracts. The legend at the top specifies where to find each particle’s name, mass, quantumnumbers, gauge boson couplings, and fermion couplings. The upper pane depicts theunbroken symmetry configuration of the SM, while the lower pane depicts the SM afterEWSB (see section 2.6). The left diagram shows the Higgs potential and the vacuumexpectation value of the Higgs field. The mixing of electroweak gauge bosons is shownbetween the two panes on the right [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 The “champagne” shape of the 휙0 component of the Higgs potential. The potential containsa circle of degenerate local minima. A choice of definite ground state breaks the 푆푈 (2)퐿 ×푈 (1)푌 invariance and provides the Higgs field with a VEV [7]. . . . . . . . . . . . . . . . . 92.3 Summary of SM cross section measurements at the ATLAS detector as of February 2022.The measurements are corrected for branching fractions, compared to the correspondingtheoretical expectations [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.1 Electron spectrum of nuclear 훽-decay. This apparent violation of energy conservationprompted Pauli’s suggestion of a “dark particle.” [22] . . . . . . . . . . . . . . . . . . . . . 143.2 The 푃(휈푒 → 휈푒) survival probability as a function of distance for 3MeV 휈푒 assuming휃13 = 10◦. The two components of 휈푒 flavour oscillation are clearly distinguishable [24]. . . 153.3 Normal double 훽-decay (left). Neutrinoless double 훽-decay (right) [22]. If the neutrino is aMajorana particle, it is its own antiparticle, and the process on the right would be allowed.This is one of the most promising methods of identifying whether a neutrino is a Majoranaparticle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4 The Weinberg operator is a dimension-5 operator that couples a neutrino-antineutrino pairto two Higgs fields [22]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.5 The three generic realizations of the seesaw mechanism, depending on the nature of theheavy field exchanged [52]. This is a “magnified” view of the Weinberg operator in fig. 3.4. 233.6 Limits on the mixing between an active neutrino and a single HNL in the mass range0.1–100GeV. The active neutrino is 휈푒 in (a), 휈휇 in (b), and 휈휏 in (c). For details seereference [58]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.1 Schematic view of CERN’s accelerator complex [70]. . . . . . . . . . . . . . . . . . . . . . 29xivList of Figures4.2 Shown is the luminosity-weighted distribution of the mean number of interactions per cross-ing for the 2018 푝푝 collision data at√푠 = 13TeV COM energy. All data recorded by ATLASduring stable beams is shown, and the integrated luminosity and the mean 휇 value are givenin the figure [76]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3 Cut-away view of the ATLAS detector [81]. . . . . . . . . . . . . . . . . . . . . . . . . . . 334.4 Cut-away of the ATLAS inner detector [81]. . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 The r-z cross section view of the layout of a quadrant of the ATLAS inner detector forRun 2. The top panel shows the whole inner detector, whereas the bottom-left panel showsa magnified view of the pixel detector region. Compared to Run 1, the IBL (shown in red inthe bottom-left panel) and its services, together with the new beam pipe, were added [83]. . 354.6 Cut-away view of the ATLAS calorimeter system [81]. . . . . . . . . . . . . . . . . . . . . 364.7 Cut-away view of the ATLAS muon system [81]. . . . . . . . . . . . . . . . . . . . . . . . 384.8 Cross section of the muon system in a plane containing the beam axis (bending plane).Infinite-momentum muons would propagate along straight trajectories which are illustratedby the dashed lines and typically traverse three muon stations [81]. . . . . . . . . . . . . . 394.9 Geometry of magnet windings [81]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.10 Bare central solenoid in the factory after completion of the coil winding [81]. . . . . . . . . 405.1 A schematic slice of the ATLAS detector in the barrel region. Different detector systems aresensitive to different particle types [99]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.2 A 3D visualization of the structure of the barrel of the ID. The beam pipe, the IBL, the pixellayers, the four cylindrical layers of the SCT and the three layers of TRT barrel modulesconsisting of 72 straw layers are shown [100]. . . . . . . . . . . . . . . . . . . . . . . . . . 435.3 Five parameters — 푑0, 푧0, 휙, 휃, 푞/푝— define a track in a perigee representation [101]. . . . 445.4 A simplified model of the track ambiguity problem in the SCT barrel. Track candidates a,b, and c, share hits. A score-based ambiguity resolution procedure is performed in orderto distinguish between true and fake tracks. Hits improve the candidate’s score while holespenalize it. The candidate with the higher score takes the ambiguous hits [105]. . . . . . . . 465.5 Run 2 tracking efficiency as a function of 휂 and 푝T is shown for Tight Primary and Looseworking points [109]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.6 An illustration of the path of an electron through the elements of the ATLAS detector. Thedashed red line indicates the trajectory of a photon produced by the electron’s interactionwith material in the ID [112]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.1 Inclusive track reconstruction efficiency for displaced charged particles produced by thedecay of long-lived signal particles. The efficiency is shown as a function of 푟prod, with truthparticles and tracks subject to fiducial selections. The efficiency for standard and LRT isadditive, and the total efficiency is the sum of both [129]. . . . . . . . . . . . . . . . . . . 55xvList of Figures6.2 In Run 2 (a), LRT tracking and displaced vertex reconstruction were only run on a subsetof data selected by applying specialized filters to the standard reconstruction. This schemerequires substantial computing and human resources and is prone to errors. In Run 3 (b),the optimization of LRT tracking allows it to be run by default in the event reconstruction.LLP analyses can be performed using the standard data stream, allowing for more flexibleanalysis designs. The full ATLAS dataset will be available for future analyses without theneed for filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.3 LRT tracks follow the same reconstruction sequence as standard tracks. By removing faketracks as early as possible in the sequence, less time is spent reconstructing them in the later(and generally more computationally expensive) stages. . . . . . . . . . . . . . . . . . . . 586.4 Δ휃, an engineered variable used in the DNN discriminant, is the angular difference betweenthe primary and secondary particle’s flight directions, assuming the track is produced in asecondary decay. This is used to estimate how “LLP-like” a track is. . . . . . . . . . . . . . 596.5 Implementing a cut on the trained DNN discriminant can reduce fake LRT tracks a further50% beyond the already-implemented optimizations. This reduction comes at the cost ofonly a 1–2% reduction in signal track reconstruction. . . . . . . . . . . . . . . . . . . . . . 606.6 A diagram of the track ambiguity-solving procedure. The DNN discriminant is appliedimmediately before the output tracks are stored. This is also the point at which tracks areextracted to train the DNN. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616.7 Three different DV models used to optimize and characterize the LRT algorithm for Run 3.Figures from [1, 123, 126]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626.8 Inclusive track reconstruction efficiency for displaced charged particles produced by thedecay of long-lived scalar particles, 푎 (figs. (a) and (b)) or by the decay of long-lived heavyneutral leptons, 푁 (figs. (c) and (d)). The efficiency is shown as a function of the radius ofproduction of displaced particles (figs. (a) and (c)) and the absolute value of the transverseimpact parameter, |푑0 | (figs. (b) and (d)). As the HNL decay products are highly boosted, thesignature has lower |푑0 | tracks, so fig. (d) focuses on the transition from standard tracking toLRT around |푑0 | = 5mm [135]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.9 The technical efficiency of LRT tracks for a SUSY signal sample compared between Run 2and Run 3 configurations is shown in (a). For most of the 푑0 range, over 85% of the Run 2efficiency is retained. The fake rate comparison for the same signal sample is shown in (b).The rate of fake tracks is reduced by 95% on average. . . . . . . . . . . . . . . . . . . . . . 64xviList of Figures6.10 A comparison of the radial distributions of reconstructed secondary vertices in a simulatedLLP sample using the Run 2 and Run 3 track reconstruction configurations is shown. Thecircular markers represent reconstructed vertices matched to truth-level LLP decay vertices.The dashed lines represent reconstructed vertices not matched to truth-level LLP decayvertices (non-LLP). The four pixel layers and the first SCT layer are shown in the figure withvertical lines, and charged-particle interactions with this material are responsible for spikesin the distributions. The Run 3 reconstruction shows a modest increase in the number of LLPvertices and considerably fewer non-LLP vertices due to the significant increase in purity ofthe LRT algorithm [135]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.11 The mean number of reconstructed tracks per event as a function of 휇 in simulated 푡푡¯ eventsfor the standard and LRT track reconstruction (Run 3 configuration). This quantity reflectsthe additional tracks reconstructed by the LRT pass for typical SM processes. The numberof real tracks is expected to scale linearly with this quantity since it is related to the numberof charged particles produced in the collisions. The number of random combinations isexpected to scale with a higher power since the enhanced combinatorics allow for more suchcandidates to be formed. The number of tracks for the LRT reconstruction increase fasteras a function of 휇 which indicates that it is more impacted by random combinations at highpileup [135]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.12 A comparison of track quantities in zero bias data (black markers) and simulated inelastic푝푝 collisions (filled red histogram) is shown. The simulation is normalized to the numberof tracks in data. Figure (a) shows the distribution of the number of hits in the pixel detector,and figure (b) shows the distribution of the absolute value of the transverse impact parameter,|푑0 | [138]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676.13 Figure (a) shows the radial distribution of reconstructed 퐾0S candidate vertices in 2018 zerobias data (black markers) and simulated inelastic 푝푝 collisions (stacked histogram). Verticesin simulation are separated into three categories based on the number of LRT tracks includedin the vertex fit. The total number of vertices in simulation is normalized to the number ofvertices in data. The four pixel layers and the first SCT layer are shown in the figure withdashed vertical lines. Figure (b) shows the fractional distribution of the same 퐾0S candidatesin data andMC comparing vertices reconstructed with two standard (STD) tracks and at leastone LRT track. Both figures indicate that LRT efficiency in data closely matches MC [138]. 686.14 Processing time (a) and disk space (b) taken per event versus average pileup 〈휇〉 to reconstructthe same data events, comparing the Run 2 (green squares) and Run 3 (purple unfilled circles)reconstruction software. The Run 3 numbers are also presented, including the impact of theadditional LRT tracking pass (blue filled circles). The bottom panels depict the time taken asa fraction of the Run 2 result. The disk space values reflect the output of the ID reconstructionin the ATLAS EDM format [130]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68xviiList of Figures6.15 Optimizing the LRT algorithm improves the yield of two types of displaced HNL decayvertices by reducing the number of fake reconstructed tracks and thus improving the displacedvertex reconstruction performance. Vertices producedwith theRun 2 reconstruction softwareare plotted with blue triangles. Vertices produced with the Run 3 LRT configuration arepurple squares and show increased signal reconstruction efficiency. Removing the filterfurther improves the efficiency, and these vertices are shown with a dashed purple line. Inthis figure, v8 refers to the final version of the LRT configuration ultimately included in thedefault reconstruction software. The quantity on the x-axis is the reconstructed HNL massas defined in chapter 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.1 The allowed combinations of |푈훼 |2/|푈tot |2 that are consistent with NuFIT fits to neutrinooscillation data [141]. The allowed regions under normal (blue) and inverted (green) hierar-chy are shown. The red cross markers represent two benchmark models that are chosen andagreed upon by the community [140]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737.2 Feynman diagrams for the HNL production and decay modes targeted in this analysis. Theflavors of the leptons in the diagrams, labeled by 훼, 훽, and 훾, are either muons or electrons.If the charged leptons in the HNL decay have the same flavour, then both the diagrams withthe virtual푊 (a,c) and virtual 푍 (b,d) contribute to the process. Lepton number conserving(a,b) and lepton number violating (c,d) processes are shown. Equivalent processes are alsovalid for an initial state푊− boson [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747.3 Kinematic distributions of truth-level quantities from simulated HNL signal in the 휇−휇휇channel. Plots are shown for a 10GeV HNL with proper lifetimes 푐휏N = 1, 10, 100mm.Each of these quantities is used in the analysis selection. . . . . . . . . . . . . . . . . . . . 767.4 The main steps in the VSI vertexing algorithm. A full description of the algorithm can befound in reference [136]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 807.5 The total displaced vertex reconstruction efficiency (휀total) as a function of displaced vertexradius (푟DV) for the custom configuration used in this analysis. The definition of the displacedvertex reconstruction efficiency can be found in reference [136]. The efficiency is shown for휇−휇휇, 휇−휇푒, and 휇−푒푒 signals with 푚N = 10GeV and 푐휏N = 10mm. . . . . . . . . . . . 817.6 A schematic outline of elements of the analysis framework pipeline and successive datastructures. Data and Monte Carlo have different entry points but are otherwise processedidentically. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 837.7 (a) HNL signal cutflow for analysis preselection requirements and signal region selection.The cutflow shown corresponds to a 휇−휇휇 HNL signal with 푚HNL = 10GeV, 푐휏 = 10mm.(b) The selection efficiency for all 푚N–푐휏N points for 휇−휇휇 HNL samples [1]. Each bin in(b) reflects the final bin in the corresponding cutflow. The cutflow shown uses an out-of-dateweighting scheme, hence the difference in value between the final bin and the efficiency map. 88xviiiList of Figures7.8 The two-dimensional distribution of 푚DV and 푟DV. Shown is the difference between the OS-and SS-vertex distributions in the VR. The 푧-axis is saturated at 30 to provide a scale thatdistinguishes between small positive (more OS- than SS-DVs) and small negative (more SS-than OS-DVs) entries. The solid red line represents the DV selection applied in each channelto remove backgrounds from heavy-flavour decays [1]. . . . . . . . . . . . . . . . . . . . . 917.9 The 푚DV distributions of OS and SS DVs in the validation region, for (a) 푒휇, (b) 휇휇, and (c)푒푒 DVs. These demonstrate that the SS and OS DV distributions generally agree well, in linewith the assumption that the dominant residual background for the search is that of random-crossing vertices, which is then estimated by a data-driven method. The disagreementsvisible here result partly from the remaining nonrandom-crossing backgrounds, which areaccounted for with a systematic uncertainty (see section 7.7) [1]. . . . . . . . . . . . . . . . 937.10 SS DVs in the VR with the metastable particle veto and material veto for 푒푒 DVs applied.SS DVs are separated by DV charge in ℓ+ℓ+ and ℓ−ℓ− DVs. The event yields are shown inthe legend of each plot. No significant differences in the two types of DVs are seen. . . . . 957.11 푚HNL distribution of SS background events, where the DV and prompt lepton are fromthe same event (gray circles) and the distribution obtained by taking SS DV and randomlyshuffling each vertex with a prompt lepton from a different event in the SR (colouredtriangles). A KS goodness-of-fit test indicates that the distributions are compatible. Theshuffling factor 푓 (ratio of the number of shuffled events to the number of original SSbackground events) is shown on each plot. . . . . . . . . . . . . . . . . . . . . . . . . . . 967.12 The overall tracking uncertainty from the tracking performance group’s central recommen-dations. The value in each bin is used as the probability that a track will be randomly removedwhen calculating the impact on the signal selection efficiency. . . . . . . . . . . . . . . . . 997.13 This cutflow shows the reduction in the number of vertices when randomly removing aproportion of tracks using the tracking performance group’s recommendations. The averagereduction in efficiency is 2.6% at the DV type cut. . . . . . . . . . . . . . . . . . . . . . . . 1007.14 Kinematic distributions of several relevant variables illustrating the effect of randomly re-moving tracks from the sample. A small reduction in total events is seen, but no clear shapedependence. Sample shown: 휇−휇휇, 푐휏N = 10mm, 푚N = 10GeV. . . . . . . . . . . . . . 1007.15 The dominant signal uncertainty is due to differences in the reconstruction of displacedvertices and tracks between data and MC produced with Pythia8.186. Only events in theVR are observed. The uncertainty is evaluated by comparing 퐾0푆 → 휋+휋− event yields inbins of 푝T and 푟DV. The data/MC ratio is normalized to the bin nearest the IP, where thetracking and vertex reconstruction algorithms are expected to be most robust. Higher-푝Tvertices are grouped in larger low-푟DV “normalization bins” since fewer displaced verticespopulate bins near the IP. The highest-푝T bin contains all vertices with 푝T > 35GeV. Thesymmetrized difference from 1.0 is applied to each signal vertex as a per-event systematicvariation [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101xixList of Figures7.16 Real and simulated data are processed differently in the DRAW pipeline. MC has only filteremulator applied to LRT objects. Data has a filter applied to standard objects as well as afilter emulator applied to LRT objects. This introduces a discrepancy in the signal acceptancebetween data and MC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027.17 The displaced lepton ID systematic is derived by dividing all reconstructed leptons by allleptons that pass quality selection in bins of |푑0 |. The systematic is calculated in relation tothe prompt, 0–3mm bin. Displaced muon ID (a) is less affected than displaced electron ID(b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037.18 Summary plots for the 2QDH (NH) (two quasi degenerate HNLs, normal neutrino masshierarchy mixing, 푥푒 = 0.06, 푥휇 = 0.48, 푥휏 = 0.46) model in the Dirac-limit (a,c) andMajorana-limit (b,d). Shown are pre-fit plots (a,b) with background and HNL signal MCstacked, and post-fit plots (c,d) in which the pre-fit signal contribution is overlaid as a dashedline (post-fit signal contribution is zero). Figure from [1] supplemental material. . . . . . . 1077.19 The 푚HNL distribution in the signal (SR) and control (CR) regions for the observed data, theshuffled-event-model background normalized by the two-bin fit described in the text with itsuncertainty, and simulated signals with a proper decay length 푐휏N = 10 mm [1]. . . . . . . 1097.20 Summary of the observed 95% CL contours for the different HNL models in Dirac limit (a)and Majorana limit (b). The observed and expected 95% CL contours are shown for the2QDH (NH) model in the Dirac (c) and Majorana (d) limits. The green and yellow bandsshow the one and two standard deviation (휎) spreads for the expected limits [1]. . . . . . . . 110xxGlossary휈MSM Neutrino Minimal Standard Model1SFH One-HNL model with Single-Flavour mixing2QDH Two Quasi-Degenerate HNL modelALICE A Large Ion Collider ExperimentAOD Analysis Object DataATLAS A Toroidal LHC ApparatuSBR Branching RatioBSM Beyond the Standard ModelCC Charged-currentCERN European Organization for Nuclear ResearchCL Confidence LevelCMB Cosmic Microwave BackgroundCMS Compact Muon SolenoidCOM Centre of MassCP Charge-ParityCR Control RegionCSC Cathode Strip ChamberCTP Central Trigger ProcessorDELPHI DEtector with Lepton, Photon, and Hadron IdentificationDNN Deep Neural NetworkDV Displaced VertexECAL Electromagnetic CalorimeterxxiGlossaryEDM Event Data ModelEM ElectromagneticEW ElectroweakEWSB Electroweak Symmetry BreakingFCC Future Circular ColliderGRL Good Run ListGSF Gaussian-sum filterGUT Grand Unified Theoryh.c. Hermitian Conjugate (terms)HCAL Hadronic CalorimeterHL-LHC High-Luminosity Large Hadron ColliderHLT High-Level TriggerHNL Heavy Neutral LeptonIBL Insertable B-LayerID Inner DetectorIH Inverted Hierarchy (of neutrino masses)IP Interaction PointKS Kolmogorov-Smirnov testL1 Level-1LAr Liquid ArgonLEP Large Electron-Positron ColliderLH LikelihoodLHC Large Hadron ColliderLHCb Large Hadron Collider beautyLLP Long-Lived ParticleLNC Lepton-Number ConservingxxiiGlossaryLNV Lepton-Number ViolatingLO Leading OrderLRT Large-Radius TrackingMC Monte CarloMDT Monitored Drift TubeMLE Maximum Likelihood EstimateMS Muon SpectrometerNC Neutral-currentNH Normal Hierarchy (of neutrino masses)NLO Next-to-Leading OrderNN Neural NetworkNNLO Next-to-Next-to-Leading OrderNP Nuisance ParametersOS Opposite Sign (charge)PDF Parton Distribution FunctionPLR Profile Likelihood RatioPMNS Pontecorvo-Maki-Nakagawa-Sakata (matrix)POI Parameter of InterestPS Proton SynchrotronPSB Proton Synchrotron BoosterPV Primary VertexQCD Quantum ChromodynamicsQED Quantum ElectrodynamicsQFT Quantum Field TheoryRF Radio FrequencyROI Region of InterestxxiiiGlossaryRPC Resistive Plate ChamberRPVLL R-Parity Violating Long-LivedRTC Random Track Crossing (background)SCT Semiconductor TrackerSM Standard Model (of Particle Physics)SNO Sudbury Neutrino ObservatorySPS Super Proton SynchrotronSR Signal RegionSS Same Sign (charge)SUSY SupersymmetryTDAQ Trigger and Data Acquisition systemTGC Thin Gap ChamberTRT Transition Radiation TrackerVEV Vacuum Expectation ValueVH4b Vector boson to Higgs to Four 푏 quarks (process)VR Validation RegionVSI Vertexing Secondary Inclusive (algorithm)WP Working PointxxivAcknowledgementsFirst, I thank my professor, Alison Lister, for making this journey possible. For over a decade, she hasopened doors, instilled knowledge, and supported my education in the world of physics. Alison has been anoutstanding leader in the CERN community and in our lab and exemplifies the influence of an advisor whocares deeply about her students. Most of all, she’s been a wonderful friend.I thank my supervisory committee, Colin Gay, Ariel Zhitnitsky, and Jeremy Heyl, for their enlightingfeedback and for their instruction in my undergraduate courses many years ago. It has been a pleasure tohave your consistent expertise throughout my education.I gratefully acknowledge the financial support provided by UBC through the International DoctoralFellowship award. I also appreciate the support provided by ATLAS Canada, which enabled me to workat CERN for a large portion of my degree and attend several international workshops and conferences. Ithank CERN for the successful operation of the LHC that made this work possible; it is a truly monumentalachievement.To those in the ATLAS UBC lab, rarely have I had the pleasure of working among such wonderfulpeople. You are outstanding both as colleagues and friends. My fellow students, Sebastien, Steffen, Felix,Dominique, Robin H, Elham, Chris, and Vincent, and my mentors Matthias, Wojtek, and Colin, thank youfor many years of guidance and support. May thanks also to Nick Zacchia whose infectious love of scienceis a joy to witness.Thanks to the CERN community for the warm welcome during my year abroad. I will never forget thehikes, runs, and parties that brought so much levity to a challenging time. I would also like to thank thedisplaced HNL team for the brilliance and determination that produced an excellent publication. Christian,Margaret, Dominique, and others on the team, collaborating with such remarkable scientists was a uniqueopportunity.To my community, thank you for everything. You made sure that life outside of my academic bubblewas outrageously fun! Your rejuvenating presence kept me afloat in challenging times and for that, I amimmensely grateful. Thank you to my family, and especially to my incredible parents. You have encouragedme from my earliest years to value inquiry and education and have endlessly supported me in accomplishingmy academic goals.I would also like to express my gratitude to the land. This precious corner of our world has been areservoir of tranquility for me. The northwest coast, with its sublime forests, resolute mountains, and pensiveseas, is a place of deep beauty from which we can learn so much.And finally, saving the best for last, I express my infinite gratitude to my beloved partner Breanna. Youheld me up when I was down, celebrated my successes, and taught me, by example, how to best care formyself. Having a partner in life with such grace and capacity is what has made any of this possible. Thankyou for being with me, full of love, on this adventure.xxvChapter 1IntroductionThe Standard Model of Particle Physics (SM) is a powerful theory of matter. It describes the knownelementary particles and their interactions, and its predictions match experimental data with astoundingprecision. Nevertheless, our understanding of the universe remains full of questions that have yet to besatisfactorily answered.The neutrino is an elusive and enigmatic particle that may play a meaningful role in answering manyof these open questions. This nearly undetectable particle, which comes in three types, was thought to bemassless until only twenty years ago. However, the discovery of its peculiar tendency to change its varietyhas shown physicists that neutrinos do have mass. Extensions to the SM, which account for these masses,may provide hints to the universe’s mysteries of dark matter and matter-antimatter asymmetry. One suchextension predicts the existence of a new type of massive neutrino, or heavy neutral lepton (HNL), whichinteracts even more rarely with other SM particles.Colliding subatomic particles into one another at outrageous speeds, aside from being quite fun, helpsprobe these neutrino masses and many other puzzles in physics. The ATLAS detector at The Large HadronCollider (LHC) studies the rare particles created when the kinetic energy from accelerated protons isconverted into exotic states of matter.Most searches for new physics concentrate on very short-lived phenomena, focusing the reconstructionalgorithms on particles which are formed and decay almost instantaneously. However, many theories predictparticles with long enough lifetimes that they would decay at some macroscopic distance from the proton-proton (푝푝) collision point. A restructuring of ATLAS’s charged particle reconstruction algorithms isnecessary to be sensitive to such long-lived particle (LLP) signatures. By reconstructing displaced tracks(charged particle trajectories which originate some distance from the detector’s centre), ATLAS can extendits physics analyses into uninvestigated regions of phase space.Certain theories predict HNLs which decay within the inner detector volume of the ATLAS detector andwhose detection would rely on such modified algorithms. The following dissertation conducts a search forHNLs in√푠 = 13TeV 푝푝 collisions, which uses displaced track reconstruction to identify potential signatures.Recent improvements to the displaced tracking algorithm will substantially increase the sensitivity of thisanalysis. Such refinements and their implications are also discussed.This dissertation is organized as follows: Chapter 2 introduces the Standard Model and some of itsknown limitations. Chapter 3 presents a short history of the discovery of neutrino masses and the theoreticalbackground which motivates the existence of HNLs. It also summarizes the results of HNL searches inseveral experiments. Chapter 4 introduces the experimental facilities, focusing on key systems in the LHCand the ATLAS detector. Chapter 5 describes the reconstruction algorithms used to compute representations1Chapter 1. Introductionof particles interacting with the ATLAS detector. Particular attention is paid to the reconstruction of chargedparticles, so-called tracks, in the inner detector. Chapter 6 discusses the large-radius tracking (LRT) algorithmand its use in the reconstruction pipeline. The algorithm used in this dissertation’s HNL analysis is presented,as well as the optimizations which will allow for even more sensitive analyses in the future. Chapter 7 detailsthe search for HNLs performed with 푝푝 collisions recorded from 2015–2018. No excess signal was found,and exclusions limits are set for a range of HNL masses and coupling strengths.2Chapter 2The Standard Model of Particle PhysicsAt the heart of the rich field of high-energy physics lies the question: “what is the universe made of, and howdo its constituents interact?” Over several centuries of investigation, a robust theory has emerged that hasrevolutionized our understanding of the fundamental nature of matter and given us extraordinarily powerfultools to predict how this matter behaves. This theory, called the Standard Model of particle physics (SM),provides an elegant description of the fundamental particles contained in the universe and the forces throughwhich they interact.Although the SM provides the most accurate picture of our universe to date, it is clear that the storyis incomplete. Carefully designed experiments have revealed phenomena that the current theory does notreadily explain. Extensions to the SM have been proposed and are the active subjects of many experiments.What is described below is a summary of the particles and forces of the SM as currently understood, and inparticular, those most relevant to this thesis. The approach is guided by references [3], [4], and [5], whichthe reader is encouraged to consult for a more rigorous description.2.1 FormalismThe Standard Model is written in the formalism of quantum field theory (QFT) which describes quantummechanical interactions in a way consistent with special relativity. It describes the particle content of theuniverse as well as the dynamics of interaction between the various particles. In this theory, each fieldcorresponds to a type of particle. A Lagrangian describes the interactions between these fields as well astheir kinematics. The SM obeys certain constraints that dictate the allowable properties and interactions ofthese fields.2.2 Particle contentIn QFT, quantum-mechanical fields represent physical particles. In the SM, matter is composed of spin-halfparticles called fermions that interact by exchanging spin-one particles called bosons. These are so named forthe statistical mechanics each type of particle follows: spin-half particles obey Fermi-Dirac statistics, whilespin-one particles obey Bose-Einstein statistics. Every field in the SM has been experimentally observed,and the properties of each have been measured to often very high degrees of precision.As a quantum-mechanical state, each field can be fully described by a set of quantum numbers —conserved quantities which correspond to eigenvalues of operators that commute with the Hamiltonian.Quantum numbers are also referred to as charges. Colour charge is related to the strong force. Isospin, weak32.2. Particle contenthypercharge, and electric charge are related to the unified electroweak (EW) force (see section 2.6). Theparticles in the SM and their properties are depicted in fig. 2.1.Figure 2.1: This diagram represents the particle content of the SM and the forces by which each particleinteracts. The legend at the top specifies where to find each particle’s name, mass, quantum numbers, gaugeboson couplings, and fermion couplings. The upper pane depicts the unbroken symmetry configuration ofthe SM, while the lower pane depicts the SM after EWSB (see section 2.6). The left diagram shows the Higgspotential and the vacuum expectation value of the Higgs field. The mixing of electroweak gauge bosons isshown between the two panes on the right [6].FermionsFermions are subdivided into two classes, quarks and leptons. Each class comes in three generations. Eachgeneration has identical quantum numbers, except for their masses. A fundamental particle’s species is alsoreferred to as its flavour.Quarks are particles with fractional electric charge, that come with 푞 = + 23 (up, charm, top) or 푞 = −13(down, strange, bottom). Quarks also carry a colour charge (see section 2.4) and appear to naturally existonly in colourless bound states; a quark and an anti-quark of the same colour (meson), or a triplet ofdifferently-coloured quarks (baryons). Familiar baryons include protons (푢푢푑) and neutrons (푑푑푢), and acommon meson is the pion (e.g., 휋+ = 푢푑¯). Together these bound states are known as hadrons. Quarks42.3. Standard Model Lagrangianinteract through the weak, electromagnetic, and strong forces.Leptons are generally less massive than quarks. The charged leptons are electrons (푒), muons (휇), andtaus (휏), each of which carries unit electric charge. Charged leptons interact through the electromagneticand weak forces. The neutral leptons, neutrinos, are the only electrically neutral fermions and are, therefore,relatively difficult to detect as they interact exclusively through the weak force.A corresponding antiparticle exists for each particle type where every quantum number is reversed.Antiparticles have masses identical to their matching particles.Gauge bosonsThe spin-one gauge bosons are particles that mediate the forces experienced by fermions. Fermions interactthrough a fundamental force by the exchanging of relevant gauge bosons. The electromagnetic force ismediated by the photon (훾), which is massless and neutrally charged. The weak force is mediated by thecharged 푊+ and 푊− and the neutral 푍 electroweak bosons, each of which is massive. The strong force ismediated by the eight gluons (g), which, like the photon, carry no mass and no electric charge, though theydo carry the colour charge of the strong force.Higgs bosonThe only fundamental spin-0 particle in the SM is the scalar Higgs boson. This boson plays a distinctiverole in the SM as it is responsible for imparting mass to the fundamental particles through the mechanismof electroweak symmetry breaking (section 2.6). The variation in masses between flavours is directly due toeach flavour’s different coupling strength to the Higgs field.2.3 Standard Model LagrangianThe Lagrangian density1 L determines the dynamics and kinematics of the fields. The existing SM La-grangian was developed over decades by a continuous exchange between theoretical formulation and exper-imental observation. At the heart of the SM Lagrangian is the idea of physical symmetries. The Lagrangian(or, more precisely, the action) must remain unchanged under some set of transformations. These transfor-mations include the external transformations of relativistic Lorentz boosts to satisfy the constraints of specialrelativity, as well as internal transformations.The most important of these internal symmetries are the gauge symmetries in which a different configu-ration of the fields results in identical observable quantities. The rich phenomena of particle physics appearto arise from the requirement that the Lagrangian remains invariant under local, continuous gauge transfor-mations. This requirement prompts the appearance of gauge fields in the Lagrangian to preserve invariance.The structure of the gauge fields and how they couple to the fermionic fields define the interactions betweenparticles of matter.1Sometimes referred to only as the Lagrangian.52.4. Strong forceThe SM is a non-abelian2 gauge theory, invariant under the symmetry group퐺 = 푆푈 (3)푐 × 푆푈 (2)퐿 ×푈 (1)푌 . (2.1)The 푆푈 (3)푐 factor corresponds to quantum chromodynamics (QCD) which mediates the strong force.The combination of 푆푈 (2)퐿 ×푈 (1)푌 corresponds to the electroweak interactions through the boson fields푊푖 (푖 = 1, 2, 3) and 퐵. Through the process of electroweak symmetry breaking (EWSB), this group gives riseto the more familiar weak and electromagnetic forces (section 2.6). The 푐, 퐿, and 푌 subscripts in eq. (2.1)do not have any group theory significance but instead indicate the physical circumstance in which they areapplied. 푐 refers to the conserved colour charge of the strong force, 퐿 to the fact that the 푆푈 (2) couplingonly acts on left-chiral fields, and 푌 indicates the conservation of the weak hypercharge quantum number.2.4 Strong forceThe strong force, or QCD, is the theory that describes how quarks and gluons interact with one another.Quarks and gluons carry a set of three quantum charges, distinct from the electric charge, which is calledcolour charge: 푟, 푔, 푏. Experimental observations find that particles only exist in nature with zero net colourcharge, i.e., colour singlets. QCD is, therefore, confining so that the strong force’s range is restricted tosmall distances, on the order of the size of a nucleus. Another consequence is that as two quarks separate, itbecomes energetically favourable to break the colour field by producing new quarks.The Lagrangian of the strong force isLQCD =∑푞푞¯(푖훾휇퐷휇 − 푚푞)푞 − 14퐺푎휇휈퐺푎휇휈 . (2.2)The summation is over all six quark flavours, 푞 = 푢, 푑, 푐, 푠, 푡, 푏. 훾휇 represents the Dirac gamma matrices,and 푚푞 is the quark mass. 퐺푎휇 is the gluon field strength tensor which dictates the gluon self-interactionstrength. The covariant derivative 퐷휇 is the ingredient necessary to keep this Lagrangian invariant underlocal 푆푈 (3) transformations.2.5 Electroweak forceIn the SM, the weak force and the electromagnetic force are each aspects of the unified electroweak force.The weak force is notable in that it is the only force that can change the flavour of the fermion with which itinteracts, and every fermion in the SM experiences weak force interactions. Furthermore, the mediators ofthe weak force are massive bosons, as opposed to the massless gluons and photons.The electroweak 푆푈 (2)퐿×푈 (1)푌 factor is chiralmeaning the transformations act differently on left-chiral(휓퐿) and right-chiral (휓푅) fermions. The weak force acts exclusively on left-chiral fermions, which transformas flavour doublets. In contrast, right-chiral fermions are singlets under the electroweak transformations and2The composition of pairs of elements in an abelian group commute. In a non-abelian group, at least one pair does not.62.5. Electroweak forcethus unaffected by the weak force. In terms of the concrete SM fields, each of the three generations containsthe following:Left-chiral doublets:(휈푖푒푖)퐿≡ 퐿퐿 ,(푢푖푑푖)퐿≡ 푄퐿Right-chiral singlets: 푢푖푅, 푑푖푅, 푒푖푅, 휈푖푅?(2.3)with 푢 and 푑 referring to the quark fields and 푒 and 휈 referring to the lepton fields. The components of theleft-chiral doublets are weak flavour eigenstates which transform into one another under 푆푈 (2). Thoughit is not part of the current SM, a placeholder for 휈푅 is shown above as its existence is central to many ofthe proposed neutrino mass models (see section 3.3.3). If it were discovered, it would be listed among theright-chiral 푆푈 (2) singlets.The electroweak Lagrangian is typically written in four parts:LEW = Lgauge + Lfermion + LHiggs + LYukawa, (2.4)each of which is described below.The electroweak interactions are described byLgauge = −14푊푖휇휈푊푖휇휈 − 14퐵휇휈퐵휇휈 , (2.5)which contains the field strength tensors 푊 푖 (푖 = 1, 2, 3) for the 푆푈 (2)퐿 symmetry, and 퐵 for the 푈 (1)푌symmetry. Before EWSB, the bosons represented by these fields are not identified with the massiveelectroweak bosons.Lfermion =∑푓퐿휓¯퐿푖 /퐷휇휓퐿 +∑푓푅휓¯푅푖 /퐷휇휓푅 (2.6)is the kinetic term for the SM fermions. The first sum is over all left-chiral doublets, and the second sumis over all right-chiral singlets. /퐷 (written with Feynman slash notation), is the covariant derivative, whichmaintains invariance of the Lagrangian under 푆푈 (2) and푈 (1) transformations.LHiggs = (퐷휇휙)†퐷휇휙 −푉 (휙) (2.7)contains the complex scalar Higgs field 휙 and its interactions with the gauge bosons and with itself. Thepotential term is푉 (휙) = 휇2휙†휙 + 휆(휙†휙)2. (2.8)휇 and 휆 relate to EWSB as described in the following section.LYukawa =∑gen.−푦푢푄퐿 휙˜푢푅 − 푦푑푄퐿휙푑푅 − 푦푒퐿퐿휙푒푅 + (ℎ.푐.) (2.9)describes the set of scalar-fermion Yukawa interactions. The first term represents up-quark-like interactions,72.6. Electroweak symmetry breaking and the Higgs mass mechanismthe second, down-quark-like ones, and the third, charged lepton interactions. The factors 푦푢, 푦푑 , and 푦푒 arethe coupling strengths for each interaction, and the summation is over the three generations of fermions. Theconjugate Higgs field 휙˜ is defined as 휙˜ = 푖휎2휙†, and (ℎ.푐.) signifies the Hermitian conjugate terms. Here theleft-chiral doublets and the right-chiral singlets couple to the Higgs doublet, which, after EWSB discussedbelow, is the source of fermion masses.Notably, fermion masses do not yet appear in the SM Lagrangian. Due to the lack of left-right chiralsymmetry in the 푆푈 (2)퐿 factor of the SM gauge group, terms such as 푚휓¯휓 would violate gauge invariance.This appears to be problematic as there is a long history of observations that the universe does indeed containmass. Furthermore, the푊± and 푍 bosons are observed to have relatively large masses, though they too arewithout a mass term in the above Lagrangian. Fortunately, the non-static nature of the Higgs potential ineq. (2.8) provides a neat solution by breaking a symmetry of the SM.2.6 Electroweak symmetry breaking and the Higgs mass mechanismAs seen previously, it is not possible to add a mass term to the SM Lagrangian “by hand,” in a way that leavesit invariant under the transformations of the gauge group. However, by allowing for the existence of a complexscalar doublet 휙 an effective mass term may be generated by spontaneous electroweak symmetry breaking(EWSB). In this process, the 푆푈 (2)퐿 ×푈 (1)푌 gauge group breaks down into the weak and electromagneticinteractions.The complex scalar doublet of 푆푈 (2)퐿 , which has become known as the Higgs field is휙 =(휙+휙0), 휙+, 휙0 ∈ C, (2.10)which has four independent degrees of freedom. The superscripts indicate positive and neutral electriccharges and C represents the set of complex numbers.The lowest-energy state, called the vacuum expectation value (VEV), is given by 〈0|휙|0〉 ≡ 〈휙〉 where|0〉 is the vacuum state with zero particles. Its value is located at the minimum of the potential 푉 (휙).Considering the Higgs potential of eq. (2.8), if 휇2 > 0, the VEV is simply a stable global minimum at theorigin, 휙†휙 = 0.However, if the potential evolves so that 휇2 < 0, as is hypothesized to have happened shortly after thebig bang, the picture becomes quite different. In this case, the global minima form a hypersphere with thevalue:휙†휙 =−휇2휆≡ 푣2 (2.11)such that푣 =√−휇2휆. (2.12)The consequence of this is that the corresponding field is no longer vanishing but has a finite VEV 푣 withunits of mass. The minima are degenerate along the hypersphere, but the axis in this four-dimensionalspace can be rotated by an 푆푈 (2) ×푈 (1) transformation to specify a particular minimum. Without loss of82.6. Electroweak symmetry breaking and the Higgs mass mechanismgenerality, one can choose the axis so that only one of the four components of 휙 is left nonzero, namely thereal part of the 휙0 component휙 =(0퐻). (2.13)The nature of the minima in the hypersphere can be visualized by depicting only the 휙0 component as seenin fig. 2.2. This choice of a definite ground state breaks the 푆푈 (2)퐿 × 푈 (1)푌 invariance, though leavesthe ground state invariant under a set of 푈 (1)푄 transformations corresponding to electromagnetism andconserving electric charge, Q.Re(휙0) Im(휙0)푉 (휙0)Figure 2.2: The “champagne” shape of the 휙0 component of the Higgs potential. The potential contains acircle of degenerate local minima. A choice of definite ground state breaks the 푆푈 (2)퐿 ×푈 (1)푌 invarianceand provides the Higgs field with a VEV [7].Expanding the ground state of eq. (2.13) as small perturbations about the chosen minimum and workingin the unitary gauge to remove the additional degrees of freedom, the scalar doublet becomes휙 =(0푣 + ℎ(푥)/√2), (2.14)where the ℎ(푥) defines a Hermitian scalar field associated with the physical Higgs boson.The scalar doublet of eq. (2.14) can then be substituted into the full SM Lagrangian. In the electroweaksector, the expansion of the scalar field in LHiggs brings about the masses of the electroweak gauge bosons.푊 푖 and 퐵 are no longer mass eigenstates, but they can be redefined by diagonalizing the mass matrix withthe linear combinations푊±휇 =1√2(푊1 ∓ 푖푊2)(푍휇퐴휇)=(cos 휃푊 − sin 휃푊sin 휃푊 cos 휃푊) (푊3휇퐵휇), (2.15)where 휃푊 is the weak mixing angle. These represent the familiar, and now massive, electroweak gaugebosons푊± and 푍 , and the massless photon field 퐴.Vitally, the expanded scalar Higgs doublet can be substituted into eq. (2.9) to generate mass terms.Considering for the moment only the electrons, the Yukawa terms of the Lagrangian take the formLYukawa,푒 = −푦푒 푒¯퐿 (푣 + ℎ/√2)푒푅 + (ℎ.푐.). (2.16)92.7. Successes and limitations of the Standard ModelTherefore the mass term is푚푒 푒¯퐿푒푅 with푚푒 = 푦푒푣 where 푣 is the Higgs VEV. The coupling strength betweenthe electron and the Higgs field ℎ is proportional to the same Yukawa coupling constant 푦푒. This form of themass term, which connects the two chiral components, is known as the Dirac mass. All fermions in the SM(perhaps except for neutrinos) gain mass by this Yukawa coupling and EWSB.2.7 Successes and limitations of the Standard Model2.7.1 SuccessesThe particle content shown in fig. 2.1 represents all visible matter in the universe. The relatively simpleLagrangian densities presented above describe the dynamics of this matter. This model is not only succinct,but it contains remarkable predictive power. The SM postulated the existence of several particles and theirproperties before experiments discovered evidence of them. Particles predicted and later discovered includethe푊± and 푍 bosons [8], the gluon [9], the top quark [10], the charm quark [11], and the Higgs boson [12].Many decades of experimental research agree with the SM’s theoretical predictions. For example,fig. 2.3 summarizes ATLAS measurements of cross sections for various production processes which agreewith theoretical predictions over ten orders of magnitude [13].However, the SM requires several experimental inputs to obtain the numerical values of its several freeparameters. In total, 19 independent parameters are inputs to the SM: nine Yukawa couplings which dictatethe particle masses; three mixing angles and one phase that defines the quark mixing matrix; three gaugecouplings corresponding to the three gauge groups; the QCD vacuum angle; and the VEV and mass of theHiggs field.2.7.2 LimitationsDespite its incredible successes, the SM still has some substantial experimental and theoretical deficiencies.For example, the lack of a satisfying explanation of gravity is seen as a considerable shortcoming of the theory.Though effective field theories exist that account for gravity, they still contain serious incompatibilities withthe SM [14]. The observation of neutrino oscillations, discussed at length in chapter 3, is another phenomenonthat the existing SM does not readily explain. One of the most prominent theoretical peculiarities is theso-called hierarchy problem in which quantum corrections to the Higgs mass require a high degree of fine-tuning in order to obtain the observed mass within the existing theoretical framework [15]. These problemspoint to the possibility that the existing SM is only the low-energy limit of a more fundamental theory.Below, selected observations inconsistent with the existing theory are discussed.Dark matterThere is firm astrophysical evidence for the existence of a type of matter that may interact with knownbaryonic matter through gravitation alone. The most direct evidence comes from galactic rotation curveswhere the observed luminous matter differs significantly from the distribution of mass indicated by thestellar velocity profile. Other compelling evidence comes from gravitational lensing measurements, cosmic102.7. Successes and limitations of the Standard Modelpp 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: February 2022ATLAS 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 2.3: Summary of SM cross section measurements at the ATLAS detector as of February 2022. Themeasurements are corrected for branching fractions, compared to the corresponding theoretical expecta-tions [13].microwave background (CMB) radiation, and other sources. A comprehensive review of the evidence isavailable in reference [16]. Such observations indicate that dark matter outweighs baryonic in our universeby over a factor of 5:1 [17]. Despite concerted efforts to identify the source of dark matter, there has yet tobe any direct observation of a dark matter candidate. This suggests that dark matter may interact with theknown SM particles only very feebly, if at all [18].Baryon asymmetryThe overabundance of (baryonic) matter in the universe, as opposed to antimatter, is another puzzlingobservation that remains unexplained by the SM. According to the prevailing cosmological theory, theuniverse produced in the Big Bang contained equal numbers of particles and antiparticles. However, twoindependent observations show that matter dominates over antimatter in the present universe.3 Analyses ofthe power spectrum of the CMB and the products of big bang nucleosynthesis each reveal asymmetry values3Other than the obvious local overabundance of matter over antimatter.112.7. Successes and limitations of the Standard Modelin agreement with one another [19].In 1967, Sakharov proposed physical conditions which would be required to produce such an asymmetry.In his proposal, a suitable theory would have baryon number violation, C-symmetry and CP-symmetryviolation, and out-of-thermal equilibrium dynamics leading to a degree of irreversibility. Certain theories,such as that of leptogenesis via a Majorana neutrino, lepton number violating processes in the early and hotuniverse could produce the observed baryon-antibaryon imbalance [20].12Chapter 3Neutrino masses and heavy neutral leptonsThe matter content of the SM contains right-handed and left-handed chiral states of each fermion exceptfor the neutrino, which only interacts via its left-handed state. Since the right-handed neutrino 휈푅 does notcouple to the SM gluons or electroweak gauge bosons, there is no evidence that it exists at all. Consequently,the current formulation of the SM is one in which neutrinos carry no mass, which was consistent withobservation for many years.However, since the late 1960s, observations began to show some anomalies that can now be interpretedas neutrinos transforming from one flavour state to another — a phenomenon only possible if neutrinos do,in fact, carry mass. Subsequent experiments have measured these oscillations with increasing sensitivity,and it is now clear that neutrinos have an exceptionally small but non-zero mass, on the order of O(0.1 eV).If the neutrino were to acquire mass the same way as other fermions, through electroweak symmetrybreaking, the peculiar smallness of its coupling to the Higgs field might be puzzling. However, an alternativecalled the seesaw mechanism leads to appropriately small SM neutrino masses while predicting right-handedcounterparts with relatively high mass. The following summary will present the relevant observations andtheoretical framework to understand the basics of the neutrino seesaw.3.1 Neutrino oscillationUnique among the SM fermions, neutrinos have no colour or electric charge and are thus only detectablethrough their weak-force interactions with charged SM fermions. The SM neutrinos, 휈푒, 휈휇, and 휈휏 , areflavour states defined by the flavour of the charged lepton with which they interact. Observations haveshown that these are not the fundamental free particle states, as evidenced by the phenomenon of neutrinooscillation. The following summarizes notable experiments which lay the observational foundation for suchoscillations. A more complete review can be found in references [21–24].3.1.1 A brief history of detectionEarly in the 20th century, a critical violation of energy conservation appeared to be taking place insideradioactive 훽-decay. In the process where a nucleus emits an electron and increases its charge,퐴푍X→ 퐴푍+1X′ + 푒−, (3.1)the electron energy was expected to equal the difference in nuclear masses Q. Instead, what was observedwas a continuous spectrum like that in fig. 3.1 [25, 26]. Nearly 20 years later, Wolfgang Pauli, in a133.1. Neutrino oscillationFigure 3.1: Electron spectrum of nuclear 훽-decay. This apparent violation of energy conservation promptedPauli’s suggestion of a “dark particle.” [22]“desperate remedy,” proposed that a neutral and relatively light particle was also being produced andescaping undetected [27, 28]. If the sum of energies of the electron and the undetected particle was equalto the nuclear mass difference, energy conservation could be saved. Enrico Fermi, who was among the firstto take Pauli’s idea seriously, gave this neutral particle an Italian moniker meaning “little neutral one,” andwith it developed the theory of 훽-decay [29].This interaction also allows for the absorption of neutrinos via the inverse beta process, 휈¯푝 → 푛푒+,though it was estimated to have an exceptionally low cross section: 휎휈¯ ≤ 10−44 cm2 at 퐸 휈¯ ∼ 2MeV. Thiswould mean the neutrino has a mean free path of thousands of light-years in water.In 1956 Reines and Cowenwere the first to definitively detect neutrinos by placing large water-tank-baseddetectors near a nuclear reactor [30] (though, as scientists at Los Alamos, a fission bomb was originallythe proposed source! [31]). The enormous neutrino flux from the reactor interacted with the protons in thewater, producing a neutron and a positron which produced gamma rays in delayed coincidence.Bruno Pontecorvo, in a 1958 paper, began to entertain the idea that oscillations may occur betweenneutrino and antineutrino states [32]. At that time, it was believed that only one flavour of neutrino existed.In the early 1960s, Maki, Nakagawa, and Sakata discussed that the neutrino associated with the electron 휈푒might be a different particle than the neutrino associated with the muon [33]. As evidence appeared thatthe neutrino did come in at least two flavours, Pontecorvo, in a seminal 1968 paper, suggested they mightoscillate into one another and that the evidence of such oscillations could be found by studying neutrinosproduced in the sun [34]. It was not until 1998 that the Super-Kamiokande experiment announced the directobservation of neutrino oscillations by measuring atmospheric neutrinos [35].3.1.2 Neutrino oscillation experimentsMethods to measure the oscillation of neutrino flavours comes in two signatures: first, the appearance ofthe “wrong” type of charged lepton from a source of known neutrino flavour and flux, and second, thedisappearance of the “right” type of charged lepton. Both have been used in various experiments to measureneutrino flux from the sun, supernovae, the atmosphere, nuclear reactors, and accelerator beams.143.1. Neutrino oscillationFigure 3.2: The 푃(휈푒 → 휈푒) survival probability as a function of distance for 3MeV 휈푒 assuming 휃13 = 10◦.The two components of 휈푒 flavour oscillation are clearly distinguishable [24].Solar neutrinos are produced in the nucleosynthesis processes of the sun. The relatively rare solarprocess of boron-8 훽-decay (85B→84Be∗ + 푒+ + 휈푒) produces electron neutrinos with energies up to 15MeV,useful for earth-based detection experiments. Radiochemical experiments (Homestake [36], SAGE [37], andGALLEX [38]) measured a deficit in the 휈푒 flux, and later Čerenkov experiments (Super-Kamiokande [39])confirmed this “solar neutrino problem.” The Sudbury Neutrino Observatory (SNO) used heavy water toseparately detect the 휈푒 and total neutrino flux from the sun. It found that the total flux matched predictionsbut detected a substantial 휈휇 + 휈휏 component. Since only 휈푒 is produced substantially in the sun, the SNOexperiment showed clear evidence of neutrino flavour transformation [40].Atmospheric neutrinos are created when cosmic rays interact with the atmosphere, mainly via theproduction of pions. Consider the dominant decay process of a 휋− or 휋+ meson:휋− → 휇− + 휈휇 → (푒− + 휈푒 + 휈휇) + 휈휇휋+ → 휇+ + 휈휇 → (푒+ + 휈푒 + 휈휇) + 휈휇(3.2)It is clear that (for sufficiently low energies)4 that the ratio of muon-type neutrinos to electron-type neutrinosfrom the atmosphere is 2:1. Since the 1980s, this ratio has been measured by several experiments includingseveral calorimeter-like detectors (NUSSEX [41], Frejus [42], Soudan 2 [43], and MACRO [44]), andwater Čerenkov detectors (Kamiokande [45] and IMB [46]). Some of these experiments indicated thatthe flux of muon-type neutrinos was significantly less than expected. In 1998 the Super-Kamiokandeexperiment announced results that demonstrated beyond any reasonable doubt that muon neutrinos wereindeed disappearing along their path from the atmosphere to the detector [35]. Furthermore, it found thatonly the 휈휇 flux was much lower if it came from beneath the detector (i.e., from the atmosphere on the otherside of the earth). This observation was strong evidence for the oscillation of muon neutrinos into othertypes.Further experiments revealed that neutrino oscillation occurs on two different length scales thus manyexperiments come in “short-baseline” and “long-baseline” types. Reactor neutrinos are produced at high4An increase in the energy of the muons decreases the fraction of those muons that decay in flight.153.2. Mass and weak eigenstatesflux from the decay of radioisotopes produced in fission reactors. The short-wavelength component,O(1 km),is often measured by reactor neutrino experiments (Daya Bay [47], RENO [48]). Accelerator neutrinos,produced in a beam by the decay of accelerated muons, are used to measure the long-wavelength component,O(100 km), in experiments such as MINOS [49].3.2 Mass and weak eigenstatesFrom these observations, it is clear that neutrinos oscillate to different flavours of charged lepton with whichthey interact. Just as is done for quarks, one can identify the mass eigenstates as the stationary states ofthe free-particle Hamiltonian, and the weak eigenstates (or flavour eigenstates) as the states interacting withthe respective charged lepton. There is no reason why mass eigenstates need to be identical to flavoureigenstates, and neutrino oscillation indicates that they are not. The following “plane wave” derivationpresents a simplified model involving two neutrinos which can be easily extended to the three-neutrino case.3.2.1 Two-neutrino systemFirst, consider a system consisting of two neutrinos where the weak eigenstates, 휈푒 and 휈휇, are coherentlinear superpositions of the mass eigenstates, 휈1 and 휈2. The mass eigenstates have rest mass 푚1 and 푚2respectively and propagate as plane waves like|휈1(푡)〉 = |휈1〉푒푖 (p1 ·x−퐸1푡) = 푒−푖 푝1 ·푥|휈2(푡)〉 = |휈2〉푒푖 (p2 ·x−퐸2푡) = 푒−푖 푝2 ·푥(3.3)where 푝 · 푥 = 퐸푡 − p · x is the Lorentz-invariant phase.A 2 × 2 unitary matrix relates the mass and weak eigenstates and can be expressed with a single mixingangle 휃 by (휈푒휈휇)=(cos 휃 sin 휃− sin 휃 cos 휃) (휈1휈2). (3.4)So a neutrino produced in the process u → de+휈푒 will propagate as the coherent superposition of the masseigenstates 휈1 and 휈2,|휈푒 (x)〉 = cos 휃 |휈1〉푒−푖 푝1 ·푥 + sin 휃 |휈2〉푒−푖 푝2 ·푥 . (3.5)The proportion of mass eigenstates then depends on both the mixing angle 휃 and the difference between thephases Δ휙12 = (푝1 · 푥) − (푝2 · 푥). To find the probability that the state that was initially produced as 휈푒 willinteract at some distance 퐿 as 휈휇 to produce a muon is found by contracting with the 〈휈휇 | state:〈휈휇 |휈푒 (퐿)〉 = sin2(2휃)sin2(Δ휙122). (3.6)At this point, some assumptions are made that, although reasonable, are not rigorous. By assuming that푚휈 퐸휈 , that 푝1 ≈ 푝2 = 퐸 , and that the mass eigenstates propagate with the same velocities (namely163.2. Mass and weak eigenstates푣 ≈ 푐), we find that the 휈푒 → 휈휇 transition probability is푃(휈푒 → 휈휇) = 〈휈휇 |휈푒 (퐿)〉 = sin2(2휃)sin2(Δ푚2124퐸퐿). (3.7)It follows that the survival probability of an electron neutrino can be found using the conservation ofprobability, 푃(휈푒 → 휈푒) = 1 − 푃(휈푒 → 휈휇). Ultimately the flavour oscillation depends on the mixing angle휃 and the mass difference of the mass eigenstates Δ푚212.A more rigorous derivation accounts for the velocity difference in mass eigenstates by treating them aswave packets. An even more formal treatment uses the framework of QFT and effectively treats the neutrinoas a virtual particle exchanged between the interactions at the source and the detector. Fortunately, each ofthese approaches gives the same result as the plane wave approximation, eq. (3.7).3.2.2 Three-neutrino system and the PMNS matrixExtending the same mass-flavour eigenstate relationship to three neutrinos is done using the 3 × 3 unitaryPontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix푈PMNS [33].©­­«휈푒휈휇휈휏ª®®¬ =©­­«푈푒1 푈푒2 푈푒3푈휇1 푈휇2 푈휇3푈휏1 푈휏2 푈휏3ª®®¬©­­«휈1휈2휈3ª®®¬ . (3.8)The unitarity of the PMNS matrix ensures푈−1 = 푈† ≡ (푈∗)푇 , and푈†푈 = 퐼.If 푈PMNS were real it could be described by three rotation angles 휃12, 휃13, and 휃23. However, it iscomplex and needs an additional six complex phases. Five of these can be absorbed into the neutrino andcharged lepton states with no physical consequences, and so the full description of푈PMNS needs only a singlecomplex phase 훿 in addition to the rotation angles.5The full expression for the survival probability of an electron neutrino is then푃(휈푒 → 휈푒) = 1 − cos4(휃13) sin2(2휃12) sin2(Δ푚2214퐸휈퐿)− sin2(2휃13) sin2(Δ푚2324퐸휈퐿), (3.9)where Δ푚2푖 푗 ≡ (푚2푖 −푚2푗).6 As experiments have found that Δ푚221 Δ푚232, this quantifies the disappearanceof 휈푒 with oscillations on two different length scales. The short-wavelength component depends on Δ푚232while the long-wavelength component depends on Δ푚221. The mass splittings can be measured by observingneutrinos at different distances or varying the neutrino production energy. The rate of oscillation in thethree-flavour scenario thus depends on six independent parameters: the three mixing angles, one complexphase, two mass differences.KamLAND (a long-baseline reactor experiment) and MINOS (a long-baseline muon-beam experiment)5In the case of three Majorana neutrinos, no independent right-handed field exists, and only three phases can be absorbed by thefields. In this case, the푈PMNS needs three complex phases instead of one. See reference [21] for a more complete description.6The oscillations depend on only two differences in 푚2 of the mass eigenstates as Δ푚221 and Δ푚232 (Δ푚231 = Δ푚232 + Δ푚221).173.3. Mass mechanismshave measured the mass differences to < 5% precision [21, 24]:Δ푚221 = (7.6 ± 0.2) × 10−5eV2, |Δ푚232 | = (2.3 ± 0.1) × 10−3eV2 . (3.10)Note that only the absolute value of Δ푚232 has been measured, which gives rise to the question of neutrinomass hierarchy. The differences in neutrino masses have been precisely measured, but not the absolutevalues. It is possible that either 푚3 > 푚1≈2 or 푚3 < 푚1≈2 and no experiment to date has determinedthe correct ordering [50]. The upper bound on the sum of neutrino masses is found from cosmologicalobservations to be∑푖 푚휈푖 < 0.2 eV [21].Results from several experiments including SNO, KamLAND, Super-Kamiokande, MINOS, Daya Bay,Reno, and Double Chooz have together measured the following values for the mixing angles [21, 24]:sin2(2휃12) = 0.87 ± 0.04, sin2(2휃23) > 0.92, sin2(2휃13) = 0.10 ± 0.01 (3.11)Only in 2012 was 휃13 found to be non-zero. Finally, the phase 훿 has yet to be measured and is the focusof next-generation experiments. Its existence has consequences for charge-parity (CP) violation in neutrinooscillations [51].3.3 Mass mechanismsThere are two common ways to extend the SM to produce a neutrino mass. The first predicts that theneutrino is a Dirac fermion, in which the corresponding mass mechanism is straightforward, though arguablyunsatisfying. The second predicts that the neutrino may be a Majorana fermion and that the small neutrinomasses are due to the presence of much heavier neutrinos that have yet to be detected. This section willfocus exclusively on the electron generation, but the argument extends naturally to the other generations ofleptons. The following combines derivations found in references [4, 21, 22, 24].3.3.1 Dirac massConsider the left-chiral lepton doublet 퐿퐿 (see eq. (2.3))퐿퐿 =(휈퐿푒퐿). (3.12)A simple extension to the SM is to introduce a new right-handed neutrino 휈푅 that transforms as a singletunder all SM gauge groups. This field is distinct from the existing right-handed lepton singlet 푒푅. TheYukawa factor in the Lagrangian of eq. (2.9) then contains the term−LYukawa ⊃ 푦휈퐿퐿 휙˜휈푅 + (ℎ.푐.)= 푦휈 (푣 + ℎ/√2) 휈¯퐿휈푅 + (ℎ.푐.)(3.13)183.3. Mass mechanismswhere the second line is the result of EWSB of the Higgs scalar doublet 휙˜ (see section 2.6). Therefore, theneutrino acquires a Dirac mass,푚퐷 = 푦휈푣 (3.14)where 푣 is the VEV of the Higgs field. This is the same mechanism by which the up-type quark acquiresmass when coupled to the quark doublet 푄퐿 in eq. (2.9). The Dirac mass term for the neutrino is then−L퐷 = 푚퐷 (휈푅휈퐿 + 휈퐿휈푅) (3.15)Aside from the Yukawa interaction with the Higgs doublet, this right-handed neutrino would have no otherinteractions via the SM since it is a singlet of the complete SM gauge group.This results in a valid mass term and implies that a right-handed chiral neutrino exists, yet this mechanismis not entirely satisfying. The neutrino masses (and therefore the Yukawa coupling constant 푦휈) are smallerthan the other fermion masses by an order of 106, which could be seen as suspicious. Perhaps there is anothermechanism responsible for the smallness of the neutrino mass.3.3.2 Majorana massAn alternative mechanism by which neutrinos can acquire mass is through a Majorana mass term. First, letthe CP conjugate field for the right-handed neutrino be defined as휈푐푅 = 퐶ˆ푃ˆ휈푅 (3.16)which corresponds to a left-handed antineutrino 휈퐿 . 퐶ˆ is the charge conjugate operator and the 푃ˆ is theparity transformation operator. The Majorana mass term, then, can be written as−L푀 = 12푀 (휈푐푅휈푅 + 휈푅휈푐푅) . (3.17)where푀 is theMajorana mass. Since this is formed from right-handed neutrino and left-handed antineutrinofields alone, both of which transform as singlets under the full SM gauge transformations, this mass termdoes not break the gauge invariance of the SM. It is worth highlighting that this proposed “bare” mass termis unique among SM fermions, the rest of which are not singlets under all SM gauge groups and therefore donot allow this type of bilinear coupling [24].3.3.3 Type-I seesaw mechanismIt is now possible to re-express the Dirac and Majorana mass terms to combine both masses in matrix form.After some algebra, it is found that the masses of the physical states notably relate to one another.Rewriting the Dirac Lagrangian of eq. (3.15) as−L퐷 = 12푚퐷 (휈퐿휈푅 + 휈푐푅휈푐퐿) , (3.18)193.3. Mass mechanismswe can combine it with the Majorana Lagrangian to form the most general renormalizable Lagrangiancontaining neutrino masses:−L퐷푀 = 12 (푚퐷휈퐿휈푅 + 푚퐷휈푐푅휈푐퐿 + 푀휈푐푅휈푅) . (3.19)This can be made more compact using a mass matrix as−L퐷푀 = 12(휈퐿 휈푐푅) ( 0 푚퐷푚퐷 푀) (휈푐퐿휈푅). (3.20)By diagonalizing the mass matrixM one can obtain the physically observable states of the system. Themasses of these states are obtained from the eigenvalue expressiondet(M − 휆퐼) = 휆2 − 푀휆 − 푚2퐷 = 0 (3.21)which then gives the masses푚± = 휆± =푀 ± 푀√1 + 4푚2퐷/푀22. (3.22)In the circumstance that the Majorana mass is much larger than the Dirac mass, 푀 푚퐷 , the masses reduceto|푚− | ≈푚2퐷푀≡ 푚휈 and 푚+ ≈ 푀 ≡ 푚N (3.23)where 푚N and 푚휈 correspond to heavy and light neutrino states respectively. The physical states of thissystem obtained from the mass matrix are휈 ≈ (휈퐿 + 휈푐퐿) −푚퐷푀(휈푅 + 휈푐푅) and N ≈ (휈푅 + 휈푐푅) +푚퐷푀(휈퐿 + 휈푐퐿). (3.24)What is fascinating about this result is that now the Dirac mass terms for the neutrinos can be of thesame order as those for the other fermions, O(GeV). The small mass of the light neutrino states is a directconsequence of the large Majorana mass 푀 , hence the “seesaw.” We no longer need to contend with asix-order-of-magnitude variation in the Yukawa coupling among fermions.Finally, the new light neutrino states 휈 couple to the weak charged-current interaction effectively thesame as the existing SM neutrinos since the 휈 states are almost entirely left-handed. Similarly, the heavystatesN are almost entirely right-handed and would rarely interact via the charged-current or neutral-currentinteractions if they exist. N is referred to as a Heavy Neutral Lepton (HNL) for its relatively large mass or asterile neutrino for its non-interaction with the rest of the SM particles.3.3.4 Searches for Majorana fermionsIf the Majorana mass term (eq. (3.17)) is nonzero, then neutrinos are Majorana fermions meaning that theneutrino is its own antiparticle: 휈 = 휈. For instance, if electrons were Majorana particles, the transition푒+ ↔ 푒− would be allowed, violating charge conservation. Interestingly, for neutrinos, the observable effects203.3. Mass mechanismsof this feature would be rather difficult to detect.To illustrate the faint effect, consider the following process: A pion decays, producing 휋+ → 휇+휈휇,where the 휈휇 then interacts via inverse-훽 decay, 휈휇푛→ 휇−푝. The number of leptons minus the number ofantileptons, or lepton number L, remains constant. If, on the other hand, the neutrino was its own antiparticle,then it could interact as a right-handed chiral state and produce 휈휇푛 → 휇+푝. What remains would be twoantimuons, breaking lepton number conservation by two units. Due to the small mass of the neutrino, it willtravel near light speed, making its helicity state and chirality state nearly identical. Therefore, this process issuppressed by O(푚2휈/푚2휇) ∼ 10−9 and is virtually impossible to measure.An alternative method of investigation is to search for signs of neutrinoless double 훽-decay (0휈훽훽)which is a process that occurs only if the neutrinos are Majorana particles. Even-even nuclei, kinematicallyforbidden from undergoing normal 훽-decay, can decay via simultaneous 훽-decay processes to lower-energyeven-even nuclei. The energy spectrum of the electrons produced this way would be continuous due to theescape of the neutrinos, similar to that shown in single 훽-decay in fig. 3.1.If the neutrino were a Majorana particle, then the process shown in fig. 3.3 could take place and wouldproduce no external neutrinos. The process would produce mono-energetic electrons, each carrying halfthe mass difference of the parent and daughter nuclei. Unfortunately, this double 훽-decay process has ahalf-life of 1019–1025 years, so observing these processes is already quite rare. To date, there is no confirmeddiscovery of neutrinoless double 훽-decay [22, 24].Figure 3.3: Normal double 훽-decay (left). Neutrinoless double 훽-decay (right) [22]. If the neutrino is aMajorana particle, it is its own antiparticle, and the process on the right would be allowed. This is one of themost promising methods of identifying whether a neutrino is a Majorana particle.3.3.5 The Weinberg operator and other types of seesawAnother way to express the Majorana term starts with the combination 퐿퐿 휙˜—a contraction of the conjugatelepton doublet and conjugate Higgs doublet—which is a singlet under all SM gauge groups. The contraction−L ⊃ 퐿퐿 휙˜훼퐶 (퐿퐿 휙˜)푇 + (ℎ.푐.) (3.25)213.3. Mass mechanismsFigure 3.4: The Weinberg operator is a dimension-5 operator that couples a neutrino-antineutrino pair totwo Higgs fields [22].is gauge invariant and becomes−L ⊃ 휈퐿훼푣2퐶휈푇퐿 + (ℎ.푐.) (3.26)under EWSB. Equation (3.25) is known as theWeinberg operator and eq. (3.26) is the same Majorana massterm that was shown in eq. (3.17). Figure 3.4 demonstrates the Weinberg operator as a coupling between apair of Higgs bosons and a pair of Majorana neutrinos.As fermion fields have mass dimension [휓] = 32 and the Higgs scalar has mass dimension [휙] = 1, theWeinberg operator is a dimension-5 operator. The Lagrangian term can be kept at dimension-4 by settingthe coupling 훼 to have mass dimension [훼] = −1. By expressing 훼 in terms of a dimensionless operator 휆and some new physics scale Λ (unrelated to the electroweak scale7), the SM neutrino mass is then푚휈 =휆푣2Λ. (3.27)Neutrino masses are then suppressed by a factor of 푣/Λ compared to charged fermions. This shouldbegin to look familiar. By taking the new physics scale to be that of the Majorana mass in eq. (3.23) andsetting it to be much larger than the electroweak scale (Λ 푣), it is exactly the relationship seen in thesuppression of the mass term for light neutrinos. Furthermore, theWeinberg operator violates lepton numberconservation like the Majorana neutrino.The Weinberg operator may behave for neutrino-Higgs interactions like the low-energy Fermi operatordoes for 훽-decay, where interactions really take place by the exchange of some massive particle as seen infig. 3.5. These possible particles are classified and result in three types of seesaw mechanism, the first ofwhich was detailed in section 3.3.3.Type I : Heavy singlet fermions 푁Type II : Heavy triplet scalar ΔType III : Heavy triplet fermions Σ7The EW scale refers to energies on the order of 100GeV where EW theory is important in describing processes at that energy.The푊 , 푍 , and Higgs boson masses are on the order of the EW scale.223.3. Mass mechanismsFigure 3.5: The three generic realizations of the seesaw mechanism, depending on the nature of the heavyfield exchanged [52]. This is a “magnified” view of the Weinberg operator in fig. 3.4.We can also see this from the perspective of an effective field theory. Physics beyond the SMcharacterizedby a high energy scale Λ will induce lower-energy effects described by an effective field theory.Leff = LSM +∑푖훼푖Λ푂푑=5푖 +∑푖훽푖Λ2푂푑=6푖 + . . . (3.28)The lower the dimension, the more relevant the operator is at low energies, and as it so happens, the onlyallowed 푑 = 5 operator that can be constructed from SM fields (and that obeys the necessary symmetries) isthe Weinberg operator. It certainly does seem reasonable to expect that Majorana neutrino masses could beone of the first indications of BSM physics [22].3.3.6 Are heavy neutral leptons beyond the Standard Model?A familiar disagreement is whether neutrino oscillations constitute evidence of physics beyond the SM.The original 푆푈 (2) ×푈 (1) Glashow-Weinberg-Salam model of electroweak interactions remains the basicframework of neutrino physics, and no evidence of theoretical extensions is yet verified [3].As shown in section 3.3, the most straightforward extension would be to introduce a lepton-numberconserving right-handed 휈푅 field, which couples to the active 휈퐿 field with a Dirac mass. This extensionrequires no lepton-number-violating Majorana fields to enter the SM Lagrangian, and the consequent massmechanism takes a familiar form. Nevertheless, a simple extension to the SM is still an extension.Perhaps one of the sources of the confusion is that the Standard Model has no standard that all physicistsagree is the authentic version. The closest example of a definitive text may be the Particle Data Group’s“Review of Particle Physics,” which has become the most-cited publication in the field. The most recentpublication [21] contains a review of neutrino masses, mixing, and oscillations which explicitly states, “Weconclude that within the SM neutrinos are precisely massless. Consequently one must go beyond the SM inorder to add a mass to the neutrino.”This dissertation will assume that the SM presented in section 2.1 does not contain any mechanismwhichallows for neutrinos with non-zero mass, and consequently, that observations of neutrino oscillations arestrictly BSM phenomena.233.4. Motivation for HNL searches3.4 Motivation for HNL searchesThough nearly completely right-chiral, the theoretical HNL contains a small admixture of an active neutrinoflavour: 휈푒, 휈휇, 휈휏 . This allows it to participate in weak interactions, albeit suppressed by a dimensionlessmixing angle푈훼, where 훼 = 푒, 휇, 휏. The discovery of such a particle, or class of particles, has the potentialto resolve three major open physics questions (see section 2.7.2).First, a right-handed neutrino would provide a mechanism by which the active neutrinos gain their non-zero masses. Moreover, if the HNL is aMajorana fermion (its own antiparticle), the mass may be imparted byamechanism different than all other SM fermions (see section 3.3). Second, if at least one HNLwere found tobe in the O(keV) mass range, it would constitute a potential dark matter candidate. The HNLwould be a typeof decaying dark matter, putting an upper bound on its mixing with active neutrinos [53]. Finally, the baryonasymmetry of the universe — the excess of matter over antimatter — could be explained by the possibleMajorana nature of the HNL. The Majorana mass term allows neutrinos to become antineutrinos, allowingfor a natural mechanism for generating a net lepton number in the hot and early universe, aka leptogenesis.Along with sphalerons furnishing the means to convert baryons to antileptons (or the conjugate inverse), theHNLs may be the fundamental source for the observed baryon asymmetry [20, 54, 55].Clearly, finding direct evidence of an HNL would have substantial impacts on physics and astronomy,and many searches for such evidence have been performed over decades. References [56–58] present anextensive review of HNL experiments and constraints, both existing and proposed. Typically, experiments todate assume that only one HNL is kinematically accessible and that other HNLs are outside the experiment’ssensitivity. Thus, only two independent variables must be considered: the mass of the HNL and the couplingstrength |푈2훼 |.Stringent constraints have been placed on sterile-active neutrino mixing in a wide mass range fromO(eV)to O(TeV) [59]. Data from oscillation experiments exclude masses of 푀푁 < 1 eV. Constraints on mixingwith 휈푒 are set by 0휈훽훽 experiments and 훽-decay energy spectra for 10 eV < 푀푁 < 1MeV. Constraintson 휈푒 and 휈휇 mixing in the range 1MeV < 푀푁 < 1GeV are set by searching for peaks in the resultingenergy spectrum of leptonic pion and kaon decays. Decay products from beam-dump experiments have setcomplementary limits on mixing to all active neutrino flavours. Lower bounds on the mixing angles are setby considerations of Big Bang Nucleosynthesis [60].3.4.1 GeV-scale HNLs and displaced verticesOf particular relevance to LHC searches GeV- to TeV-scale HNLs with masses up to the the TeV scale beingprobed in the Majorana limit using prompt leptons while dedicated searches looking for displaced verticesprobe the GeV range. In 푝푝 colliders, searches for Majorana HNLs in this mass range often focus on a“smoking gun” lepton-number violating (LNV) signature of same-sign, same-flavour dilepton plus jets withno missing transverse energy: 푝푝 → 푊∗ → 푁ℓ± → ℓ±ℓ± 푗 푗 [59]. There is a distinct interest in searching forHNLs with masses below the electroweak scale (below the푊 , 푍 , and Higgs boson masses). In a GeV-scaleseesaw model, HNLs can simultaneously explain the masses of active neutrinos and the observed baryonasymmetry. A simple extension to the SM with three HNLs below O(100GeV) including a dark matter243.4. Motivation for HNL searchescandidate at O(keV) is known as the neutrino Minimal Standard Model (휈MSM) [61, 62]. Depending onthe exact masses of the three HNLs, 휈MSM has the potential to solve all three of the above SM limitationswithout involving a new energy scale. GeV-scale HNLs may also play a role in flavour violation, leptonuniversality violation, and 0휈훽훽 (see reference [56] and references therein for details).A broad range of experiments probes HNLs in the range 100MeV < 푀푁 < 500GeV. 0휈훽훽 searches,peak searches in meson decays, beam dump experiments, rare LNV decays of mesons, 푍 boson decays,electroweak precision tests, and direct collider searches are all used to place complementary limits on thesterile-active mixing angles. Readers are directed to reference [59] for a detailed overview of these searches.One method to constrain theoretical HNL properties is to search for their decay products since the HNL’smixing with active neutrinos allows it to participate in weak interactions. This enables (if kinematicallyallowed) HNL decays via charged-current (CC) and neutral-current (NC) processes, resulting in visible finalstates, including charged leptons, pions, or kaons. Collider experiments, in particular, make use of thisavenue of discovery. The DELPHI experiment at LEP1 used neutrinos from 푍 boson decays, which untilthe LHC experiments, provided the tightest constraints in the HNL mass range 2–75GeV [63]. HNLs areprobed in hadron colliders using 푊 rather than 푍 boson decays due to the higher production cross sectionand certain trigger requirements. Graphical overviews of the limits referenced above are shown in fig. 3.6.253.4. Motivation for HNL searches(a)(b)(c)Figure 3.6: Limits on themixing between an active neutrino and a singleHNL in themass range 0.1–100GeV.The active neutrino is 휈푒 in (a), 휈휇 in (b), and 휈휏 in (c). For details see reference [58].26Chapter 4Experimental apparatusTo test the full range of particles and interactions in the SM, exotic forms of matter must be created and theirbehaviour measured. Many of the particles of interest are relatively massive, so large amounts of energymust be imparted to each interaction for high-mass particles to be produced. Furthermore, many processesof interest occur with a very low probability, so an enormous number of interactions must be producedand recorded to enable a statistically robust measurement. Colliding beam experiments are currently thebest-suited method to provide large numbers of the highest-energy collisions in a controlled environment.The LHC is a hadron collider that delivers primarily proton-proton (푝푝) collisions. At√푠 = 13TeV,the produced collisions have the highest centre-of-mass (COM) energy ever achieved by humans at thetime of this writing. The LHC also operates in alternative heavy-ion modes which studies lead-lead orproton-lead collisions. The major experiments located at the LHC collision points are ATLAS and CMS,general-purpose particle detectors, LHCb, which focuses on b-hadron physics, and ALICE, which studiesheavy-ion collisions.The following chapter describes the experimental apparatus that enables the analyses presented inchapters 6 and 7. Section 4.1 describes the LHC and its relevant parameters. Section 4.2 presents a summaryof the components of the ATLAS detector. Although the LHC is capable of colliding heavy ions, discussionin this chapter is restricted to the proton-proton collisions.4.1 The Large Hadron ColliderThe LHC is the world’s largest and highest-energy particle accelerator and collider [64]. By most metrics,it is the largest machine ever built [65]. The subterranean collider is, on average, 100m underground inthe 26.7 km tunnel initially constructed for the Large Electron-Positron Collider (LEP) collider. The LHC,a synchrotron accelerator, is designed to be capable of√푠 = 14TeV centre-of-mass (COM) collisions bycolliding two separate proton beams, each sectioned into bunches.Each beam travels in an ultrahigh vacuum beam pipe, with pressures reaching as low as 10−11mbar. Thecollider is separated into eight straight sections and eight arcs. The straight sections, each roughly 528mlong, contain experiments and collimation, acceleration, and beam dumping utilities. Figure 4.1 shows aschematic of the sections of the LHC and the four major experiments.Acceleration of the beam takes place in one utility segment using a radio frequency (RF) cavity system.As the acceleration occurs, powerful dipole magnets steer the beams, and quadrupole magnets focus them,repeating the circuit several million times until the beams cross at the four interaction points where theexperimental detectors are positioned. The following sections will describe the LHC beam parameters and274.1. The Large Hadron Colliderinjection chain in the Run 2 data-taking period.4.1.1 Accelerator and injection chainFor the proton beams to reach the highest energies, they undergo a sequence of accelerations in an injectionchain [64]. The protons within the LHC beam begin their journey supplied by an unassuming 10L tankof hydrogen [66].8 The hydrogen molecules are stripped of electrons, and the resulting bare protons areaccelerated to 50MeV by the Linac2 linear accelerator.9 The beam feeds into the Proton Synchrotron Booster(PSB), where the protons accelerate to 1.4GeV, then are injected into the Proton Synchrotron (PS). The PS,CERN’s first synchrotron in operation since 1959, boosts the energy of the protons to 25GeV. The nextdestination for the proton beam is the Super Proton Synchrotron (SPS) which brings each proton to 450GeV.Finally, the beam is ready for injection into the LHC.Until this point, all protons travel together, circulating in the same direction. The SPS injects protonsinto the two separate beam pipes of the LHC so that the resulting beams travel in opposing directions. Acomplete fill of the LHC takes a minimum of 16 minutes. Only after this filling process does the accelerationstage begin. On each pass through the accelerating segment of the LHC, each beam passes through an RFcavity operating at 400 MHz. Accelerating the beam from 450GeV to the maximum energy of 7TeV takesapproximately 20 minutes.Each machine in the injection chain was developed initially to enable several other lower-energy ex-periments before they were re-commissioned to supply high-energy protons to the LHC. It is a testamentto CERN’s re-use of existing infrastructure that many of the chain’s components are upgraded versions ofdecades-old accelerators. Not surprisingly, the proposed Future Circular Collider (FCC) would likely usethe LHC as the final injection synchrotron [69].4.1.2 Beam characteristicsPhysics studied in the ATLAS detector depends on the nature of particles produced by collisions in the LHC.It is vital to understand the properties of the beams and the frequency with which protons collide inside thedetector.BunchesInstead of a continuous beam, the protons are separated into individual packets called bunches. The complexprocedure for separating a continuous beam into bunches occurs at the PS stage for ultimate injection into theLHC ring. When filled, each LHC beam contains 2808 bunches spaced by 25 ns, with each bunch measuring1.06 ns [64].10 Each bunch contains on the order of one hundred billion protons.8The number of protons used by the LHC is relatively small, and the 10L hydrogen bottle would well outlast the lifetime of theLHC. In reality, the bottle is changed roughly three times per year as other experiments at CERN consume more protons than theLHC [67].9In 2019, the Linac2 was replaced by the Linac4, which accelerates protons to 160MeV and allows for a more luminousbeam [68].10The beams are travelling so close to light speed that length is measured in units of seconds. To convert to metres, multiply bythe speed of light.284.1. The Large Hadron ColliderLINAC 2North AreaLINAC 3IonsEast AreaTI2TI8TT41TT40CLEARTT2TT10TT66e-ALICEATLASLHCbCMSSPSTT20nppRIBsp1976 (7 km)ISOLDE19922016REX/HIE2001/2015IRRAD/CHARMBOOSTER1972 (157 m)AD1999 (182 m)LEIR2005 (78 m)AWAKEn-ToF2001LHC2008 (27 km)PS1959 (628 m)201120162015HiRadMatGIF++CENFp (protons) ions RIBs (Radioactive Ion Beams) n (neutrons) –p (antiprotons) e- (electrons)2016 (31 m)ELENALHC - Large Hadron Collider // SPS - Super Proton Synchrotron // PS - Proton Synchrotron // AD - Antiproton Decelerator // CLEAR - CERN Linear Electron Accelerator for Research // AWAKE - Advanced WAKefield Experiment // ISOLDE - Isotope Separator OnLine // REX/HIE - Radioactive EXperiment/High Intensity and Energy ISOLDE // LEIR - Low Energy Ion Ring // LINAC - LINear ACcelerator // n-ToF - Neutrons Time Of Flight // HiRadMat - High-Radiation to Materials // CHARM - Cern High energy AcceleRator Mixed field facility // IRRAD - proton IRRADiation facility // GIF++ - Gamma Irradiation Facility // CENF - CErn Neutrino platForm2017The CERN accelerator complexComplexe des accélérateurs du CERNFigure 4.1: Schematic view of CERN’s accelerator complex [70].294.1. The Large Hadron ColliderEnergyThe possible physics processes ultimately depend on the COM energy of each 푝푝 collision√푠. The LHCwas designed so that each beam could accelerate protons to 7TeV, reaching a COM energy of√푠 = 14TeV.In Run 1, from 2010–2013, the LHC provided 7TeV, then 8TeV collisions. Run 2 from 2015–2018 providedcollisions of 13TeV. In July of 2022, Run 3 began an achieved collisions up to 13.6TeV [71]. The mainlimiting factor in achieving higher energies is the high magnetic field required of the superconducting dipolemagnets used to steer the protons along their trajectory [72].LuminosityThe collision rate of a collider is called the luminosity [73]. Instantaneous luminosity L is effectively theoutgoing flux of particles per unit area and time after a collision of proton bunches. For a Gaussian beamdistribution, the instantaneous luminosity isL = 푁2푛푏 푓rev4휋휎푥휎푦· 푆 (4.1)where 푁 is the number of particles in each bunch, 푛푏 is the number of bunches in one beam, 푓rev is therevolution frequency of the beam,휎푥,푦 represents the beamwidth in the transverse axes, and 푆 is a geometricalfactor accounting for the angle of the bunch crossing.Integrated luminosity 퐿 measures the collisions over a period of time and is the traditional metric for theoutput of collider experiments. The number of occurrences of a particular process 푁푖 is a product of theluminosity and the cross section of the process being studied 휎푖:푁푖 = 휎푖∫L 푑푡 = 휎푖퐿. (4.2)Cross section is conventionally measured in units of femtobarns (fb) and conversely, integrated luminosity ismeasured in units of inverse femtobarns (fb−1). One inverse femtobarn is approximately equivalent to 1012푝푝 collisions [74]. The luminosity of the beam in each fill is not constant but decays due to degradation ofbeam intensity and beam shape or emittance. Considering all these factors, the beam’s luminosity reducesby a factor of 1/e in approximately 15 hours.Since the processes of interest are often relatively rare, achieving a high luminosity is essential for record-ing a sufficient number of events. The LHC is designed for a peak instantaneous luminosityL =1034 cm−2 s−1at the high-luminosity collision points. In 2016 it achieved this rate and had doubled the peak luminosity by2017 [75, 76]. In ATLAS, primary luminosity measurements are obtained using the LUCID-2 detector [77].PileupUnfortunately, a high peak luminosity comes at a price. When a bunch crossing occurs, several distinct 푝푝interactions take place. The resulting particles will overlap in the detector and complicate the identificationof physics objects originating from the process of interest. The mean number of inelastic 푝푝 interactions is304.1. The Large Hadron Collidercalled the pileup parameter 휇, and the time-averaged quantity is 〈휇〉. This is also called in-time pileup. Thehigher the luminosity, the higher the pileup, and the more crowded the energy deposits in the detector [78].Additionally, because the timing between bunch crossings is so short (25 ns), detector systems aresensitive to particles from collisions that happen after and before the triggered event. This is known asout-of-time pileup and primarily affects systems with long signal integration time, such as calorimeters(section 4.2.3).Over the entirety of Run 2 the average pileup was 〈휇〉 = 33.7 and reached a maximum of 〈휇〉 = 70 [76].Figure 4.2 shows the distributions of pileup in each data-taking year of Run 2.0 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 calibrationFigure 4.2: Shown is the luminosity-weighted distribution of the mean number of interactions per crossingfor the 2018 푝푝 collision data at√푠 = 13TeV COM energy. All data recorded by ATLAS during stablebeams is shown, and the integrated luminosity and the mean 휇 value are given in the figure [76].4.1.3 Run 2Because several of the processes of interest are relatively rare, one must record many collisions to makestatistically significant measurements. The LHC and the associated detectors operate for several years toobtain sufficient data.The LHC operates in multi-year runs in which data is taken more-or-less continuously. Scheduled shortand long shutdowns allow for maintenance, repair, and upgrades to the accelerator and detectors. A regularwinter shutdown and spring ramp-up period conveniently segments each data-taking period (roughly) intocalendar years.In the initial operational phase, called Run 1, collisions were produced in 2010–2011 at√푠 = 7TeV and2012 at√푠 = 8TeV delivering an integrated luminosity of 28 fb−1. This data was sufficient for discoveringa particle consistent with the SM Higgs boson [79].314.2. The ATLAS detectorRun 2 took place from 2015–2018 with collisions of√푠 = 13TeV. It was possible in 2017 and 2018 toincrease the luminosity to twice the nominal specification [80] with the LHC delivering, in total, 156 fb−1 of13TeV data. The analysis presented in this dissertation uses data collected in Run 2.Run 3 began in 2022 and plans to deliver an additional 290 fb−1 of data from collisions at√푠 = 13.6TeVthrough 2025. The high-luminosity LHC program will substantially increase the instantaneous luminosityof the collisions while maintaining the COM energy, obtaining an integrated luminosity 3000 fb−1. Thus,the data recorded so far from the LHC is only 1/20 of its ultimate lifetime output.4.2 The ATLAS detectorRecording exotic physics processes several million times per second requires a powerful camera. TheATLAS (A Toroidal LHC ApparatuS) detector, aside from a strained acronym, is one of the most complexand powerful “cameras” ever constructed. It is a general-purpose cylindrical detector situated about one ofthe four LHC collision points. Like its titanic namesake, ATLAS is an enormous machine measuring 46metres in length and 25 metres in height, weighing 7000 tonnes and containing nearly 3000 km of cables forits 100 million readout channels [81, 82].The detector body is broadly separated into a central barrel and two end-caps, which provide a near-complete solid-angle coverage. It is formed of several concentric subdetector systems which specialize inmeasuring different parameters of various particles produced in 푝푝 collisions. The inner detector measurescharged particle momentum, the electromagnetic and hadronic calorimeters measure particle energy, and themuon spectrometer identifies muons that pass through the rest of the detector. Two powerful magnet systemsencase the detector so that the trajectory of charged particles can reveal their momentum. This design makesATLAS an extraordinarily versatile detector, enabling several hundred distinct physics analyses to operate inparallel.Figure 4.3 shows a cutaway schematic of the ATLAS detector with a clear view of its systems. Afterdefining the coordinate system and commonly-used terminology, this section will describe in further detailthe major systems.4.2.1 Coordinate systemThe ATLAS detector uses a right-handed coordinate systemwith the origin defined at the nominal interactionpoint (IP) in the centre of the detector. The x-axis points towards the centre of the LHC ring, the y-axispoints away from the centre of the earth, and the z-axis is aligned with the LHC beam pipe. Cylindricalcoordinates (푟, 휙, 푧) are used in definitions of detector elements and material distributions. The x-y plane,orthogonal to the beam axis, is referred to as the transverse plane.Spherical coordinates (푟, 휙, 휃) are useful in defining particle trajectories where the azimuthal angle휙 is measured about the beam axis and the polar angle 휃 is measured from the beam axis. A commonparameterization of the polar angle is pseudorapidity, defined as 휂 = − ln tan 휃/2. Pseudorapidity is oftenpreferred over 휃 as differences in pseudorapidity are Lorentz invariant under relativistic boosts (in themassless limit). Coordinates generally used to describe a particle’s four-momentum are (푝T, 휂, 휙) where324.2. The ATLAS detectorFigure 4.3: Cut-away view of the ATLAS detector [81].푝T refers to the transverse momentum of a particle — the component of its momentum in the transverseplane. The angular separation Δ푅 =√(훿휂)2 + (훿휙)2 quantifies the distance between particles. This quantity,defined in terms of pseudorapidity, is also Lorentz invariant.4.2.2 Inner detectorThe inner detector (ID) is the first system encountered by the debris of 푝푝 collisions. It is composed ofthree separate subsystems, which together are used to determine the direction and momentum of chargedparticles as well as identify the vertices from which they were produced. Together the barrel and end-capsections of these detectors provide coverage up to 휂 < 2.5. A thin solenoid magnet surrounds the full ID andproduces a strong magnetic field along the z-axis, so charged particles are deflected along the 휙-axis. TheID is a non-destructive detector — particles will pass through the material with minimal interference. Howthe energy deposits in the ID are interpreted as physical particles is detailed in section section 5.1.Pixel detectorThe pixel detector is the innermost part of the ID [83]. 1744 identical sensors contain over 80 million pixelsin total, each with a separate readout channel. Each pixel is made from oxygenated n-type wafers, specificallydesigned to operate continuously in a high-radiation environment [81]. The nominal pixel size is 50 µm(푟-휙) × 400 µm (푧) which provides a spatial resolution of 10 µm (푟-휙) × 115 µm (푧). The three barrel layersare located at 푟 = 50.5, 88.5, and 122.5mm and the end-cap disks at |푧 | = 495, 580, and 650 mm. A detailedschematic is shown in fig. 4.5. This configuration provides individual three-dimensional measurements of acharged particle’s trajectory with high precision.Between Run 1 and Run 2, an additional layer of high-resolution pixels was inserted near the beam pipe334.2. The ATLAS detectorFigure 4.4: Cut-away of the ATLAS inner detector [81].at 33.3mm. This insertable B-layer (IBL) was installed to provide substantially improved vertexing andidentification of displaced 푏-hadrons. The IBL consists of an additional 12 million pixels of dimensions50 µm (푟-휙) × 200 µm (푧), corresponding to a spatial resolution of 8 µm (푟-휙) × 40 µm (푧). Of particularrelevance to this dissertation, the insertion of the IBL improves the capacity to reconstruct secondary vertices,which are critical in the search for many exotic physics signatures with long-lived particles.Semiconductor trackerThe semiconductor tracker (SCT) is the next system encountered by outwardly radiating particles. Forreasons of cost and reliability, single-sided p-in-n sensors are used, different from that of the pixel sensors.Each layer of the SCT module holds two sensors on each side, each of dimensions 80 µm (푟-휙) × 12 cm (푧).The rectangular geometry of the SCT sensors leads to the often-used alias strips. The strips are offset by astereo angle of 4mrad which enables a more precise resolution in the z-axis: 17 µm (푟-휙) × 580 µm (푧). Thebarrel contains four layers at 푟 = 299, 371, 443, and 514mm, and the end-caps contain 9 disks each between|푧 | = 854 and 2720mm. The 4088 silicon strip modules are read out by approximately 6.3 million channels.Transition radiation trackerThe final element of the ID is the transition radiation tracker (TRT). This section consists of gaseous drift tubedetectors as opposed to the silicon-based detectors in the other two sections. It is composed of approximately300,000 straw tubes, each 4mm in diameter, with a gold-plated tungsten wire at the centre. A potentialdifference is kept between the wire and the tube wall. Each tube is filled with a Xe-based gas mixture11which, when ionized by charged particles, causes electrons to drift to the wire where they are amplified andread as signal. The tubes are embedded in a matrix of polypropylene fibres which causes incident particles344.2. The ATLAS detectorFigure 4.5: The r-z cross section view of the layout of a quadrant of the ATLAS inner detector for Run 2.The top panel shows the whole inner detector, whereas the bottom-left panel shows a magnified view of thepixel detector region. Compared to Run 1, the IBL (shown in red in the bottom-left panel) and its services,together with the new beam pipe, were added [83].to produce transition radiation, further amplifying the signal.The straw tubes are 144 cm long in the barrel region, aligned with the z-axis, and 39 cm in the end-cap region, radially arranged perpendicular to the z-axis. Because of their length, hits in the straws onlyprovide 2-dimensional trajectory information. However, with 130 µm resolution and dense packing, the TRTcomplements the silicon detectors with continuous tracking for particles within |휂 | < 2.0. Furthermore,transition radiation has an additional benefit: themagnitude of the radiation is related to the incident particle’smass. Therefore, the TRT can be used for particle identification, mainly to distinguish between electron andcharged hadron (e.g., pion) tracks.4.2.3 CalorimetersBeyond the ID and solenoid magnet lies the calorimetry system. The ATLAS calorimeters destructivelymeasure the energy of the particles produced in the 푝푝 interaction. They effectively absorb nearly all theenergy from SM particles, except for muons and neutrinos, stopping them in dense material. The systems11In Run 1, the tubes were only filled with the Xe-based mixture, but due to large irreparable leaks, many channels were convertedto the much cheaper Ar-based mixture. The TRT’s tracking performance is largely unaffected by this change; however, particleidentification efficiency is impacted [84].354.2. The ATLAS detectorare separated by the type of particles they are designed to absorb: the electromagnetic calorimeter (ECAL)effectively absorbs energy from electrons and photons, while the hadronic calorimeter (HCAL) is designedto absorb charged and neutral hadrons.The calorimetry system has a coverage of |휂 | < 4.9. This near-hermetic coverage, as well as the thicknessof the calorimeters, is important to fully capture the total energy of the jets. The ECAL and HCAL systemsboth use a sampling calorimeter design. This type of calorimeter alternates dense absorbing layers withactive layers which measure the deposited energy. The layout of the calorimeter subsystems can be seen infig. 4.6.Figure 4.6: Cut-away view of the ATLAS calorimeter system [81].Electromagnetic calorimeterThe electromagnetic calorimeter (ECAL) [85] measures the energy of electrons and photons while alsopreventing the resulting particle showers from reaching the subsequent detector layers. As a samplingcalorimeter, the ECAL is composed of alternating absorbing and active layers in an accordion arrangementto provide total coverage in 휙. The absorber is made of lead plates which produce electromagnetic showerswhen struck by incident electrons and photons. The active material is cryogenically cooled liquid argon(LAr), which produces electron-ion pairs when ionized by electromagnetic showers. These pairs drift tocharged electrodes, where they are digitized and read out.Composed of a barrel and two end-caps, The ECAL covers the region of |휂 | < 3.2. Resolution variesacross the ECAL, but is at its finest granularity in the |휂 | < 2.5 region: 0.025× 0.025 (휂× 휙). In this region,the tracking detector provides complimentary charged particle information. The thickness is conventionallymeasured in radiation lengths 푋0 where one radiation length corresponds to the distance in which the energyof an electron will be reduced to a factor of 1/e due to bremsstrahlung interactions [86]. The ECAL has athickness of more than 22 푋0 in the barrel and more than 24 푋0 in the end-caps. Approximately 173,000channels read data from this system.364.2. The ATLAS detectorHadronic calorimeterThe hadronic calorimeter (HCAL) is located directly outside the ECAL envelope and measures the energyof charged and neutral hadrons [87]. Hadronic showers are generally more complex than electromagneticshowers since the hadrons are subject to strong force interactions. Hadronic fragmentation and escapingstable particles leave some of the incident hadronic energy invisible to the detector. Therefore, the totalenergy of the hadronic interaction must be estimated from the recorded energy.One barrel and two extended-barrel region sections cover |휂 | < 1.7 and are composed of sampling steel-plastic tile calorimeters. Charged and neutral hadrons form cascading particle showers when interacting withthe steel tiles. These particles then interact with the scintillating polystyrene active layers. The generatedlight is transmitted via fibre optic cables to photomultiplier tubes, and then the signal is digitized and readout. Compared to EM showers, hadronic showers have a greater lateral spread; therefore, a lower resolutionis necessary for the HCAL systems. The finest spatial resolution in the tile calorimeter is 0.1 × 0.1 (휂 × 휙).The end-cap HCAL is a LAr calorimeter very similar to the ECAL system. It covers the range from |휂 | > 1.5to |휂 | < 3.2 and also has a minimum spatial resolution of 0.1 × 0.1 (휂 × 휙). A forward calorimeter (FCal),set within the end-caps close to the beampipe, provides further coverage for 3.1 < |휂 | < 4.9. Two separatesections of the FCal are optimized for electromagnetic and hadronic calorimetry.4.2.4 Muon spectrometerThe outermost system of ATLAS, the Muon Spectrometer (MS), detects charged particles that escape thecalorimeter system [88, 89]. The momentum calculation is based on the magnetic deflection of muon tracksby superconducting toroid magnets. These magnets are arranged to provide a field roughly orthogonal to themuon trajectory to maximize deflection. The system is subdivided into separate trigger and high-precisiontracking chambers.High-precision tracking is primarily achieved by Monitored Drift Tube chambers (MDT) [90], whichare chosen for their simplicity and high accuracy. Each chamber, composed of three to eight layers of drifttubes, achieves an average resolution of 35 µm per chamber and covers a pseudorapidity range |휂 | < 2.7. Tocomplement the MDTs, Cathode Strip Chambers (CSC) [91] are used in the innermost tracking layer for theregion 2.0 < |휂 | < 2.7. These multiwire proportional chambers are used in this region for their higher rateand time resolution capabilities. The resolution of each chamber is 40 µm x 5mm (푟 × 휙).The muon fast trigger system provides track information within tens of nanoseconds of particle crossing.Resistive Plate Chambers (RPC) [92] in the barrel region and Thin Gap Chambers (TGC) [93] in the end-capregion serve simultaneous purposes. They are capable of fast momentum determination necessary for L1trigger selection (see section 4.2.6) and with a 15–25 ns time resolution, they are able to identify individualbunch crossings. The RPC and TPC coordinates in the non-bending plane complement the high-precisioncoordinates from the MDTs in the bending plane.374.2. The ATLAS detectorFigure 4.7: Cut-away view of the ATLAS muon system [81].4.2.5 Magnet systemThe magnet system is a defining feature of the ATLAS detector due to its strength and unique geometry. It iscomposed of a hybrid system of four large superconducting magnets — three toroids and one solenoid. Theentire system is 22m in diameter by 26m in length, and stores an energy of 1.6GJ.The central solenoid magnet provides a 2T axial magnetic field through the inner detector. Its layout iscarefully optimized to reduce material thickness upstream of the calorimeter cells, achieving approximately0.66 radiation lengths at normal incidence. The diameters of the solenoid are 2.46m (inner) and 2.56m(outer) and is 5.8m long. In total, the coil mass is 5.4 tonnes and stores 40MJ of energy at the nominal7.7 kA operational current.Beyond the calorimeter envelope, the toroid magnets produce fields for momentum measurements in theMS system. The barrel toroid consists of eight coils encased in vacuum vessels with diameters of 9.4m(inner) and 20.1m (outer) and length of 25.3m. It produces a field of 1.5T and stores 1.1GJ of energy atits nominal operating current of 20.5 kA. Each end-cap toroid is a single cold mass unit containing eightsquare coil units. They produce an average field of 1T, storing 0.25GJ of energy each.4.2.6 Trigger푝푝 interactions of interest that may reveal new physics are rare, and the vast majority of them may besafely discarded without impacting most ATLAS analyses. Furthermore, bandwidth and storage capacitylimitations make it impractical to record the full readout of the detector systems at the 40MHz rate of particlecollisions. The Trigger and Data Acquisition system (TDAQ) is a combined hardware and software systemthat determines the events of interest to physics analyses in real-time and stores the relevant detector responsedata [94].384.2. The ATLAS detectorFigure 4.8: Cross section of the muon system in a plane containing the beam axis (bending plane). Infinite-momentum muons would propagate along straight trajectories which are illustrated by the dashed lines andtypically traverse three muon stations [81].The Level-1 (L1)12 trigger uses a hardware-based system to rapidly process reduced-resolution signalsfrom the calorimeters (L1Calo) and muon detectors (L1Muon). Combining information from severaldedicated custom electronics, the Central Trigger Processor (CTP) makes a pass/no-pass decision for theevent within 2.5 µs of the bunch crossing. The L1 trigger seeks out high-momentum objects (leptons,photons, jets), high 퐸missT (see chapter 5), and events with overall high energy deposits. The rate of eventreadout is reduced by a factor of 400 to an upper limit of 100 kHz. In addition, it specifies Regions-of-Interest(ROIs) in 휂 and 휙, which are to be examined in more detail by the next trigger stage.The High-Level Trigger (HLT), the second stage of the trigger system, is a software-based system thatperforms a more precise object reconstruction similar to the offline reconstruction discussed in chapter 5.The HLT requests detector information at full resolution from the data readout buffers within the ROIsdefined in L1. This more computationally-expensive selection reduces the event rate by another factor of100 to a rate of 1 kHz.The precise decision criteria are determined by a trigger menu which, for Run 2, contained roughly 1500individual event selections. These menus specify the physics signatures, selection algorithms, event rate, andbandwidth. Each trigger menu is determined by the physics goals for a data collection period, accountingfor the instantaneous luminosity, data transfer, and storage constraints. For events which pass both the L1Trigger and HLT systems, the complete detector information is read out (approximately 1.5MB/event) andsent to the local Tier 0 computing centre for permanent storage and full event reconstruction.12In Run 1, the HLT consisted of a L2 trigger and Event Filter stage, but these were replaced by a single HLT system in Run 2 toreduce complexity and optimize performance.394.2. The ATLAS detectorFigure 4.9: Geometry of magnet windings [81].Figure 4.10: Bare central solenoid in the factory after completion of the coil winding [81].40Chapter 5Object reconstructionThe entire detector response information is read to permanent storage for collision events that successfullypass a trigger. However, at this stage, an event is simply a raw collection of voltages. A tremendous compu-tation is undertaken in which the detector response is combined with geometrical information and physicaldomain knowledge to produce a representation of reality. The final output of the several reconstructionalgorithms is a collection of physics objects, which are digital descriptions of the physical entities producedin the collision. These objects are stored in so-called xAOD format, which is a custom event data model(EDM) design used in ATLAS [95]. Physics objects in the EDM are represented as C++ classes in the xAODnamespace such as xAOD::Muon or xAOD::Electron. The framework used in the reconstruction of theseobjects is the Athena software package [96, 97]. Additional metadata is stored which records the detectorconditions for each data-taking segment. Data is recorded in continuous chunks called luminosity blocks.Figure 5.1 shows a schematic representation of how fundamental particles interact with the ATLASsubdetectors. In the ID, charged particles produce tracks which are then combined to produce vertices, eachof which is described in section 5.1. The ECAL records the electromagnetic jets produced by electronsand photons, the reconstruction of which is detailed in section 5.2. Charged and neutral hadrons producecollimated showers of particles in the HCAL. These showers are called jets and are described in section 5.4.Muons, as explained in section 5.3, can pass through the entire detector, leaving signals in the ID and theMS. Finally, the ATLAS detector does not see neutrinos directly, but their existence is inferred by measuringthe transverse energy that is missing from an event. This is called 퐸missT , and its reconstruction is detailed inreference [98].Simulated physics data is heavily used in ATLAS, and the same reconstruction algorithms are applied toreal and simulated data. After applying calibrations, the remaining efficiency differences in simulation withrespect to data are corrected by applying scale factors.5.1 Tracks and VerticesThe trajectories of charged particles, or tracks, are calculated using energy deposit information from theID. Figure 5.2 depicts a visualization of the detector elements used in the tracking of charged particles.The primary vertex (PV) corresponding to the hard-scatter interaction is determined from the tracks. Thestandard reconstruction of tracks focuses on prompt tracks, defined as those originating from nearby thePV. As detailed in chapter 6, an additional pass to reconstruct tracks and vertices from secondary particledecays may also be performed. Tracking is computationally intensive due to a high density of chargedparticles in each 푝푝 bunch crossing. A sequence of complex and carefully optimized algorithms is required415.1. Tracks and VerticesFigure 5.1: A schematic slice of the ATLAS detector in the barrel region. Different detector systems aresensitive to different particle types [99].to reconstruct the tracks within a reasonable computational budget.5.1.1 ReconstructionTrack reconstruction is performed by “connecting the dots” of detector deposits in an iterative process. Eachstep reduces the number of potential candidates, so more intensive fits are only performed on likely tracks.After the primary inside-out tracking pass is completed, an additional outside-in pass is performed using theremaining deposits.Five parameters and a reference point describe each track in a perigee representation. These parametersare depicted in fig. 5.3. The transverse impact parameter 푑0 is defined as the track’s point of closest approachto the reference point in the transverse plane, while the longitudinal impact parameter 푧0 is the point of closestapproach in the longitudinal plane. The reference point used is the average position of the 푝푝 interactions— the beam-spot position. The remaining three parameters are the azimuthal angle 휙 and the polar angle 휃of the track momentum, and the ratio 푞/푝 is the charge of the reconstructed track divided by the magnitudeof its momentum.ClusterizationThe first step in charged particle reconstruction is to combine ID energy deposit information into spatiallydistinct clusters. In the pixel and SCT detectors, deposits from adjacent sensors are combined to form three-dimensional space-points, or hits, which approximate the point where the charged particle traversed the ID425.1. Tracks and VerticesFigure 5.2: A 3D visualization of the structure of the barrel of the ID. The beam pipe, the IBL, the pixellayers, the four cylindrical layers of the SCT and the three layers of TRT barrel modules consisting of 72straw layers are shown [100].material. Three-dimensional hits are formed from individual layers in the pixel detector or by combining bothlayers, axial and stereo, of an SCT module. In dense environments, clusters can be formed by contributionsfrom more than one charged particle and each cluster can be used to form multiple tracks.Inside-out trackingThe primary pass used in track reconstruction is the inside-out sequence. Initially, track seeds are formedfrom three hits in separate layers. Seeds can be formed from three SCT hits, three pixel hits, or three hitsfrom a combination of the two detectors, and the degree of confidence in a seed’s purity follows that order.This approach allows for a large set of space-point combinations while providing a rough track trajectory andmomentum estimate. Seeds must pass a loose selection which requires that the charged particle originatesnear the IP. In particular, the impact parameters of the track seed, 푑0 and 푧0, are required to be 10mm and250mm, respectively, and the seed momentum is required to be above 500MeV. If these criteria are notmet, the potential track is discarded. A seed can be confirmed by replacing its inner- or outermost hit withone from the next available silicon layer, then checking if the new trajectory is compatible with the old. Aconfirmed seed’s reconstruction is prioritized over those which cannot be confirmed.435.1. Tracks and VerticesFigure 5.3: Five parameters — 푑0, 푧0, 휙, 휃, 푞/푝— define a track in a perigee representation [101].Candidate formationOnce a track seed is established, there is sufficient trajectory information to extend it to a track candidateby selectively adding hits in additional detector layers. This is accomplished using a combinatorial Kalmanfilter [102, 103]. This algorithm iteratively predicts the location of the subsequent hit along the tracktrajectory and then, if found, updates the trajectory calculation and track parameters. The filter createsmultiple track candidates if more than one space-point is compatible. As the track parameters are moreaccurate at this stage, additional selections are applied to the candidates. Candidates are rejected if they failto meet the criteria in table 5.1.Ambiguity resolutionThe collection of fully-formed candidates contains all potentially valid combinations of hits, meaning manytracks overlap, share hits, or contain incorrect hits. The ambiguity solving stage attempts to resolve theseduplications and inconsistencies in the candidate collection. Figure 5.4 illustrates a set of tracks in the SCTwith ambiguous hits.The ambiguity resolution begins by assigning each candidate a score — a higher score is more likely tocorrectly represent the trajectory of a charged primary particle. In order of decreasing score, candidates arefitted and accepted into the output container. Critically, the hits that compose the accepted track are recorded,and restrictions are imposed on whether they can be reused in subsequent candidates. Each track can havea maximum of two shared hits. Each hit can be used by a maximum of two tracks. Preference is given totracks already accepted by the ambiguity solver, which is the purpose behind the initial score-ordering. If acluster causes either the candidate or an accepted track to fail the criteria, it is removed from the candidatein question, which is then re-scored and returned to the ordered list of remaining candidates. If this removalcauses the candidate to fail any of the criteria in table 5.1 it is rejected.445.1. Tracks and Verticesparameter criteriamin. 푝T 400MeVmax. |휂 | 2.5min. si. hits 7 (12 are expected)max. shared hits 1 pix or 2 SCTmax. si. holes 2max. pix holes 1max. |푑퐵퐿0 | 2mmmax. |푧퐵퐿0 sin(휃) | 3mmTable 5.1: This set of minimum requirements is imposed on each track candidate used in the inside-outtracking pass. A hole is defined as an intersection of the track trajectory that contains a sensitive detectorelement but does not contain a cluster. Quantities with si. refer to silicon — the combined pixel and SCTdetectors. 푑퐵퐿0 is the transverse impact parameter calculated with respect to the measured beam-line position.푧퐵퐿0 is the longitudinal impact parameter measured from the primary vertex, and 휃 is the polar angle of thetrack [104].In dense environments, it is possible that multiple charged particles will traverse the same sensors. Inthis case, it is appropriate for two or more tracks to share hits without being penalized by the ambiguitysolver. Identifying these merged clusters is vital to achieving good reconstruction efficiency in environmentswith high track multiplicity. A neural network (NN) is used to identify merged clusters. It uses as inputs themeasured charge (proportional to the deposited energy), the relative position of pixels in the cluster, and theparticle’s incident angle, which is provided by the track candidate. The NN identification efficiency is 90%for clusters formed from two charged particles and 85% for three or more charged particles. The NN does notdistinguish between three or more than three contributing particles. The rate at which the NN misidentifiessingle-particle clusters as having been formed from more than one particle is a few percent [104].The score used in candidate ordering is calculated with a reward/penalty strategy based on simplemeasures of track quality. Each cluster in the candidate increases the score while each hole decreases it.Measurements from the more precise pixel detector are given a stronger scoring weight than measurementsfrom the SCT. The fit quality is considered by applying the 휒2 per number of degrees of freedom to thescore. Energetic tracks gain an increase in score by applying the logarithm of the 푝T of the candidate. Thisassignment also suppresses the tracks with incorrectly assigned clusters which generally have a low 푝T.Track fittingAfter applying the selections listed in table 5.1, a high-resolution fit is performed on each track byminimizinga global 휒2 value. The position and uncertainty of each cluster used in the fit are estimated using a NN.A set of linear equations is solved via matrix inversion using these positions, uncertainties, and additionalparameters to account for material effects. This calculation is among the most computationally intensivein the track reconstruction process and is therefore delayed until necessary for ambiguity resolution. Fittedtracks which pass all selections after ambiguity resolution are added to the output track collection.455.1. Tracks and VerticesFigure 5.4: A simplified model of the track ambiguity problem in the SCT barrel. Track candidates a, b, andc, share hits. A score-based ambiguity resolution procedure is performed in order to distinguish betweentrue and fake tracks. Hits improve the candidate’s score while holes penalize it. The candidate with thehigher score takes the ambiguous hits [105].TRT extensionAfter ambiguity resolution and fitting, the algorithm attempts to extend the track candidates to the TRT byincorporating compatible measurements in the TRT straws without modification to the silicon-only tracks.The collection of extension candidates is refit and scored using the same framework as the ambiguity solver.Tracks in the output collection are only extended if their score improves with the addition of TRT information.Outside-in trackingAn additional reverse tracking sequence is performed to recover tracks missed by the inside-out sequence.Outside-in tracking begins by forming standalone TRT segments in regions of interest determined by theECAL. Any hits not already used by the inside-out pass are incorporated into the TRT segment if compatiblewith the candidate trajectory, then fitted. Looser requirements are imposed on these track candidates than onthe inside-out tracks, particularly reducing the minimum required silicon hits.This sequence is designed to account for tracks originating from secondary decay vertices inside the ID,including퐾0S mesons and other undiscovered signatures. Photon conversions with insufficient silicon detectoractivity may also fail the inside-out pass but can be recovered with the outside-in sequence. The resultingtracks from the inside-out and outside-in sequences form the final collection of reconstructed standard tracks.465.1. Tracks and Vertices5.1.2 PerformanceTo measure track reconstruction performance, the following track classifications are used. Truth-matchingprobability (푝match) is a contrived quantity used in simulation to define the likelihood that a reconstructedtrack is formed from an individual charged particle. The clusters used to reconstruct a single track object mayoriginate from one or more charged particles. 푝match is the ratio of the weighted number of measurementsoriginating, at least in part, from the same simulated particle to the weighted number of all measurementsused in a track [104]. This quantity is not available in data as there is no record of the origin of the detectorclusters. The weights reflect the average number of measurements in each subdetector. Pixel hits have aweight of ten, SCT hits a weight of five, and TRT hits a weight of one. Typically for a track to be consideredproperly reconstructed, it must have a 푝match of at least 0.5. This definition is used in the present dissertation.Conversely fake tracks are those with a 푝match below 0.5. These are formed from combinations of hitswhich do not originate primarily from a single charged particle. The high detector occupancy that leads tolarge numbers of fakes is often due to high pileup.An additional source of fake tracks is due to the mechanics of the ATLAS detector simulation. After theevent generation and showering procedures, the particle trajectory and detector response are simulated usingGeant4 [106–108]. As charged particles interact with detector material, they radiate energy in the form ofbremsstrahlung and subsequent pair production, forming secondary tracks. To reduce computational costs,the Geant4 simulation ceases to keep track of the parentage of secondary particles once they fall below acertain momentum threshold. It is a matter of definition and preference whether to count these secondaries asfake tracks. Low-momentum objects are generally poorly reconstructed, and subsequently, these secondarytracks rarely contribute to physics of interest and should be suppressed by the reconstruction algorithm.For this reason, combinatorial fake tracks and low-momentum secondary particles are classified withoutdistinction in the remainder of this dissertation.Additional selection criteria are imposed to define standard Tight and Loose working points, for whichthe specific criteria can be found in reference [109]. Tracking efficiency 휀trk is defined as휀trk =푁matchedrec푁gen. (5.1)In this ratio, 푁matchedrec is the number of reconstructed tracks matched to true charged particles and 푁gen is thenumber of true charged particles generated in simulation. Tracking efficiency is a quantity estimated usingonly simulated events since the true number of particles is required for the measurement. The efficiency asa function of 푝T and 휂 are seen in fig. 5.5.5.1.3 Primary vertex reconstructionClosely connected to the reconstruction of tracks is the identification and reconstruction of the primary vertex(PV), which is defined as the point at which a 푝푝 interaction occurred. The tracks used in PV reconstructionare selected with tight requirements to reduce the rate of fake tracks or tracks from secondary interactions.The full set of constraints can be found in reference [110]. Vertices are then reconstructed in the following475.2. Electrons and photonsη2.5− 2− 1.5− 1− 0.5− 0 0.5 1 1.5 2 2.5Track Reconstruction Efficiency0.60.811.2ATLAS = 13 TeVs Simulation Preliminary Track SelectionsLooseTight Primary [GeV]Tp0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Track Reconstruction Efficiency0.60.811.2ATLAS = 13 TeVs Simulation Preliminary Track SelectionsLooseTight PrimaryFigure 5.5: Run 2 tracking efficiency as a function of 휂 and 푝T is shown for Tight Primary and Looseworkingpoints [109].steps:• A seed position is selected using the centre of the beam spot and the mode of the 푧-coordinates of thetracks.• An iterative annealing fit is performed, which repeatedly down-weights less compatible tracks andrefits the vertex position.• Tracks incompatible with the determined vertex are removed and allowed to be used to find additionalvertices.• The procedure is repeated using the tracks not already belonging to a vertex.The output of this procedure is a set of three-dimensional vertex positions and their covariance matrices.Vertex reconstruction efficiency is determined from data by taking the ratio between events with areconstructed vertex and events with at least two reconstructed tracks [111]. The efficiency reaches above99% for events with five or more tracks. In high-pileup conditions, vertex reconstruction efficiency is reduceddue to the merging of vertices from separate interactions.5.2 Electrons and photons5.2.1 ReconstructionElectron reconstruction combines information from energy deposits in the ECAL and charged particle tracksin the ID by matching the 휂 × 휙 coordinates of each [112, 113]. Reconstruction of electrons is restricted to|휂 | < 2.47 to benefit from the high-granularity region of the ECAL. A schematic of the path of an electronthrough the detector elements is shown in fig. 5.6.First, energy deposits in the ECAL and HCAL are combined into EM topo-clusters using the ‘4-2-0’threshold (see reference [114] for a detailed description). Electrons lose significant energy to bremsstrahlung485.2. Electrons and photonssecond 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 5.6: An illustration of the path of an electron through the elements of the ATLAS detector. Thedashed red line indicates the trajectory of a photon produced by the electron’s interaction with material inthe ID [112].interactions with the detector material, often forming electron-positron pairs via the emitted photons. Thesecollimated emissions are typically reconstructed as a single cluster. Clusters with measured energy over400MeV are considered for matching with tracks from the ID. Tracks that are loosely matched in 휂 and 휙 tothese topo-clusters undergo a fitting procedure using a Gaussian-sum filter (GSF). The GSF is a nonlinearversion of the Kalman filter, which better accounts for bremsstrahlung losses [115].Together, these GSF tracks and EM topo-clusters are used to form dynamic, variable-size superclusters.High-energy seed topo-clusters combine with nearby satellite topo-clusters, so the resulting superclusterincludes bremsstrahlung emissions. An electron object is defined by the supercluster and its matched trackor tracks. Calibrations are applied to the electron energy and resolution to account for differences in real andsimulated data [116].5.2.2 IdentificationReconstructed electron candidates are subject to a likelihood-based (LH) identification to separate theprompt electron signal from backgrounds. These background sources include jets, photon conversions,and non-prompt electrons from heavy-flavour hadron decays. The electron LH is based on the product ofseveral probability distribution functions of discriminating variables determined to differ between signaland background sources. These discriminants, listed in full in reference [112], include quantities related tohadronic leakage, EM shower width, track parameters, and energy deposit ratios. Simulation of 푍 → 푒푒and 퐽/휓 → 푒푒 processes are used to obtain distributions for signal variables, and simulation of two-to-two(dijet) events are used for background distributions. The distributions are corrected to accurately model data.The final discriminant is defined so that a larger value represents a more electron-like candidate and alower value a more background-like one. Electrons are grouped by quality according to a set of workingpoints (WPs), each with a specific minimum discriminant value that the candidate must pass. DifferentWPs allow for a trade-off between background rejection and reconstruction efficiency. The WPs relevant495.3. Muonsto this dissertation are LHTight, LHMedium, LHLoose, LHVeryLoose, and a specialized LHVeryVeryLooseWP designed for the analysis in chapter 7. The working points are designed so that an electron meeting therequirements of a tighter WP will also pass all looser WPs. (e.g., an LHMedium electron will also count asan LHLoose electron.)5.2.3 IsolationPrompt electrons are expected to be spatially well-separated from other produced particles. By measuringthe track and calorimeter activity in the vicinity of the electron candidate, the isolation metric is used toreject background processes.Calorimeter-based isolation sums the transverse energy of topo-clusters within a cone around the elec-tron’s centre. Track-based isolation, used in this dissertation, is calculated as the transverse momentumscalar sum of tracks within a cone centred around the electron trajectory, excluding those tracks matched tothe electron. Only tracks with 푝T > 1GeV are considered. The isolation variable is labelled according to theradius of the cone defined as Δ푅 =√(Δ휂)2 + (Δ휙)2. For example, the Σ푝 (0.3)T quantity measures the activitynear the electron within a radius of Δ푅 = 0.3.5.2.4 PhotonsPhotons produced in LHC collisions are detected similarly to electrons and reconstructed using the sameframework. There are two major classes of centrally-produced photons: converted and unconverted. Con-verted photons are those which interact with some material in the ID and produce an electron-positron pair.If both charged particles are distinguishable, they form a conversion vertex. A supercluster matched to aconversion vertex is used to identify the photon and its trajectory. Unconverted photons do not interact withthe ID but only appear as energy deposits in the calorimeters. These are distinguished by a supercluster withno matching tracks or conversion vertices.Photons undergo calibration, identification, and isolation like electrons but with distinct algorithms andworking points. Because of the similarity of their signatures, it is necessary to resolve ambiguities betweencandidates that resemble both electrons and photons. Details of these procedures are given in detail inreference [113].5.3 Muons5.3.1 ReconstructionIn ATLAS, muons appear as minimum-ionizing particles that produce some combination of tracks in theMS, tracks in the ID, and distinctive energy deposits in the calorimeters.In the ID, muon reconstruction begins with the tracking algorithm described in section 5.1. In the MS,nearby hit patterns are combined into straight-line “segments” within eachmuon chamber. A segment-seededcombinatorial search is performed to form track candidates by selecting for fit quality and relative orientationof nearby segments. These segments are loosely fit with a first-order parabolic trajectory approximation.505.4. Hadronic jetsThe precision measurements in the bending plane are combined with measurements from the muon triggerdetectors (RPCs and TPCs) to provide a three-dimensional track candidate. To calculate precise trajectory, aglobal 휒2 fit of the candidate is executed using the hits from each segment, then iteratively refit by removingoutliers and including unassociated hits.Muon signatures are sorted into four classes depending on which detectors contribute to their iden-tification: combined, segment-tagged, calorimeter-tagged, and MS extrapolated. Combined muons linkindependently-formed tracks from the ID and MS which are then globally refit. Segment-tagged muons areformed from ID tracks matched to one or more track segments in the MS. This accounts for muons withlow momentum or which pass through MS regions of low acceptance. Calorimeter-tagged muons are IDtracks that can be matched to a calorimeter deposit consistent with a minimum-ionizing particle signature.MS extrapolated muons extend the |휂 | region uncovered by the ID and are formed solely from candidates inthe MS. Though they have no ID or calorimeter matching requirement, extrapolated muon trajectories areloosely constrained to originate from the IP. The search presented in this dissertation uses only combinedand MS extrapolated muons. The reconstruction efficiency over most of the covered phase space is close to99%. Calibrations are applied to the muon momentum scale and resolution to account for differences in realand simulated data [117]. After reconstruction, isolation is calculated for muons using the same definitionsas those used for electrons (section 5.2.3).5.3.2 IdentificationFurther quality requirements are applied to distinguish centrally-produced muons from backgrounds, mainlyfrom pion and kaon decays. They are categorized into four WPs: Loose, Medium, Tight, and High-푝T. TheMedium WP is the default muon definition in ATLAS and the WP used in the analysis presented in thisdissertation.Only combined and MS extrapolated muons are used in the Medium selection, and the latter only in the2.5 < |휂 | < 2.7 region. For a combined muon to be considered to be medium, it must have ≥ 3 hits in ≥ 2MDT layers, except for those in the |휂 | < 0.1 region. An additional condition on the ID and MS momentumcompatibility is required in the form of 푞/푝 significance used to suppress hadrons misidentified as muons.푞/푝 significance is the absolute difference between the ratio of the charge and momentum of the muonsmeasured in the ID and MS divided by the sum in quadrature of the corresponding uncertainties. Mediummuons must have a 푞/푝 significance < 7.For muons with 푝T between 4 and 100GeV, the Medium identification efficiency is 96% with less than0.4% misidentification of hadrons as muons as measured in simulated samples of 푍 → 휇휇 and 퐽/휓 → 휇휇events.5.4 Hadronic jetsQCD confinement is the feature of the strong force that restricts free quarks from propagating, requiringthey exist only in colour singlet combinations. Quarks are often produced in LHC 푝푝 collisions, but due toconfinement, they form showers of secondary quarks and gluons. These showers hadronize, forming colour-515.4. Hadronic jetsneutral hadrons, mainly in the form of pions with some contribution from kaons and light baryons [24]. Thesehigh-momentum showers are relativistically boosted into collimated jets. Jets deposit their energy in thecalorimeters and form tracks in the ID. Algorithms combine information from these detectors to reconstructthe energy and trajectory of the centrally-produced particle.5.4.1 ReconstructionJets are reconstructed using a clustering algorithm with four-vectors from topologically associated energydeposits and charged-particle tracks. ATLAS uses topologically connected calorimeter cell signals knownas topo-clusters. The algorithm which constructs the topo-clusters explores the three-dimensional spatialdistribution of energy deposits in nearby calorimeter cells. The procedure is detailed in reference [114].The primary observable that controls the cluster formation is the cell signal significance 휍EMcell defined asthe ratio of the cell signal amplitude to the cell’s expected noise:휍EMcell =퐸EMcell휎EMnoise,cell. (5.2)First, a seed cell with high significance is selected, then neighbouring cells with sufficient significance areiteratively added.Once the topo-clusters are formed, they are clustered using an anti-푘푡 algorithm (described in detailin reference [118]) as implemented in the FastJet software package [119]. The anti-푘푡 algorithm is asequential recombination procedure that uses the distance 푑푖 푗 between every pair of topo-clusters. Thedistance is defined as푑푖 푗 = min(푝−2T,푖 , 푝−2T, 푗) (푦푖 − 푦 푗)2 + (휙푖 − 휙 푗)2푅2, 푑푖퐵 = 푝−2T,푖 (5.3)in terms of the transverse momenta 푝T, rapidities 푦, and azimuthal angles 휙. 푅 is a tunable parameter of thealgorithm which controls the size of the output jet. 푑푖퐵 is the distance of the object from the beam. In orderof increasing distance, objects 푖 and 푗 will be combined into a new object by adding their four-momenta. If,for some object 푗 , the distance 푑푖 푗 > 푑푖퐵, then object 푖 is classified as a jet, removed from the list of objects,and the remaining distances recalculated.High-momentum objects cluster with nearby low-momentum objects before low-momentum objectscluster amongst themselves. This results in conical jets of radius 푅 with edges resilient to soft radiation butflexible to hard radiation.52Chapter 6Large-radius trackingMany theories of physics beyond the Standard Model (BSM) contain particles with lifetimes that are longcompared to SM particles at the weak scale (see references [120, 121] and references therein). Long-livedparticle (LLP) signatures are a promising yet relatively new domain for discovering new physics at the LHC.However, as searches at colliders have typically focused on low-lifetime phenomena, the reconstructionalgorithms have been optimized to search for charged particles originating near the interaction point (IP).The default ATLAS track reconstruction algorithm, in particular, imposes strict pointing requirementsthat lower the sensitivity to charged particle tracks originating some macroscopic distance from the IP. Anadditional pass of the tracking algorithm with relaxed pointing requirements can be applied to improvesensitivity to LLPs in the ID (referred to simply as LLPs for the remainder of this chapter). The large-radiustracking (LRT) pass used in Run 2 analyses provided a high track reconstruction efficiency, but it alsoproduced many incorrectly reconstructed (fake) track candidates that need to be removed downstream byindividual analyses. Additionally, this large number of fake tracks made the LRT algorithm computationallyexpensive, and therefore only a small subset of the recorded data could be reconstructed using LRT tracking,significantly affecting the sensitivity of many LLP searches.In preparation for Run 3, a small team within ATLAS undertook a substantial retuning of the standardand LRT tracking algorithms focused on reducing the computational cost while maintaining a high track-reconstruction efficiency. These improvements enable the LRT pass to be run by default on all ATLASevents, streamlining the workflows of LLP searches and expanding their sensitivity.This chapter presents the LRT algorithm and data preselection workflow used in Run 2 analyses. Im-provements to the algorithm for Run 3 and Run 2 data reprocessing are then discussed as well as potentialtechniques for further refinement. Metrics of performance on simulation, data, and resources are presented,and the impact on future analysis workflows is estimated.6.1 MotivationMany BSM models contain predictions of neutral particles with long lifetimes.13 These particles may havemacroscopic decay lengths when travelling near light speed. The proper lifetime 휏 of a particle is calculatedas the inverse of its decay width, which in the framework of QFT is푑Γ ∼ 1푚|M|2푑Π (6.1)13Some particles in the SM also have long lifetimes, such as charged and neutral kaons, charged pions, and B mesons.536.2. Run 2 LRTwhere 푚 is the particle’s mass,M is the matrix element of the decay, and 푑Π is the available phase space.Suppression of the matrix element, kinematic suppression of the available phase space, or a low mass willincrease the lifetime of a decaying particle. One such example of an LLP search is that presented in chapter 7of this dissertation, which describes how the presence of a massive right-handed neutrino with low couplingstrength produces a displaced leptonic vertex.Because of the exponential decay times of LLPs, the highest density of decays occur close to the IP. Fordecays with lifetimes between O(.01)–O(1.0) ns, the ATLAS ID provides substantial coverage for LLPsin such models. In recent years, several ATLAS analyses have published results which use LRT tracks toseek direct evidence of BSM phenomena [122–128]. The reconstruction of displaced tracks is crucial forachieving sensitivity to these signatures.6.2 Run 2 LRTThe LRT configuration and procedure described here are used in the analysis presented in chapter 7. Adetailed presentation of the algorithm and its performance can be found in reference [129], from which textand figures in this section are drawn.In the default reconstruction procedure, stringent requirements are placed on the transverse and longi-tudinal impact parameters of the reconstructed candidate tracks relative to the primary vertex (푑0 and 푧0,respectively). This is intended to keep the computation time reasonable while still being very efficient inreconstructing primary particles with high purity. The specific constraints, referred to as standard tracking,are discussed in section 5.1. The standard tracking procedure comprises two tracking passes, inside-out andoutside-in, referring to the portion of the ID where track seeds are formed.LRT is not a separate algorithm but an additional pass of the inside-out tracking algorithm with substan-tially loosened selections on track impact parameters and the number of hits. The most significant differencesin these selections are listed in table 6.1. These differences allow for the reconstruction of tracks originatingfurther from the IP. Crucially, the only hits used in the LRT pass are those that have not been associatedwith any tracks already reconstructed by standard tracking. The number of leftover hits depends on thereconstruction efficiency and fake rate of the previous passes.Table 6.1: Important selections that differ between the standard and the LRT setups in the Run 2 configura-tion [129].Track parameter Standard Large-radiusMax. |푑0 | 10 mm 300 mmMax. |푧0 | 250 mm 1500 mmMax. track |휂 | 2.7 5.0Min. track 푝T 500 MeV 900 MeVMin. Si hits 7 7Min. un-shared Si hits 6 5Max. shared silicon modules 1 2Seed extension Combinatorial SequentialThe new requirements are applied to all stages of the tracking algorithm: seeding, track finding, ambiguity546.2. Run 2 LRTresolution, and TRT extension. The extension of seeds into track candidates uses a sequential Kalman filteras opposed to the combinatorial Kalman filter used in standard tracking, preventing the creation of multiplecandidates from a single seed. In Run 2, the resulting LRT tracks are merged with the standard tracks toform the final track collection. This direct merging is possible without overlap removal since LRT tracks, byconstruction, do not share hits with standard tracks.6.2.1 PerformanceTo gain insight into the LRT performance, the reconstruction efficiency is measured for two BSM physicsprocesses, one supersymmetry (SUSY) model producing displaced leptons (via squark pair production) andanother SUSY model producing displaced hadrons (via gluino pair production). These two processes werechosen to quantify the leptonic and hadronic performance of LRT, covering the common final-state signaturesin ATLAS searches. The following studies use the definition of truth-match probability (푝match) as definedin section 5.1.2. The efficiencies are measured as a function of the production radius of displaced particles(푟prod).In fig. 6.1, the inclusive reconstruction efficiency is defined as the ratio of reconstructed tracks matchedto a truth particle (푝match ≥ 0.5) over the number of truth particles:reconstruction efficiency =# signal truth particles matched to reconstructed tracks# signal truth particles. (6.2)For both the numerator and denominator, the truth particles are subject to simple fiducial selections:푝T > 1GeV, |휂 | < 2.5, 푟prod < 440mm, charge = ±1, from LLP decay (signal). [mm]prodr0 50 100 150 200 250 300Reconstruction effiency00.20.40.60.811.21.41.6Simulation Preliminary ATLASDisplaced leptons Standard tracksLarge radius tracksCombined(a) Displaced leptons [mm]prodr0 50 100 150 200 250 300Reconstruction effiency00.20.40.60.811.21.41.6Simulation Preliminary ATLASDisplaced hadrons Standard tracksLarge radius tracksCombined(b) Displaced hadronsFigure 6.1: Inclusive track reconstruction efficiency for displaced charged particles produced by the decayof long-lived signal particles. The efficiency is shown as a function of 푟prod, with truth particles and trackssubject to fiducial selections. The efficiency for standard and LRT is additive, and the total efficiency is thesum of both [129].At low 푟prod, standard tracking is very efficient, and few hits are left over to form tracks in the LRT step.Tracks which are produced far from the interaction point are unlikely to be reconstructed by the standardtracking; without LRT, fewer than 20% of the tracks with 푟prod > 50mm originating from the LLP decay556.3. Improvements for Run 3would be reconstructed. Adding the LRT step substantially increases the reconstruction efficiency beyond푟prod of 50mm for both benchmark samples, maintaining above 50% efficiency to nearly 300mm.Notably, the average number of fake tracks per event (fake rate) is not reported in the Run 2 optimizationof LRT [129]. It is found that an average of 70% of LRT tracks in Run 2 are fake.6.3 Improvements for Run 3ATLAS’s Run 2 LRT approach is highly efficient in reconstructing the trajectories of displaced tracks, butthe relaxed constraints allow for more combinatorial fake track candidates to be formed (see section 5.1.2for a definition of fakes). Consequently, the time needed to run the complete ATLAS event reconstruction,including LRT, increases by about a factor of 2.5 compared to the standard configuration [129]. A corre-sponding increase in required storage space is also seen. The ATLAS computing budget does not allow theentire recorded dataset to undergo this secondary reconstruction, and so only a subset of the data is processedin this way. Which data is processed through the LRT pass is selected using a filtering scheme described insection 6.3.1.Given the unavoidable inefficiencies of such filters and the human development and validation effortrequired, our LRT optimization team undertook the task of including LRT by default in preparation for theRun 3 data-taking period. The primary aim of this effort was to reduce the LRT pass’s computational load sothat it could be run on the full ATLAS dataset while staying within the CPU and storage budget, removingthe need for filters for most analyses.14While designing the HNL analysis presented in chapter 7 it became clear that the deficiencies in theexisting LRT strategy caused the analysis sensitivity to suffer. Not only was the filter removing a substantialportion of relevant data, but the large number of fake tracks reconstructed by the existing LRT configurationled to poor-quality signal vertices and a large background originating from random-track-crossings (seesection 7.5.5). A motivating factor in undertaking the LRT optimization was to improve the signal sensitivityfor subsequent HNL analyses.15In parallel, a similar campaign was conducted to optimize the standard tracking pass, expanding theflexibility of the computing budget allocated for tracking. A full description of the standard trackingoptimizations is discussed in reference [130]. Incidentally, the optimization of standard tracking reconstructsfewer tracks (both real and fake), leaving more hits for the LRT pass. If LRT were not also optimized, theadditional leftover hits would translate to an increase in fake LRT tracks.6.3.1 FiltersCurrent Run 2 LLP analyses rely on a set of filters to select a subset of events to be further processed.A schematic of the procedure is shown in fig. 6.2(a). The complete Run 2 dataset undergoes a standardreconstruction, fromwhich the filters select events of interest. Approximately 10% of the raw data is selected.The reconstruction algorithms are then run again on this smaller subset, but with LRT and displaced vertex14The filter scheme is still retained in Run 3 for a few analyses which require secondary reconstruction algorithms beyond LRT.15Indeed, an effort is currently underway to re-analyze the Run 2 dataset with the new LRT configuration.566.3. Improvements for Run 3finding (DV) enabled, allowing for use by LLP analyses. The filters are defined for each analysis in a way thatoptimizes the selection of signal events while keeping the total fraction of filtered events low. For example,the filter for the HNL analysis defined in section 7.2.4 selects approximately 50% of the simulated signalevents but only approximately 2.6% of all recorded data.Though passable, this method of filtering and reprocessing the data is problematic. It is cumbersome,computationally expensive, requires substantial development and validation labour, and is prone to errors.16As well as being burdensome, the filters discard potentially relevant data. This difference is significant forsearches looking for only a few signal events.standard analysesLLP analysesRAWdatastandard reconstructed data~10% of RAW datafiltersprompt reconstructionsecondary reconstructionLRT, DVspecialized reconstructed data(a) Run 2analysesRAWdatastandard reconstructed dataprompt & displaced reconstruction(b) Run 3Figure 6.2: In Run 2 (a), LRT tracking and displaced vertex reconstruction were only run on a subset ofdata selected by applying specialized filters to the standard reconstruction. This scheme requires substantialcomputing and human resources and is prone to errors. In Run 3 (b), the optimization of LRT trackingallows it to be run by default in the event reconstruction. LLP analyses can be performed using the standarddata stream, allowing for more flexible analysis designs. The full ATLAS dataset will be available for futureanalyses without the need for filters.6.3.2 Selection criteriaTrack reconstruction takes place in sequential steps, with roughly increasing computational complexity. Inorder to minimize the time spent reconstructing fake tracks, they are removed as early as possible in thesequence and suppressing them at any point before final storage reduces the impact on disk space. Belowis a summary of the carefully chosen selections applied at each step which optimize the LRT algorithm forRun 3. The numerical stages in the following descriptions refer to those in fig. 6.3.16In preparing the data used in this dissertation, a configuration bug caused the primary reconstruction used by the filter to specifythe incorrect ID alignment geometry. The months-long reconstruction effort had to be discarded, causing a significant delay fornearly a dozen analyses. Not to mention a substantial consumption of energy and resources from the LHC computing grid.576.3. Improvements for Run 3Space Point Formation Seed Finding Track FindingTRT ExtensionAmbiguity Resolution1 2 3 4 5Figure 6.3: LRT tracks follow the same reconstruction sequence as standard tracks. By removing fake tracksas early as possible in the sequence, less time is spent reconstructing them in the later (and generally morecomputationally expensive) stages.• SCT seeding (2) — Only SCT hits are used to produce three-hit seeds, as opposed to SCT or pixelhits.• Seed ranking (2)—The seed ranking is modified. This ranking decides the order in which tracks areprocessed and prioritizes signal-like tracks.• Seed confirmation (2)— Seeds, formed from three space-points, must be confirmed. This confirma-tion is achieved by replacing the outermost hit with one from the next silicon layer. If the old and newseed parameters are compatible with one another, the seed in confirmed. The confirming hit can be apixel or SCT space-point.• Tightened cuts (2-4) — Several cuts are tightened compared to the Run 2 configuration. Impactparameters, minimum required hits, maximum allowed holes, and fit quality are all tuned to minimizethe rate of fake tracks. A complete description of changes is listed in table 6.2.• Neural network cut (4) — Though not enabled by default, a neural network model is trained andimplemented to substantially reduce fake tracks in the ambiguity resolution step.6.3.3 DNN discriminantIn the standard and LRT tracking passes, several requirements are applied in the ambiguity-solving stageto remove fake tracks. These direct cuts are effective but one-dimensional. Multivariate discriminants arepowerful tools useful for separating collections with correlations in multiple dimensions.As part of the LRT optimization effort, a deep neural network (DNN) was implemented to differentiatebetween good and fake tracks (see section 5.1.2 for definitions). The inputs to this network are eight carefullychosen track parameters: 푧0, 푑0, 휂, number of SCT hits, number of SCT holes, number of silicon hits,number of degrees of freedom, and an engineered variable named Δ휃. Δ휃, as shown in fig. 6.4 is definedas the angular difference between the primary and secondary particle’s flight directions, assuming the trackis produced in a secondary decay. Each of these quantities is available after the global 휒2 fitting of thetracks. Many other quantities are available, but an effort was made to exclude quantities known to have pooragreement between data and MC (e.g., 휒2, pixel holes), as the DNN may exploit features of the simulationit was trained on, which may hinder its performance on real particle data.586.3. Improvements for Run 3Table 6.2: Differences introduced for Run 3 optimization of LRT. The following changes drastically reducethe fake rate while maintaining high reconstruction efficiency of displaced tracks.Cut name Run 2 LRT Run 3 LRTMin. 푝T 0.9GeV 1GeVMax. |휂 | 5 3Max. |푧0 | 1500mm 500mmMin. secondary 푝T 0.5GeV 1GeVMin. clusters 7 8Min. Si. not shared 5 6Max. SCT hole 2 1Max. double holes 1 0Max. holes gap 2 1Max. 휒2 15 9Max. 휒2 no add. 35 25Road width 20 5Min. weighted clusters 6 8Max. 푑0 on seeds 1000mm 300mmDo Z boundary false trueStrip seeding only false trueRequire confirmed seed false trueSeed score 푑0 Δ휃LLPPVdaughterpoint of closest approachd0z0θθ'Δθ = θ - θ'Figure 6.4: Δ휃, an engineered variable used in the DNN discriminant, is the angular difference between theprimary and secondary particle’s flight directions, assuming the track is produced in a secondary decay. Thisis used to estimate how “LLP-like” a track is.A model was produced using Keras [131] with TensorFlow [132] backend. The input layer has eightinput parameters, followed by four hidden layers with 24, 18, 8, and 8 inputs, each using a relu activationfunction. The output layer has one output and uses a sigmoid activation function. The model is trained usinga binary cross-entropy loss function.The DNN was trained on a collection of tracks from MC simulation samples, extracted and evaluated596.3. Improvements for Run 3at the end of the ambiguity solver stage after fitting, as shown in fig. 6.6. These are the tracks that remainafter all other optimizations from section 6.3 are applied. The samples were split into training, testing, andvalidation sets, and each track was categorized as good or fake. The categories were balanced, the featuresnormalized, and the data weighted to avoid preferential treatment of the over-represented low-푝T tracks. Thenetwork’s output is a value between zero and one, with a higher value representing the similarity of the inputtrack to a good track. By implementing a cut at an arbitrary threshold, tracks that the DNN considers similarto fake tracks are removed.By selecting 0.1 as the DNN score threshold, it is possible to remove 50% of fakes while only removing2% of good tracks. Figure 6.5 shows the effect of this cut for a VH4b sample (see section 6.4.1). As theDNN is applied relatively late in the track reconstruction pipeline, this additional selection aims to reduce therequired storage space rather than the reconstruction time. However, the evaluation of the DNN discriminantis very fast, and the removal of fake tracks from the TRT extension actually reduces the total time spent ontrack reconstruction.η00.20.40.60.81Technical Efficiency InternalATLASVH4bRun 3Run 3 + NN (.1)2− 0 2η0.951ratio(a) Technical efficiencyη0123456Fake tracks / event InternalATLASVH4bRun 3Run 3 + NN (.1)3− 2− 1− 0 1 2 3η00.51Ratio(b) Fake rateFigure 6.5: Implementing a cut on the trained DNN discriminant can reduce fake LRT tracks a further 50%beyond the already-implemented optimizations. This reduction comes at the cost of only a 1–2% reductionin signal track reconstruction.This trained model was implemented in the ATLAS reconstruction pipeline using the lwtnn (LightweightTrained Neural Network) interface [133]. However, it is not used in default reconstruction and must bemanually enabled. One reason for this is that the previous optimizations to LRT were sufficient to reducethe computing time to within acceptable limits. Another reason was that there remains skepticism from thetrack reconstruction experts that this network would not rely upon features poorly modelled in simulation.For example, the detector simulation takes an optimistic view of the damaged pixel sensors in the ID. TheDNN may assign a high penalty to the number of silicon holes in each track, and as the pixel sensors aredamaged by radiation throughout Run 3, the performance of the DNN may fall or introduce bias.606.4. Performance study on simulationMake cuts on trackpropertiesShare >2 hits withoutput tracks?Score and order tracksProcess highest firstFit track candidateRemove shared hitfrom candidateInput trackcandidatesRejected tracksOutput tracksDNN discriminant appliedpassyesfailnoLoop until no candidates remainFigure 6.6: A diagram of the track ambiguity-solving procedure. The DNN discriminant is applied immedi-ately before the output tracks are stored. This is also the point at which tracks are extracted to train the DNN.6.4 Performance study on simulationPerformance studies were conducted on real and simulated data to quantify the improvements to the LRTparameters. The studies were used to iterate on the tuning and demonstrate the maintained reconstructionefficiency to the physics analysis groups most likely impacted by the changes.6.4.1 SamplesThree sets of simulated BSM physics signals are studied to analyze the performance of the LRT pass onsignatures of interest. Each of these signals is characterized by the production of a long-lived neutral particlewhich subsequently decays into charged SM particles. These signals have a high probability of producingcharged particles from vertices originating in the ID, producing a high number of displaced tracks. Figure 6.7shows the models with displaced vertices (DVs) used in the performance studies. Data and 푡푡¯ samples arealso used in certain studies.• SUSY (massive DV) — A supersymmetric (SUSY) long-lived neutralino model is used to studyhadronic DVs with high mass and a high multiplicity of low-momentum tracks. This signal issimulated similarly to that in reference [126] but with coupling parameters tuned such that the vertexis displaced.• VH4b (light DV) — A Higgs-portal model is used to study hadronic DVs with lower mass, producing616.4. Performance study on simulationg˜g˜χ˜01χ˜01ppq qλ′′qqqq qλ′′qqq(a) SUSY`±`∓bbbbggZ∗ZHaa(b) VH4b𝑊+ℓ+𝛼ℓ−𝛽ℓ+𝛾𝜈𝛾N 𝑊+∗(c) HNLFigure 6.7: Three different DV models used to optimize and characterize the LRT algorithm for Run 3.Figures from [1, 123, 126].a few tracks in their decay vertices. The simulation of these samples is detailed in reference [123].In the following performance plots, this model is labelled as VH4b (vector boson to Higgs to four 푏quarks).• HNL (lepton DV) — A heavy neutral lepton (HNL) model which produces a di-muon DV is usedto study leptonic decay vertices. This is the same model as studied in chapter 7 and reported inreference [1].• tt¯ (backgrounds) — To simulate common backgrounds which appear in dense environments, top-antitop (푡푡¯) MC simulation is used with both top quarks decaying hadronically. The parameters of thesimulation are reported in reference [134].• Data — √푠 = 13TeV data from the 2018 data-taking period is used to measure the accuracy of thesimulation. An unbiased sample of events (zero bias) is used, in which data is collected by triggeringrandomly filled bunches.6.4.2 EfficiencyThe efficient reconstruction of charged-particle tracks is important, but with the revised LLP analysis strategy,a sacrifice in efficiency is unavoidable. In tuning the LRT pass, the goal is to keep the reconstruction efficiencyas high as possible in key regions of phase space.Truth particles are subject to the same fiducial selections described in section 6.2.1. Distributions of thestandard and LRT tracking efficiency, as well as their combination, are shown in fig. 6.8. The performance forboth hadronic and leptonic signals is quite high. As in the performance studies for the Run 2 configuration,LRT recovers the substantially diminished tracking efficiency at high displacement.A technical efficiency is also defined to separate the algorithmic efficiency from restrictions arising fromthe detector limitations. The technical efficiency is used to determine the reconstruction performance fortruth particles expected to leave enough hits in the detector to be reconstructed by the tracking algorithmsemployed. Selections similar to the track reconstruction requirements are applied to the truth particles in the626.4. Performance study on simulation0 50 100 150 200 250 300Production Radius [mm]00.20.40.60.811.21.4I nc lu si ve E ff i ci en cyCombinedLarge Radius TrackingStandard Tracking = 13 TeVsATLAS Simulation Preliminarybbbb→aa→VH, H = 100 mmaτ = 55 GeV, cam(a) Displaced hadrons0 50 100 150 200 250 300| [mm]0|d00.20.40.60.811.21.4I nc lu si ve E ff i ci en cyCombinedLarge Radius TrackingStandard Tracking = 13 TeVsATLAS Simulation Preliminarybbbb→aa→VH, H = 100 mmaτ = 55 GeV, cam(b) Displaced hadrons0 50 100 150 200 250 300Production Radius [mm]00.20.40.60.811.21.4I nc lu si ve E ff i ci en cyCombinedLarge Radius TrackingStandard Tracking = 13 TeVsATLAS Simulation Preliminaryνll→Nl, N→W = 100 mmNτ = 15 GeV, cNm(c) Displaced leptons0 2 4 6 8 10| [mm]0|d00.20.40.60.811.21.4I nc lu si ve E ff i ci en cyCombinedLarge Radius TrackingStandard Tracking = 13 TeVsATLAS Simulation Preliminaryνll→Nl, N→W = 100 mmNτ = 15 GeV, cNm(d) Displaced leptons (zoomed)Figure 6.8: Inclusive track reconstruction efficiency for displaced charged particles produced by the decay oflong-lived scalar particles, 푎 (figs. (a) and (b)) or by the decay of long-lived heavy neutral leptons, 푁 (figs.(c) and (d)). The efficiency is shown as a function of the radius of production of displaced particles (figs.(a) and (c)) and the absolute value of the transverse impact parameter, |푑0 | (figs. (b) and (d)). As the HNLdecay products are highly boosted, the signature has lower |푑0 | tracks, so fig. (d) focuses on the transitionfrom standard tracking to LRT around |푑0 | = 5mm [135].denominator. The selections are: 푝T > 1GeV, |휂 | < 5, 푟prod < 300mm, number of silicon hits ≥ 7. Thismeasures the efficiency of the tracks that could have been reconstructed.A direct comparison of technical reconstruction efficiency between Run 2 and Run 3 configurations isshown in fig. 6.9(a). The hadronic and leptonic signatures show a 10–15% reduction in track reconstruction636.4. Performance study on simulationefficiency. This was seen as acceptable by the physics analysis groups in light of the tremendous reductionin fake tracks and the ability to gain access to the full recorded dataset.| [mm]0|d00.20.40.60.81Technical efficiency InternalATLASRPVLFRun 2Run 30 100 200 300| [mm]0|d0.70.80.91Run 3Run 2(a)| [mm]0|d01020304050607080Fake tracks / event InternalATLASVH4bRun 2Run 30 50 100 150 200 250 300| [mm]0|d00.20.4Run 3Run 2(b)Figure 6.9: The technical efficiency of LRT tracks for a SUSY signal sample compared between Run 2 andRun 3 configurations is shown in (a). For most of the 푑0 range, over 85% of the Run 2 efficiency is retained.The fake rate comparison for the same signal sample is shown in (b). The rate of fake tracks is reduced by95% on average.6.4.3 Fake rateFake tracks include both combinatorial fakes and secondary fakes. Combinatorial fakes are defined asreconstructed tracks that have a 푝match < 0.5, where 푝match is a weighted measure of how many hits arematched to a single truth particle. Secondary fakes are tracks with no matching truth link in simulation andgenerally from material interactions. Both are discussed in more detail in section 5.1.2.A useful measure of optimization is the signal sensitivity defined as the signal count divided by the squareroot of the background count, 푠 = 푆/√퐵 [5].17 For any given analysis design, one can simulate the number푆 of expected signal events, and the expected number 퐵 of background events. The Run 3 optimizationsdescribed above reduce the fake rate by 95% in both signal (HNL, VH4b, SUSY) and background (hadronic푡푡¯) compared to the Run 2 configuration. Figure 6.9(b) shows the drastic reduction in the fake rate betweenRun 2 and Run 3 configurations. This equates to an increase in signal sensitivity of 400%! By enabling theDNN discriminant, the fake rate can be decreased by an additional 50% at the cost of only 1–2% efficiencyreduction or a sensitivity increase of 550%. This reduction in fake tracks also has downstream effects onvertex creation.17A general statement of the significance 푠 of the hypothetical signal observation is then given by the number of Gaussianstandard deviations of the background distribution to which the signal corresponds, 푠 = 푆/휎(퐵). If the systematic uncertainty onthe background can be neglected, this is given by 푠 = 푆/√퐵 , where we have assumed a Poisson distribution for the backgroundevent counts, thus making the standard deviation equal to the square root of the mean [5].646.4. Performance study on simulation6.4.4 VertexingMany LLP analyses use additional secondary vertex reconstruction algorithms (VSI), with vertices oftenformed from LRT tracks [136]. (See section 7.3.3 for a summary of the VSI algorithm). A high number offake tracks contaminating the event translates to a large fake vertex background. This background particularlyimpacts light LLP signatures, for which fake vertices can be difficult to reject. As such, the purity of thetrack collection (ratio of good to fake tracks) is crucial in reconstructing high-quality vertices.The impact of the considerable reduction in fake LRT tracks is found to reduce the number of fakesecondary vertices by up to a factor of ten. Not only are the fake vertex backgrounds reduced, but thereconstruction efficiency improves due to fewer fake tracks interfering with the vertex reconstruction. Fig-ure 6.10 shows the vertexing efficiency and fake rate for a VH4b signal comparing LRT reconstruction withRun 2 and Run 3 configurations. The definition of reconstruction efficiency and fake vertices is found inreference [136].0 50 100 150 200 250 300 350 [mm]xyL0.20.40.60.811.21.41.61.822.2310×Vertices / 8 mmIBL PIX1PIX2PIX3SCT10 50 100 150 200 250 300 350 [mm]xyL2−101−101Run 3 / Run 2LLP Run 2 ReconstructionLLP Run 3 ReconstructionNon-LLP Run 2 ReconstructionNon-LLP Run 3 ReconstructionActive layersATLAS Simulation Preliminary-1 = 13 TeV, 139 fbsbbb b→ aa →VH, H = 100 mmaτ = 55 GeV, camFigure 6.10: A comparison of the radial distributions of reconstructed secondary vertices in a simulatedLLP sample using the Run 2 and Run 3 track reconstruction configurations is shown. The circular markersrepresent reconstructed vertices matched to truth-level LLP decay vertices. The dashed lines representreconstructed vertices not matched to truth-level LLP decay vertices (non-LLP). The four pixel layers andthe first SCT layer are shown in the figure with vertical lines, and charged-particle interactions with thismaterial are responsible for spikes in the distributions. The Run 3 reconstruction shows a modest increasein the number of LLP vertices and considerably fewer non-LLP vertices due to the significant increase inpurity of the LRT algorithm [135].6.4.5 Pileup robustnessThe average pileup is expected to increase to 〈휇〉 = 50 in Run 3 (with extremes up to 90) compared to between20–40 in Run 2, further motivating the need to optimize LRT and other reconstruction algorithms [137]. In656.5. Comparison to dataanticipation of this increase, it is helpful to characterize the LRT algorithm’s response to pileup and ensurethat the number of fake tracks does not increase at an unsuitable rate. The difference in slopes in fig. 6.11indicates that high-pileup environments increase the fake rate more for LRT tracks than for standard tracks.Regardless, pileup sensitivity for LRT tracks is improved by a factor of six from the Run 2 configuration.0 10 20 30 40 50 60µ10210310410510Number of TracksStandard TrackingLarge Radius Tracking = 13 TeVsATLAS Simulation Preliminary all hadronicttFigure 6.11: The mean number of reconstructed tracks per event as a function of 휇 in simulated 푡푡¯ events forthe standard and LRT track reconstruction (Run 3 configuration). This quantity reflects the additional tracksreconstructed by the LRT pass for typical SM processes. The number of real tracks is expected to scalelinearly with this quantity since it is related to the number of charged particles produced in the collisions. Thenumber of random combinations is expected to scale with a higher power since the enhanced combinatoricsallow for more such candidates to be formed. The number of tracks for the LRT reconstruction increase fasteras a function of 휇 which indicates that it is more impacted by random combinations at high pileup [135].6.5 Comparison to dataThe reconstruction algorithms must produce similar results in data and MC simulation as many analysesrely heavily on simulation for background estimates and expected signal efficiency. A comparison of severaldistributions is made to ensure that the modifications to the LRT algorithm do not inadvertently produceunacceptable data/MC differences. Zero bias data (i.e., data collected from pseudo-randomly selectedevents18) from the 2018 data-taking period is compared to simulated samples of inelastic 푝푝 scatteringevents, both reprocessed using the Run 3 reconstruction software [130]. Simulated events are reweightedsuch that the number of interactions per bunch crossing is consistent with that of the data, with a meanvalue 〈휇〉 = 34. The distributions of track transverse momenta are found to be consistent between data andsimulation [138]. Figure 6.12 shows examples of quantities used to characterize tracks, with MC and data in18The zero bias data stream selects events gathered one complete beam revolution after a high-푝T trigger is fired. This is intendedto be a “random” bunch collision but proportional to the bunch’s instantaneous luminosity.666.6. Performance study on computing resourcesgood agreement.0 1 2 3 4 5 6 7 8 9Number of pixel hits21031041051061071081091010101110LRT tracks0 1 2 3 4 5 6 7 8 9Number of pixel hits0.80.911.11.2data/MCDataSimulationATLAS Preliminary = 13 TeVsData 2018, Zero bias events(a)0 50 100 150 200 250 300| [mm]0|d20406080100610×LRT tracks / 4 mm0 50 100 150 200 250 300| [mm]0|d0.80.911.11.2data/MCDataSimulationATLAS Preliminary = 13 TeVsData 2018, Zero bias events(b)Figure 6.12: A comparison of track quantities in zero bias data (black markers) and simulated inelastic푝푝 collisions (filled red histogram) is shown. The simulation is normalized to the number of tracks indata. Figure (a) shows the distribution of the number of hits in the pixel detector, and figure (b) shows thedistribution of the absolute value of the transverse impact parameter, |푑0 | [138].As displaced vertices are often the final product of LRT tracks, a “standard candle” in data is needed. 퐾0Smesons are good candidates as they have a mean decay length of 푐휏 = 27mm and are produced in abundancein LHC 푝푝 collisions. 퐾0S decays are identified by reconstructing two-track vertices using both standardand LRT tracks and selected by requiring 472MeV < 푚DV < 522MeV. Simulation is normalized to databy the total number of DVs. Figure 6.13 shows that LRT efficiency in data and MC are in good agreementand that LRT tracks are vital for efficiently reconstructing vertices produced beyond the first layer of thepixel detector.19 퐾0S decays are important for estimating displaced vertexing and tracking uncertainties asdiscussed in section 7.6.4.6.6 Performance study on computing resourcesThe optimization of LRT for Run 3 is best seen in the context of the parallel optimizations of standardtracking. Improvements to both algorithms drastically reduce the CPU time and required disk space. Bothresult from the reduction of fake tracks in the reconstruction pipeline.The time taken for track reconstruction in the software release used during Run 2 compared to thenew release prepared for Run 3 is shown in fig. 6.14(a) as a function of 〈휇〉 [139]. The reconstructiontime is shown for both standard-only and standard+LRT tracking. Even with LRT, the total time neededfor tracking reconstruction is reduced substantially compared to Run 2, up to 40% at 〈휇〉 = 60. The newtracking optimization also scales less sharply with 〈휇〉. In terms of disk space, similar reductions are seenin fig. 6.14(b).19In these figures, 푅푥푦 represents the same quantity as 푟DV in chapter 7: the DV’s reconstructed distance from the IP in the x-yplane.676.6. Performance study on computing resources0 50 100 150 200 250 300 350 [mm]xyR310410510610710810 candidate vertices / 4 mmS 0KIBL PIX1PIX2PIX3SCT10 50 100 150 200 250 300 350 [mm]xyR0.80.911.11.2data/MCDataSTD+STD (MC)LRT+STD (MC)LRT+LRT (MC)Active layersATLAS Preliminary = 13 TeVsData 2018, Zero bias events(a)0 50 100 150 200 250 300 [mm]xyR00.20.40.60.811.21.4 candidate vertices / 5 mmS 0Fraction of KIBL PIX1PIX2PIX3STD (data)LRT (data)STD (MC)LRT (MC)Active layersATLAS Preliminary = 13 TeVsData 2018, Zero bias events(b)Figure 6.13: Figure (a) shows the radial distribution of reconstructed 퐾0S candidate vertices in 2018 zerobias data (black markers) and simulated inelastic 푝푝 collisions (stacked histogram). Vertices in simulationare separated into three categories based on the number of LRT tracks included in the vertex fit. The totalnumber of vertices in simulation is normalized to the number of vertices in data. The four pixel layers and thefirst SCT layer are shown in the figure with dashed vertical lines. Figure (b) shows the fractional distributionof the same 퐾0S candidates in data and MC comparing vertices reconstructed with two standard (STD) tracksand at least one LRT track. Both figures indicate that LRT efficiency in data closely matches MC [138].20 25 30 35 40 45 50 55 605000100001500020000250003000035000400004500050000CPU [a.u]ATLAS Preliminary>µATLAS Tracking CPU vs <Run 2 Data ReconstructionLHC Fill 6291Run 2 ReconstructionRun 3 Reconstruction without LRTRun 3 Reconstruction80 85 905000100001500020000250003000035000400004500050000Not on GRLLHC Fill 735820 25 30 35 40 45 50 55 600.20.40.60.811.2Run 3 / Run 2〉 µ 〈0.20.40.60.811.280 90(a) CPU20 25 30 35 40 45 50 55 60050100150200250300350400Disk Space [kb/event] PreliminaryATLASInner Detector onlyLHC Fill 6291Run 2 ReconstructionRun 3 ReconstructionRun 3 Reconstruction w/o LRT80 85 90050100150200250300350400LHC Fill 7358Not on GRL20 25 30 35 40 45 50 55 600.40.60.8Run 3 / Run 2〉µ〈0.40.60.880 90(b) Disk spaceFigure 6.14: Processing time (a) and disk space (b) taken per event versus average pileup 〈휇〉 to reconstructthe same data events, comparing the Run 2 (green squares) and Run 3 (purple unfilled circles) reconstructionsoftware. The Run 3 numbers are also presented, including the impact of the additional LRT tracking pass(blue filled circles). The bottom panels depict the time taken as a fraction of the Run 2 result. The disk spacevalues reflect the output of the ID reconstruction in the ATLAS EDM format [130].A back-of-the-envelope calculation can estimate the additional savings by removing filtered and repro-cessed data. In the default reconstruction scheme (without LRT), for an estimated 25 × 109 events in Run 3at 400 kB/event, the expected AOD size is ∼ 10 PB. Storing LRT tracks for each event increases the sizeby an additional 11.7% for events with 〈휇〉 between 40 and 90 (a conservative estimate). Approximately an686.7. Impact on analysesadditional 1.17 PB of data and 2.17 PB ofMCwill be required by enabling LRT. However, if the filter schemeis carried on into Run 3, a duplicated 2.40 PB of raw and 2.22 PB of reconstructed data must be stored.Additionally, the derived AODs (copies of AODs with only analysis-relevant data retained) are expected toreduce in size by 80% due to the removal of 95% of fake tracks, translating to approximately 1.44 PB insavings. Summing these debits and credits, it is possible to recover on the order of 2.72 PB of space bystoring LRT information in the standard stream instead of in a duplicate data stream.6.7 Impact on analysesFor a sample of LLP analyses, the LRT optimization team collected the estimated impact of switching froma Run 2+filters configuration to a Run 3 configuration without filters. Each analysis generally sees thesignal reconstruction efficiency increase or remain constant. The feedback reported here is taken from anintermediate optimization with roughly 5% reduced LRT efficiency, except for the HNL signal, which reportsthe final configuration with 10-15% reduced LRT efficiency. An attempt was made to separate the impact ofonly the LRT optimization and the removal of the LLP filter.In a sample HNL signal with a di-muon displaced vertex (see chapter 7), the reconstruction efficiencyincreases by 8% over the Run 2 configuration simply by optimizing LRT to reduce fake tracks. By removingthe filter, that gain increases to 28%. For an HNL sample with an 푒휇 displaced vertex, LRT optimizationshows gains of 21% and removing the filter increases that to 45%. This shows that for the HNL analysis,the optimized LRT pipeline would correspond to an improved sensitivity equivalent to gaining an additional63 fb−1 of data. Distributions of the reconstructed HNL mass and the total yields are shown in fig. 6.15.A VH4b sample of displaced hadrons shows nearly a 100% increase in signal efficiency by using theRun 3 LRT with no filter. The signal remains effectively constant for a displaced 휏 lepton sample whilefakes are reduced by 80%. A SUSY DV analysis generally sees more DVs in regions where 푚DV is less than800GeV.In addition to the signal gains, backgrounds are heavily suppressed for each of these analyses. Forexample, the dominant background in the search for HNLs is due to two-track vertices formed by the randomcrossing of unrelated tracks (see section 7.5.5). It is suspected that the majority of these are due to thecrossing of fake tracks. For signals with multi-track vertices, fake tracks attached to the vertex can distortthe calculation of the invariant mass and other quantities. Run 3 is expected to show tremendous gains insensitivity and accuracy due to the increased track purity.6.8 Inclusion in Run 3 and Run 2 reprocessingAfter performance studies on the efficiency and computing load were presented, the collaboration agreed toinclude the LRT pass in the default ATLAS reconstruction pipeline. The standard and LRT track collectionsare stored as separate entities in the ATLAS EDM, but a virtual view is implemented, allowing analyzers toaccess the merged collections easily. This implementation is preferred as it minimizes disruption to ongoinganalyses that would otherwise be suddenly inundated with displaced tracks if stored in a single collection.696.8. Inclusion in Run 3 and Run 2 reprocessing0 5 10 15 20HNL mass [GeV]0510152025303540entries68.09, Run 2 LRT with filter82.64, Run 3 LRT v8 with filter99.13, Run 3 LRT v8 NO filter-1 Ldt = 140 fb∫ = 13 TeV, sVSI, 10GeV, 10mmµeµchannel: LNC, InternalATLAS(a) 휇−푒휇0 5 10 15 20HNL mass [GeV]01020304050607080entries126.74, Run 2 LRT with filter136.79, Run 3 LRT v8 with filter162.83, Run 3 LRT v8 NO filter-1 Ldt = 140 fb∫ = 13 TeV, sVSI, 10GeV, 10mmµµµchannel: LNC, InternalATLAS(b) 휇−휇휇Figure 6.15: Optimizing the LRT algorithm improves the yield of two types of displaced HNL decayvertices by reducing the number of fake reconstructed tracks and thus improving the displaced vertexreconstruction performance. Vertices produced with the Run 2 reconstruction software are plotted with bluetriangles. Vertices produced with the Run 3 LRT configuration are purple squares and show increased signalreconstruction efficiency. Removing the filter further improves the efficiency, and these vertices are shownwith a dashed purple line. In this figure, v8 refers to the final version of the LRT configuration ultimatelyincluded in the default reconstruction software. The quantity on the x-axis is the reconstructed HNL massas defined in chapter 7.Subsequent reconstruction algorithms which rely on tracks, particularly leptons, use these views to create a“standard” and a “LRT” version of the reconstructed objects.With LRT now able to run by default on all recorded data, LLP analyses can follow the same pipelineas standard analyses. LRT, as well as many other reconstruction optimizations, will be part of reprocessingthe raw data from the full Run 2 dataset and will be used for processing all data from the upcoming Run 3.Not only will considerable time and effort be freed, but the remaining 90% of the ATLAS dataset will beavailable for the LLP analyses. Access to the full dataset, higher-purity displaced tracks, and more accuratelymodelled background processes are all expected to increase these analyses’ signal sensitivity.70Chapter 7Heavy neutral lepton analysisAs described in detail in chapter 3, the mass of the neutrino provides an alluring window into BSM physics.The theoretical right-handed component of the neutrino carries no SM gauge charges and is therefore alsoknown as a sterile neutrino, referring to its non-interaction with the other SM particles. However, theseesaw mechanism (section 3.3.3) postulates the existence of a heavy neutrino state N that contains a smalladmixture of an active neutrino flavour: 휈푒, 휈휇, 휈휏 . This allowsN to participate in weak interactions, albeitsuppressed by a dimensionless mixing coefficient푈훼, where 훼 = 푒, 휇, 휏.With all the necessary ingredients presented in previous chapters, this chapter will detail a direct searchfor heavy neutral leptons (HNLs) using the ATLAS detector [1]. In the decay channels studied, the HNL,produced via the decay of a 푊 boson, decays into a neutrino and two charged leptons,20 which form adisplaced vertex. Feynman diagrams of the relevant decays are shown in fig. 7.2. The search is performedusing 139 fb−1 of√푠 = 13TeV 푝푝 collision data.For HNLs with low mass and low mixing angles, the decay vertex can occur at some macroscopicdistance from the interaction point. These displaced vertex (DV) signatures provide sensitivity to lowcoupling strengths with very little background contamination. Historically, searches for new particles (suchas for the Higgs boson) assume the particle decays very quickly, leaving a vertex within millimetres of theinteraction point. However, without any discovery of new physics, an effort is underway in high-energyphysics to probe unexplored regions of phase space by searching for long-lived particles (LLPs).The defining feature of this analysis is that it searches for HNLs that are long lived, decaying somemacroscopic distance from the primary vertex (PV). HNLs may produce displaced vertices due to a smallcoupling between the HNL and the states to which it decays. The quantity 푐휏 is often used to characterizethe decay length of LLPs. This is a measure of distance defined as the product of the LLP’s proper lifetime휏 and the speed of light 푐, which is a reasonable approximation of the speed of the decay products. 푐휏 isthe proper decay length of the particle which can be mapped to how far the particle will travel before itdecays [5]. In this dissertation, and in much of the literature, 푐휏 is sometimes referred to as the “lifetime” ofthe LLP. This analysis searches for HNLs that decay between 4 and 300mm, which is inside ATLAS’s innerdetector volume.7.1 ModelsExperiments to date have presented results that assume only one HNL is kinematically accessible and thatother HNLs are outside the experiment’s sensitivity. These experiments place exclusion limits on the HNL20In this chapter the term leptons refers to electrons or muons unless otherwise specified.717.2. Samplesmass푚N and the mixing angle |푈훼 |2.21 This is referred to as a “one-HNLmodel with single-flavour mixing”(1SFH). Though useful for deriving generic bounds and benchmark measurements, a 1SFH model is notphenomenologically viable as it does not account for the two observed neutrino mass splittings and flavouroscillations. A minimal model that can account for these splittings is that of “two quasi-degenerate HNLs”with close masses and couplings (2QDH).22The interactions of each HNL via the weak force are suppressed by the mixing angles 푈훼퐼 between anactive neutrino flavour 훼 = 푒, 휇, 휏 and a specific HNL 퐼. Experimentally, only the cumulative mixing can bemeasured, so the following definitions are applied:|푈훼 |2 ≡∑퐼|푈훼퐼 |2 and |푈tot |2 ≡∑훼,퐼|푈훼퐼 |2 (7.1)where 퐼 is the number of HNLs in the model. In 1SFH models, as reported in other experiments, 푈훼 and푈훼퐼 are equivalent, so no distinction is made, but the clarification is important in defining the 2QDHmodels.The fractional mixing 푥훼 is defined as푥훼 = |푈훼 |2/|푈tot |2. (7.2)In the following analysis, two 1SFH models and two 2QDH models are used to interpret the observeddata. The 1SFH models are the common benchmarks in which the HNL mixes either completely with theelectron neutrino (|푈훼 |2 = |푈푒 |2) or completely with the muon neutrino (|푈훼 |2 = |푈휇 |2). The possiblerealistic values of the HNL mixings in the 2QDH models are constrained by neutrino oscillation data asdiscussed in reference [140]. Two values are selected for the 2QDH parameters — one consistent withthe normal hierarchy (NH) of neutrino masses and one for the inverted hierarchy (IH). A ternary diagramshowing the oscillation data fits from NuFIT [141] and the four selected mixings is shown in fig. 7.1.Furthermore, for each benchmark, this analysis considers the case in which the HNL is a Majoranaparticle or a Dirac particle. In the Majorana limit, the HNL decay has an equal chance of being lepton-number violating (LNV) or lepton-number conserving (LNC), whereas in theDirac case only LNC is allowed.A complete summary of the models used in the interpretation of results can be found in table 7.1.7.2 Samples7.2.1 Monte Carlo samplesTo study the signal sensitivity, Monte Carlo (MC) signal samples are generated using Pythia 8.212 [142]with the A14 set of tuned parameters [143] and the NNPDF2.3lo PDF set [144]. The impact of multiple 푝푝interactions per bunch crossing (pileup) are modelled by adding simulated minimum-bias events generatedwith Pythia 8.210 using the A3 tune [145] and the NNPDF2.3lo PDF set. Particles are propagated througha detector simulation [107] based on Geant4 [108].21In a direct search such as this, the mixing angle dictates both the production and decay rates, and therefore only the square ofthe coupling constant can be measured.22While two HNLs can account for active neutrino masses and matter-antimatter asymmetry of the universe, a third HNL atO(keV) scale could be a viable dark matter candidate.727.2. SamplesL2r #2M+?K `Fb pbX M2mi`BMQ Qb+BHH iBQM +QMbi` BMib3 f NElectron-onlyMuon-onlyIHNHFigure 7.1: The allowed combinations of |푈훼 |2/|푈tot |2 that are consistent with NuFIT fits to neutrinooscillation data [141]. The allowed regions under normal (blue) and inverted (green) hierarchy are shown. Thered cross markers represent two benchmark models that are chosen and agreed upon by the community [140].Table 7.1: A summary of the eight models that are used in the interpretation of the analysis results. Modelsare defined according to the number of HNLs (one or two), the fraction of LNC and LNV decays, and therelative strength of the mixing between the lepton generations. The inverted (IH) and normal (NH) hierarchybenchmarks are used for 2QDH models, while only the 1SFH model is used for the single-flavour mixinginterpretation.Model Fraction of Fraction of (푥푒, 푥휇 , 푥휏 ) ChannelsLNV decays LNC decays 푥훼 = |푈훼 |2/|푈tot |21SFH muon-only in ‘Majorana-limit’ 1/2 1/2 ( 0, 1 , 0 ) 휇−휇휇, 휇−휇푒, 휇−푒푒1SFH muon-only in ‘Dirac-limit’ 0 11SFH electron-only in ‘Majorana-limit’ 1/2 1/2 ( 1 , 0 , 0 ) 푒−푒푒, 푒−푒휇, 푒−휇휇1SFH electron-only in ‘Dirac-limit’ 0 12QDH IH mixing in ‘Majorana-limit’ 1/2 1/2 ( 1/3 , 1/3 , 1/3 ) 휇−휇휇, 휇−휇푒, 휇−푒푒,2QDH IH mixing in ‘Dirac-limit’ 0 1 푒−푒푒, 푒−푒휇, 푒−휇휇2QDH NH mixing in ‘Majorana-limit’ 1/2 1/2 (0.06, 0.48, 0.46) 휇−휇휇, 휇−휇푒, 휇−푒푒,2QDH NH mixing in ‘Dirac-limit’ 0 1 푒−푒푒, 푒−푒휇, 푒−휇휇In this search, six decay modes (channels) are generated whose combinations define each model. Thesechannels are defined as 훼− 훽훾 according to the flavour of the prompt lepton (훼) and the flavours of thetwo charged leptons produced in the HNL decay (훽훾). The relevant channels using this nomenclature areshown in fig. 7.2. For each 훼−훽훾 final state, signal samples are generated with HNL masses in the range3GeV < 푚N < 20GeV and proper decay lengths 푐휏N = 1, 10, and 100mm.2323In this chapter, a distinction is made between the HNL’s mass 푚N used in signal generation and the reconstructed mass 푚HNLused in the event selection (see section 7.3.4).737.2. Samples푊+ℓ+훼ℓ−훽ℓ+훾휈훾N 푊+∗(a)푊+ℓ+훼휈훽ℓ+훾ℓ−훾N 푍∗(b)푊+ℓ+훼ℓ+훽ℓ−훾휈¯훾N 푊−∗(c)푊+ℓ+훼휈¯훽ℓ+훾ℓ−훾N 푍∗(d)Figure 7.2: Feynman diagrams for the HNL production and decay modes targeted in this analysis. Theflavors of the leptons in the diagrams, labeled by 훼, 훽, and 훾, are either muons or electrons. If the chargedleptons in the HNL decay have the same flavour, then both the diagrams with the virtual푊 (a,c) and virtual 푍(b,d) contribute to the process. Lepton number conserving (a,b) and lepton number violating (c,d) processesare shown. Equivalent processes are also valid for an initial state푊− boson [1].Cross sectionTo compute the cross section, two of the HNL’s three interdependent properties — mass, mixing angle, andlifetime — must be specified. The branching ratio (BR) for the 푊 boson decaying to an HNL (N ) and acharged lepton (ℓ) is directly proportional to the coupling strength |푈훼 |2 and can be expressed as [146]퐵푅(푊 → ℓ훼N) = 퐵푅(푊 → ℓ훼휈) · |푈훼 |2(1 − 푚2N푚2푊)2 (1 + 푚2N2푚2푊). (7.3)The total HNL cross section 휎N for a specific 훼−훽훾 lepton channel is then휎N = 휎(푝푝 → 푊) · 퐵푅(푊 → ℓ훼N) · 퐵푅(N → ℓ훽ℓ훾휈) (7.4)= 휎(푝푝 → 푊) · 퐵푅(푊 → ℓ훼푣) · 푥훼 · |푈tot |2 ·(1 − 푚2N푚2푊)2 (1 + 푚2N2푚2푊)· 퐵푅(N → ℓ훽ℓ훾휈). (7.5)747.2. SamplesThe cross section timesBR for푊 boson production and subsequent leptonic decay (휎(푝푝→푊) ·BR(푊 →ℓ휈))in√푠 = 13TeV 푝푝 collisions is taken from the ATLAS measurement in reference [147]. It is measuredas (20.6 ± 0.6) nb.|푈훼 |2 is factored as 푥훼 · |푈tot |2, allowing for the variation of the fraction 푥훼 to define each model. Thetotal mixing angle |푈tot |2 for one Majorana HNL particle is computed for each of the generated 푚N–푐휏Nsamples using a direct Fermi theory computation described in reference [148]. The proper time 휏N itselfhas a strong dependence on the 푚N as well as the mixing angle |푈 |2. The HNL decay is a three-bodycharged-current-mediated processes and so the lifetime scales as휏N ∝ 1푚5N |푈tot |2. (7.6)These computations include additional corrections due to the finite masses of the final-state fermions.Individual HNL decay branching ratios 퐵푅(N → ℓ훽ℓ훾휈) depend on 푚N and the mixing fractions 푥푒,푥휇, and 푥휏 . In the case of displaced leptons of the same flavour (훽 = 훾), the BR is modified by interferencefrom a virtual 푍 boson decay shown in fig. 7.2 (b,d). The BR is calculated for each 푚N in each HNL decaychannel. The calculated mixing angles and BRs are used in eq. (7.5) to compute the cross section for aMajorana HNL with a given 푚N and 푐휏N for each N → ℓ훽ℓ훾휈 decay. The cross sections for the remainingmodel benchmarks are calculated by scaling the appropriate contributions from each channel according tothe 푥훼 values in table 7.1. For each model, the Majorana limit and the Dirac limit are studied. In 1SFHmodels, this is simply a matter of only considering LNC decays (Dirac) or allowing for equal probabilities ofLNC and LNV decays (Majorana). As presented in reference [140], 2QDH models are enhanced by a factorof two. In the 2QDH Dirac limit, all decays are LNC, and in the 2QDH Majorana limit, they are equal partsLNC and LNV. The modifications to the cross sections are summarized in table 7.2.Table 7.2: The cross section for LNC and LNV decays for one HNL model in the Dirac or Majorana cases,a quasi-degenerate HNL pair in the Majorana case and a quasi-degenerate HNL pair in the Dirac case. Thetotal cross section is the sum of the LNC and LNV contributions.One HNL One HNL Quasi-degenerate pair Quasi-degenerate pairMajorana-limit Dirac-limit Majorana-limit Dirac-limitLNC decays 휎푀 2휎푀 2휎푀 4휎푀LNV decays 휎푀 0 2휎푀 0Total 2휎푀 2휎푀 4휎푀 4휎푀Signal kinematicsKinematic distributions of truth-level24 quantities are shown in fig. 7.3 for simulated HNL signals decayingin the 휇−휇휇 channel. At truth level, kinematic differences between the signal channels are negligible sinceelectrons and muons with 푝T of order O(GeV) can be treated as equivalent (massless) objects.24Truth-level indicates quantities of the particles produced by the event generator, as opposed to those quantities reconstructed inthe detector simulation.757.2. Samples0 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, (a) HNL mass 푚HNL0 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, (b) DV mass 푚DV0 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, (c) DV transverse displacement 푟DV0 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, (d) Tri-lepton mass 푚푙푙푙Figure 7.3: Kinematic distributions of truth-level quantities from simulated HNL signal in the 휇−휇휇 channel.Plots are shown for a 10GeV HNL with proper lifetimes 푐휏N = 1, 10, 100mm. Each of these quantities isused in the analysis selection.Spin correlationsTo properly simulate spin correlations between 푊 boson decay products, which are not accounted forin Pythia 8 [149–151], events are weighted to reproduce the angular distributions obtained with Mad-Graph5_aMC@NLO 2.9.3 [152] using theHeavyNmodel [153, 154]. The weighting procedure is validatedby comparing the momentum spectra of each of the charged-lepton flavours and the neutrino between theweighted Pythia 8 and MadGraph5_aMC@NLO samples. Further details of the reweighting procedurecan be found in reference [155].7.2.2 Data samplesThis analysis uses 139 fb−1 of√푠 = 13TeV 푝푝 collision data recorded by the ATLAS detector in the2015–2018 data-taking period. The recorded data is subjected to a few quality requirements, then consideredvalid for use in the analysis [156].• Good Run Lists (GRLs)— GRLs specify the luminosity blocks in which the beam conditions were767.2. Samplesstable, and the relevant detector subsystems were operational. Luminosity blocks which are not presentin the GRLs are discarded.• Event cleaning— Further cleaning takes place on the individual event level. Events may be flaggedif there are problems in the liquid argon system, tile calorimeter system, SCT inner detector system,or if the event is incomplete. Such problematic events are discarded.• Primary vertex—Each event is required to contain a PV formed from two or more associated trackswith 푝T > 500MeV.• Trigger— Events must have passed at least one of the triggers described in section section 7.2.3.• Filter— Events must pass at least one RPVLL filter as described in section 7.2.4.7.2.3 TriggerThe 푊 boson decay produces a high-푝T prompt lepton (one produced close to the IP) which provides anideal trigger for the analysis. The trigger is responsible for signalling that an entire event is of interest andshould be stored (see section 4.2.6 for details). The triggers used to select events in this analysis are thelowest 푝T unprescaled single muon and single electron triggers from 2015–2018 [157, 158]. The list of HLTtriggers is shown in table 7.3, each of which is seeded by a specific L1 trigger not mentioned here. Theoverall trigger efficiency for the HNL signal is approximately 30–40%. The trigger requirement is ignoredin the selection of events for the inverted prompt lepton validation region (section 7.4.4). For that region,any event that passes any trigger and any RPVLL filter is considered.Table 7.3: Single 휇 and single 푒 triggers from 2015–2018 are used to collect signal region data. mu20 andmu26 signify that the trigger requires a ≥20GeV muon and a ≥26GeV muon, respectively. Similarly, e24and e26 correspond to a ≥24GeV and a ≥26GeV electron.Trigger name 2015–2016 2017 2018휇HLT_mu20_iloose_L1MU15 ×HLT_mu26_ivarmedium × × ×푒HLT_e24_lhmedium_L1EM20VH ×HLT_e26_lhtight_nod0_ivarloose × × ×7.2.4 FilterAs this analysis searches for displaced vertices, it relies on the reconstruction of large-radius tracks (LRTs)(see chapter 6) that can not be run on every event as it is computationally intensive. A dedicated datastream is used so only a subset of data is reconstructed using LRT. A set of filters to select this data subsetis defined by several analyses focused on LLP signatures. A initial prompt reconstruction is performed onthe entire dataset, and events which pass at least one filter are saved in their detector level (RAW) format.This data subset is internally referred to as DRAW_RPVLL since it is “derived” from the complete “RAW”777.3. Reconstruction and object definitiondataset and was originally used for supersymmetric R-parity violating long-lived (RPVLL) particle analyses.The DRAW_RPVLL data is then fully reconstructed including the LRT tracking, and the output is stored inDAOD_RPVLL format, analogous to the standard ATLAS xAOD format.25Approximately 10% of the full Run 2 dataset successfully passes the complete set of DRAW filters.26 Thesignal region of the present analysis uses only events that pass one of four custom HNL filters. Each filterrequires at least one prompt lepton with 푝T > 28GeV and one displaced lepton with 푝T > 5GeV. Additionalrequirements such as quality and isolation are also applied to these objects. A complete set of the filterrequirements is shown in table 7.4. The real and simulated data are both subject to these filter requirements,however, a subtle discrepancy arises as discussed in section 7.6.5.Table 7.4: The four HNL filters included in the DRAW filter in the DRAW_RPVLL data stream.Prompt 휇 Prompt 푒 Prompt 푒 Prompt 휇displaced 휇 displaced 휇 displaced 푒 displaced 푒filter filter filter filterHLT trigger Single 휇 trig. Single 푒 trig. Single 휇 trig.Promptlepton푝T > 28GeV|휂 | < 2.5Muon type Combined - CombinedElectron ID - Loose -Isolation Σ푝 (0.3)T /푝T < 0.05Displacedlepton푝T > 5GeV|휂 | < 2.5Muon type Combined, MS extrapolated -Electron ID - NoneIsolation Σ푝 (0.3)T /푝T < 1.0푑0 > 0.1mm for combined muon > 1mmwith 휒2/푛dof < 57.3 Reconstruction and object definitionThis search requires the reconstruction of the prompt lepton expected from the푊 boson decay and a displaceddilepton vertex in the ID. The reconstruction of displaced tracks is discussed in detail in chapter 6. In thisanalysis, leptons are reconstructed using both standard and LRT tracks so modifications to their definitionsare necessary. The following sections summarize the relevant definitions and details of muon, electron, andDV reconstruction. The invariant mass of the dilepton DV is calculated as well as the mass of the HNL usingan estimate of the neutrino trajectory.25A default secondary vertexing (VSI) is also run in this stream, but this analysis instead uses a customVSI configuration executedin a later derivation.26This is by construction as 10% is what the computing budget allows.787.3. Reconstruction and object definition7.3.1 MuonsIn this analysis, the only muons used in event selection are of combined type, formed by matching ID andMS muon tracks and refitting as a single particle. A detailed description of muon reconstruction is presentedin section 5.3. Additionally, only Medium quality muons are considered, and the standard calibrations areapplied to account for known discrepancies between data and simulation.Thepromptmuon is defined as the highest-푝Tmuon in the eventwith |푑0 | < 3mm and | (푧0−푧PV) sin 휃 | <5mm that does not overlap with any tracks in the DV. 푧0 is the track’s longitudinal impact parameter, and푧PV is the 푧 coordinate of the PV. The candidate is also required to have a 푝T > 3GeV. 휃 is the polar angledescribed in section 4.2.1. The DRAW filter used to select events in this analysis also requires that each promptmuon has a track-based isolation of Σ푝 (0.3)T /푝T < 0.05 (see section 5.2.3).A displaced muon is defined as a muon object whose associated ID track is part of a DV. The displacedmuon is also required to have a 푝T > 3GeV. The DRAW filter requires that each displaced muon has atrack-based isolation of Σ푝 (0.3)T /푝T < 1.0.7.3.2 ElectronsThe reconstruction of electrons combines tracks from the ID and energy deposits from the ECAL. Section 5.2presents a detailed description of the electron reconstruction process.Electrons are classified by quality using a likelihood-based identification. This analysis only usesMedium,and a customized working point (WP) which is looser than all of the standard WPs. The LHVeryVeryLooseWP was designed to accommodate displaced electrons by removing requirements that constrain the trackto originate near the IP. The 푑0-related requirements are removed, along with requirements on the numberof Pixel and SCT hits (however, tracks that are included in the DV must pass their own minimum hitrequirements). Since the custom LHVeryVeryLoose WP is non-standard and has no collaboration-widecalibrations, the scale factors corresponding to the loosest low-푝T WP available (LHLooseBLayer withGradient isolation) are applied to the electron collection.27 Scale factors similar to the LHVeryVeryLooseWP in the 푝T ≥ 20GeV regime were produced for another analysis and found to be very similar to thosefor the LHLooseBLayer WPs. It was thus assumed that applying the LHLooseBLayer scale factors to theLHVeryVeryLoose electron collection was appropriate.The kinematic requirements for an electron to be considered the prompt electron are nearly identical tothe prompt muon, except that the minimum 푝T requirement is 4.5GeV. The prompt electron is required topass the LHMedium quality WP. The kinematic requirements for a displaced electron are similar to thosefor a displaced muon except that the candidate must have 푝T > 4.5GeV. Displaced electrons are required topass the custom LHVeryVeryLoose quality WP.27Producing and validating data/MC calibrations is a substantial undertaking that dedicated groups in ATLAS generate only forwidely-used and critical WPs.797.3. Reconstruction and object definition7.3.3 Displaced verticesVertices from displaced decays are reconstructed using the displaced vertexing algorithm known asVrtSecInclusive (VSI) described in the ATLAS public note [136]. This algorithm uses the combinedcollection of standard and large-radius tracks to determine the position of vertices formed of two or moretracks that originate at a macroscopic distance from the primary vertex. The present analysis uses a cus-tomized version of VSI optimized for the displaced two-lepton decays found in the displaced HNL signalmodels. Several of the optimizations used are inspired by the tuning of the LRT algorithm discussed inchapter 6. For instance, tightening the 푑0 and 푧0 criteria for the tracks used for vertexing substantiallydecreased the reconstruction of fake vertices. More details about the definition and optimization of thecustom VSI configuration can be found in reference [155].The main steps of the VSI algorithm are summarized in fig. 7.4. First, tracks are preselected for vertexseeding with a series of quality cuts. For the custom configuration, this track preselection also requires thatthe tracks are matched to muon or electron objects. After the track selection, there is an initial two-trackvertex finding step, which forms vertices with all compatible two-track pairs. Only the pairs of tracks that aredeemed loosely compatible are kept. These two-track seed vertices are then combined into n-track verticesusing an incompatibility graph method. Then vertices that share multiple tracks are merged together. Atthis point, all tracks (lepton matched and non-lepton matched tracks) that are not initially preselected forvertex seeding are not associated with any DV. The final step in this reconstruction chain attempts to attachall tracks to compatible vertices. The attached tracks are required to meet basic quality checks (푝T, 휒2 cuts)and are required to be nearby the candidate vertex, both in 푑0 and 푧0 significance.trackattachmentvertex mergingtrack selectiontwo-trackvertex findingn-trackvertex findingFigure 7.4: The main steps in the VSI vertexing algorithm. A full description of the algorithm can be foundin reference [136].To evaluate the vertex reconstruction efficiency on the signal MC samples, a truth matching procedure isused to determine if LLP decays are reconstructed as DVs. This truth matching procedure follows the samedefinitions adopted in reference [136]. The total efficiency 휀total is given by휀total = A · 휀seed · 휀core (7.7)where the acceptanceA is the fraction of signal decays with reconstructed tracks in the fiducial region, 휀seedis the fraction of two-track signal decays that pass selection requirements, and 휀core is the fraction of signaldecays that match a reconstructed vertex.The vertexing efficiency for three signal types is shown in fig. 7.5 as a function of radial decay position,푟DV =√푥2 + 푦2. The total efficiency peaks between 0.15–0.25 depending on the signal sample. Totalefficiency at very low values of 푟DV is suppressed in part due to a minimum |푑0 | cut of 1mm for at least one807.3. Reconstruction and object definitiontrack and at high values of 푟DV due to requirements on the number of hits per track.1−10 1 10 210 [mm]DVr00.050.10.150.20.250.30.350.4totalε µµ-µeµ-µe-eeATLAS Simulation = 13 TeVsCustom Vertexing Configuration = 10 mmNτ=10 GeV, cNmFigure 7.5: The total displaced vertex reconstruction efficiency (휀total) as a function of displaced vertex radius(푟DV) for the custom configuration used in this analysis. The definition of the displaced vertex reconstructionefficiency can be found in reference [136]. The efficiency is shown for 휇−휇휇, 휇−휇푒, and 휇−푒푒 signals with푚N = 10GeV and 푐휏N = 10mm.7.3.4 HNL mass and DV massThe displaced vertex mass 푚DV is calculated as the invariant mass of the two tracks in the vertex. Theinvariant mass of the DV is reconstructed using the track kinematics (푝T, 휂, 휙) calculated with respect tothe DV position and using a pion mass assumption. Since the neutrino is invisible to the detector, the HNLsignal is reconstructed using only the two charged leptons in the vertex, thus 푚DV will always underestimatethe true HNL mass. The resulting distribution of the DV mass in signal is a broad distribution that cuts off atthe simulated HNL mass, as can be seen in fig. 7.3. A variable cut on 푚DV is used to suppress backgroundsfrom metastable meson decays.By using known quantities of the proposed signal signature to constrain the neutrino four-momentum,the invariant mass of the HNL can be calculated. Reference [155] contains an in-depth overview of thisvariable’s calculation. The calculation applies four-momentum conservation in the 푊 and HNL decaysusing the kinematics of the charged leptons, the known푊 mass, and the approximation that the leptons andneutrino are massless. The flight direction of the HNL is given by the vector connecting the PV and DV andconstrains two of the three degrees of freedom from the unknown neutrino momentum, while the final degreeof freedom is constrained by the 푊 boson mass assumption. This calculation yields a quadratic equationwith two solutions, of which the positive-radical solution is used to define the invariant mass of the HNLcandidate (푚HNL). The resulting distribution of 푚HNL, as seen in fig. 7.3, nicely peaks around the true HNLmass. 푚HNL is used as the final discriminating variable to define signal and control regions.817.4. Analysis design7.4 Analysis designThrough the reconstruction step, nearly all data processing is designed and executed by multiple largeteams within the collaboration. The trigger design, reconstruction, calibration, simulation etc., is less ofan exploratory exercise, and the collaboration uses stringent coding guidelines and computational resourcemanagement practices up to the level of the xAOD physics object (in this case, the analogous DRAW_RPVLL)format. This centralized effort serves the dozens of ATLAS analyses that can readily access relevant datasets,trusting their provenance. Each analysis team designs and implements a set of algorithms and data structuresto perform their specified search or measurement. Recommendations and shared frameworks are common,but the team ultimately determines the approach.As this analysis is focused on identifying long-lived particles, its structure incorporates several new or un-conventional techniques. Though every ATLAS analysis is a complex enterprise, according to reference [5],“Long-lived particle searches are without doubt the hardest analyses to perform, since they often require acomplete rethink of how object reconstruction works.” A new discriminating variable, clever backgroundestimation techniques, and unique systematic uncertainties arising from displaced tracking are all aspects ofthis analysis that add to its complexity.7.4.1 Analysis frameworkA multi-step pipeline is used to ultimately produce a calibrated, concise, and correct set of events andobservables with which a statistical analysis is performed. Figure 7.6 shows a schematic diagram of theworkflow and data structures used. Once passing through the trigger and filter, RAW detector signals arereconstructed into representations of physical objects as discussed in chapter 5. Additionally, the relevantsignal must be simulated and reconstructed as discussed in section 7.2.1.The displaced HNL analysis framework, depicted in fig. 7.6, can be divided into eight algorithmic steps:1. Trigger — The trigger system operates in real-time to decide which data is to be recorded by thedetector. The system is described in section 4.2.6 and this analysis uses standard single-lepton triggersto select data events section 7.2.3.2. DRAW Filter— The data is required to pass one of the DRAW filters (see section 7.2.4).3. Reconstruction — Events that are selected by the DRAW filter are then reconstructed using a set ofreconstruction algorithms which use LRT and displaced vertexing (VSI). In this step, only the defaultVSI configurations are run. The output of this reconstruction step is a collection of DAOD_RPVLL filesin the xAOD format. For more details about the reconstruction, see chapter 5.4. Derivation—Aderivation step is used to skim away information that is not required for this displacedHNL analysis. This derivation step also reruns VSI to reconstruct the custom lepton-only DVs(section 7.3.3). The output is a derived xAOD format called a DAOD and the derivation name used forthis analysis is EXOT29.2828Nearly all ATLAS analyses use some form of derived data with superfluous information and irrelevant events skimmed away.827.4. Analysis designRAWDRAW_RPVLLDAOD_RPVLLDAODEXOT29flat ntuplemicro-ntuplehistogramstransienttriggerfilterreconstructionderivationcleaning &flatteningeventselectionstatisticalanalysisfilter emulatoralgorithm data structureMonte Carloevent generationdatadetectorsimulationFigure 7.6: A schematic outline of elements of the analysis framework pipeline and successive data structures.Data and Monte Carlo have different entry points but are otherwise processed identically.837.4. Analysis design5. Filter emulator— As no information is stored in data about which filter(s) selected a given event, afilter emulator is run on the secondary-reconstructed data in the ntuple making code. This is used toapproximate the event selection applied by the four HNL filters. This is run on both data and MC toensure that both collections are subject to the same selection criteria.6. Cleaning & flattening — The DAOD files are processed using “DHNL Algorithm” producing flatntuples. Ntuples are array-like structures that contain relevant and necessary information abouteach event, implemented as ROOT TTrees [159]. In this analysis, existing lepton object and DVinformation and engineered quantities are recorded. This is also the step where calibrations areapplied to the physics objects, and basic data event cleaning is performed.7. Event selection — Event selection code called “DHNL Ntuple Analysis” consumes the ntuplesproduced in the previous step and applies the main event selection described in the sections below.This step saves micro-ntuples at specified selection levels, which are fed into the statistical analysisframework.8. Statistical analysis — The final step in the analysis pipeline is the statistical analysis of selectedsignal and background events. The details of the statistical analysis framework, implemented withTRExFitter, are described in section 7.8.One unique feature about the DRAW_RPVLL data stream is that there is not an equivalent DRAW filter stepfor the signal Monte Carlo. The MC is only reconstructed once with LRT enabled vs. data where the filter isapplied to events reconstructed using the default reconstruction. This can be seen visually in fig. 7.6 wherethe signal Monte Carlo only enters the analysis pipeline at the reconstruction step. Furthermore, the datafilter uses a preliminary set of detector conditions, resulting in slightly different reconstructed quantities.The differences introduce a systematic uncertainty which is discussed in section 7.6.5.Code-base for the analysis stepsSeveral considerations go into selecting a software stack to analyze the data, including processing speed,development speed, language familiarity, and existing tools. As the initial DAOD_RPVLL dataset is extremelylarge, fast execution is vital. However, as the data footprint is reduced, differences in execution time becomeless consequential. What is important is the analysis team’s ability to explore the data using familiarlanguages with well-supported libraries.The ntuple production code, called DHNLAlgorithm, is based on the open-source frameworkxAODAnaHelpers (xAH) [160]. xAH, written in C++, acts as a minimal wrapper for the existing ATLASEDM processing tools. Individual analyses can extend the classes of xAH to augment the output ntuples.DHNLAlgorithm (and its intermediary DVAnalysisBase) is an extension of xAH that calculates and recordsnon-standard quantities such as the DV invariant mass, the track-to-lepton matching, and the DRAW filterdecision. The primary execution code is written in C++ but is steered using a Python configuration file. InTo keep track of the dozens of derivation formats, a naming schema is used and EXOT29 refers to this analysis falling under theATLAS Exotics working group.847.4. Analysis designthis step, fast execution time and existing tools made a C++-based algorithm the natural choice. However,aside from rudimentary data cleaning, very little event selection is performed by DHNLAlgorithm, whoseprimary function is to produce calibrated, flat ntuples.The event selection functionality is implemented in the Python-based DHNLNtupleAnalysis. Withits emphasis on code readability, Python allows for rapid exploration of datasets, allowing physicists toidentify relationships and fine-tune analyses. As Python rapidly grows in popularity for applications indata science [161], a community of developers is providing a Python ecosystem for particle physics dataanalysis [162]. DHNLNtupleAnalysis uses the uproot package to read and process the ntuples produced inthe previous step.The statistical analysis presented in section 7.8 is implemented in TRExFitter — a framework, writtenin C++, for binned template profile likelihood fits in a HistFactory [163] format. The statistical modelling isexpressed using RooFit [164] with additional classes provided by RooStats [165] for interval estimation andhypothesis testing. Inference performed with TRExFitter uses the methods discussed in reference [166].7.4.2 PreselectionThe displaced HNL event selection relies on reconstructing two types of physics objects: a prompt leptonand a DV. The event selection can be broken down into two distinct sections split roughly the same way.First, the event preselection imposes conditions on overall event properties and prompt lepton quantities.The top panel of table 7.5 summarizes the event selection criteria. Criteria are chosen based on their abilityto suppress background while maintaining an acceptable signal reconstruction efficiency. In addition to theevent cleaning (section 7.2.2), trigger (section 7.2.3) and filter (section 7.2.4), the following criteria are used:• Primary vertex— Consistent with standard ATLAS data selection criteria, each event is required tocontain a PV formed from two or more associated tracks with 푝T > 500MeV. If multiple PVs arereconstructed, the one with the highest total 푝T is selected.• Prompt lepton quality — Selected events are required to have one prompt lepton (either a muon oran electron depending on the channel) as defined in section 7.3. Prompt muons (electrons) must be ofMedium (LHMedium) quality.• Trigger-matched lepton — A record is maintained of which lepton (or leptons) was responsiblefor firing the single-lepton trigger, enabling objects in the analysis to be trigger-matched. Thisselection requires that at least one Medium muon or LHMedium electron is trigger-matched and has푝T > 27GeV. The trigger-matched lepton can either be the prompt lepton or one of the two displacedleptons. In approximately 10% of events, leptons from the HNL decay have enough momentum topass single lepton trigger requirements resulting in a small acceptance to signal events with promptleptons (from the on-shell푊 boson decay) whose 푝T is below the single lepton trigger thresholds.• Prompt lepton impact parameters— The prompt lepton must have impact parameters |푑0 | < 3mmand | (푧0 − 푧PV) sin 휃 | < 5mm.857.4. Analysis designTable 7.5: Description of the selection criteria used in the signal region. The lepton quality selectionLHMedium for prompt electrons is defined in reference [116] and Medium for muons is defined in refer-ence [167]. TheDisplaced lepton quality requirement for displaced electrons is described in reference [128].In the 푍 mass veto, 훼 and 훽 refer to flavours of the prompt and one of the two displaced leptons, respectively.Selection ValuePreselectionEvent cleaning Standard ATLAS event cleaningTrigger Pass at least one single muon or electron triggerPrimary vertex At least one (standard ATLAS selection)Filter emulator Pass any HNL filterPrompt ℓ quality Medium (muons) or LHMedium (electrons)Trigger-matched ℓ At least one lepton with Medium (or LHMedium) qualityPrompt ℓ impact parameters |푑0 | < 3mm and | (푧0 − 푧PV) sin 휃 | < 0.5mmSR selectionCosmic veto√(Σ휂)2 + (휋 − Δ휙)2 > 0.05Displaced lepton-only vertex At least oneNumber of tracks in DV 2Fiducial volume 4 < 푟DV < 300mm|푧DV | < 300mm (only for 푒푒 DVs)DV charge Opposite-sign (OS) tracksPrompt + displaced ℓ charge OS leptons (1SFH in Dirac-limit)DV type 푒푒, 푒휇 or 휇휇 vertexDisplaced ℓ quality Medium (muons), Displaced (electrons)Material veto Applied for 푒푒 DVs onlyMetastable particle veto 휇휇 DVs: 푚DV > 5.5GeV푒푒 or 푒휇 DVs: 푚DV-푟DV correlation cut푍 mass veto 푚(ℓ±훼ℓ∓훽 ) < 80GeV or 푚(ℓ±훼ℓ∓훽 ) > 100GeV, if 훼 = 훽Tri-lepton mass 40GeV < 푚DV+ℓ < 90GeVHNL mass 푚HNL < 20GeV7.4.3 Signal region selectionThis section describes the variables used to discriminate between signal and background beyond the prese-lection requirements. The selections are summarized in the lower panel of table 7.5.• Cosmic veto—DVs must also pass a veto that requires the two leptons within the DV to not be back-to-back, defined as√(Σ휂)2 + (휋 − Δ휙)2 < 0.05 [127]. This cosmic veto reduces backgrounds fromsingle cosmic-ray muons passing through the ATLAS detector and reconstructed as two back-to-backmuons. This cut results in no signal loss.• Displaced lepton-only vertex— Events are required to include a DV that is reconstructed using thecustom lepton-only vertex configuration described in section 7.3.3. The DV is required to have exactlytwo tracks matched to displaced leptons. The DV is also required to be within the fiducial volumedefined by 4mm < 푟DV < 300mm. 푒푒 DVs must have a longitudinal impact parameter 푧DV < 300mm• DV charge — As HNLs, being neutral, will decay into particles whose total charge is zero, the DVwill contain two opposite-sign (OS) leptons. Only OS DVs are selected for the signal region.867.4. Analysis design• DV type — Depending on the flavour of the prompt lepton and the particular model considered, theleptons in the DV can have three different combinations of flavours: 휇휇, 푒휇 or 푒푒. Six channels canthus be defined: 휇−휇휇, 휇−휇푒, 푒−푒휇, 푒−푒푒, 휇−푒푒, 푒−휇휇, where the first lepton is the prompt leptonand the second two leptons in the channel name correspond to the flavour of the leptons in the DV.• Prompt + displaced ℓ charge — For HNL decays that conserve lepton number, the charge of theprompt and displaced lepton that couples to the HNL must have opposite charges. In the notation offig. 7.2 (a), ℓ훼 and ℓ훽 must have opposite charge. Thus, for the models where only LNC decays arepossible (Dirac limit), requiring these leptons to have the opposite charge keeps 100% of the signaland should remove approximately half of the expected background events. Experimentally, it is notpossible to determine which lepton in the DV couples directly to the HNL unless the lepton flavoursin the DV are different and only single-flavour mixing is considered. In such a case, an additionalcharge selection is applied between the charge of the same-flavour lepton pair in the event. This chargeselection can only be applied for 푒−푒휇 and 휇−휇푒 channels in the 1SFH Dirac limit models.• Displaced ℓ quality—Muons in the DV must be of Medium quality, and the electrons must pass thecustomized LHVeryVeryLooseWP.• Material veto — DVs can be formed from particle interactions with detector material. This back-ground, primarily leading to 푒푒 DVs, is suppressed by disallowing DVs produced in detector regionswith substantial material. See section 7.5.1 for details.• Metastable particle veto — As will be discussed in section 7.5.2, metastable particles produced inLHC 푝푝 collisions can have lifetimes beyond 4mm that contaminate the low-푟DV parameter space.Dedicated cuts in the 푚DV-푟DV plane are imposed to remove this background.• Z mass veto — 푍 → ℓℓ decays may mimic the displaced HNL signal if one of the leptons from the푍 is identified as prompt and the other forms a random crossing vertex with a third, unrelated lepton.If the prompt and displaced leptons have the same flavour and opposite sign, the invariant mass ofthese two particles is calculated. Events are vetoed if this invariant mass is between 80 and 100GeV.Further details can be found in section 7.5.3.• Tri-lepton mass — The tri-lepton mass 푚푙푙푙 is the invariant mass of the prompt lepton and the twodisplaced leptons. Similar to the DV mass, the tri-lepton reconstructs three out of four of the particlesfrom the 푊 boson decay (only the neutrino is missing). As a result, the 푚푙푙푙 variable underestimatesthe true푊 boson mass.• HNLmass (푚HNL)—By reconstructing the neutrino four-momentum, the invariant mass of the HNLcan be calculated, as discussed in section 7.3.4. This analysis requires that 푚HNL < 20GeV as it isnot sensitive to higher-mass signals. Distributions of 푚HNL for signal and background are shown infig. 7.19.The selection efficiency (the fraction of generated signal events remaining after applying all selectioncriteria) ranges from 0% to 4.2% for the 푚N–푐휏N samples considered. The efficiency depends strongly on877.4. Analysis designall trigger PV 4-filtermedium prompt muonplep overlapDV fiducial2-track DVOS DVmumu DVcosmic vetolepton pt2-medium-lepton DVtrig. matchlllm B-hadron vetoZ mass vetoHNLm020406080100120140Events122.5746.9746.9729.6927.9527.929.338.548.3 8.237.957.957.616.756.186.083.433.433.43ATLAS Internal-1 = 13 TeV, 139.0 fbsVSI_LeptonsMod signal, 10GeV, 10mmµµµLNC (a) cutflow1 mm 10 mm 100 mmLifetime [mm]344.557.51012.51517.520Mass [GeV]ATLAS Simulation0 0 00 0 00 0 00 0 00.47% 1.02% 0.32%0.90% 2.93% 1.14%0.87% 3.75% 1.55%0.64% 4.03% 1.84%0.64% 4.17% 2.36%0.20% 2.64% 1.56%- selection efficiency0.000.010.020.030.040.050.060.070.08Selection eff.(b) efficiencyFigure 7.7: (a) HNL signal cutflow for analysis preselection requirements and signal region selection. Thecutflow shown corresponds to a 휇−휇휇 HNL signal with 푚HNL = 10GeV, 푐휏 = 10mm. (b) The selectionefficiency for all 푚N–푐휏N points for 휇−휇휇 HNL samples [1]. Each bin in (b) reflects the final bin in thecorresponding cutflow. The cutflow shown uses an out-of-date weighting scheme, hence the difference invalue between the final bin and the efficiency map.the 푚N and 푐휏N of the signal. The highest selection efficiency is for samples with a 10mm lifetime and 푚Nbetween 10 and 20GeV.887.4. Analysis design7.4.4 Data blinding strategyIn order to mitigate bias, the data in regions expected to be populated by signal are not observed until theanalysis design is complete and approved by other collaboration members. Designing a blind analysis in thisway relies on comparing simulation to data in final states similar to the signal region (SR) but in which anyactual signal is unlikely to be found. Control regions (CRs) are defined as regions that are used in the finalHNL mass fit but are not the SR. Validation regions (VRs) are any other regions that are not directly used inthe final fit. This analysis defines three orthogonal regions: one SR, one CR, and one VR.Control regionThe CR is defined using the same SR selections as in table 7.5, except that the HNL mass cut is invertedto require that 20GeV < 푚HNL < 50GeV. Since HNLs with 푚N > 20GeV have very short proper decaylengths, they fail the 푟DV requirements, resulting in negligible signal contamination in the CR. This region isused to study the relative abundance of OS and same-sign (SS) DVs in data similar to signal. The numberof observed OS events in the CR constrains the background in the final 푚HNL fit, as discussed in section 7.8.Validation regionThe VR is used for data-driven background modelling and evaluation of systematic uncertainties. The VRcomprises events that passed one of the DRAW filters, underwent LRT reconstruction, and do not contain aprompt lepton. The DVs in the VR must satisfy the 푟DV requirements and pass the cosmic-ray muon veto.The detector material veto is also applied to 푒푒 DVs. The VR selection is defined in table 7.6.This VR has higher statistics than the SR and is used to study background sources that produce OS DVs.This region is also used to select a collection of random crossing two-lepton DVs that are used to estimaterandom crossing backgrounds (see section 7.5 for more details). It is also used in the estimation of thesystematic uncertainty in displaced vertexing reconstruction (section 7.6.4). The signal contamination in theVR is found to be negligible.Table 7.6: Definition of the VR event selection.Level Selection ValuePreselectionEvent cleaning Standard ATLAS event cleaningTrigger Pass any triggerPrimary vertex At least one (standard ATLAS selection)DRAW filter Pass any DRAW filterPrompt lepton veto 0 prompt leptonsDV selectionDisplaced lepton-only vertex At least oneCosmic veto√(Σ휂)2 + (휋 − Δ휙)2 > 0.05Number of tracks 2Fiducial volume 4 < 푟DV < 300mmDV type 푒푒, 푒휇, or 휇휇 vertex897.5. Backgrounds7.5 BackgroundsAll non-signal processes whichmimic the signature of the relevant HNL decay are referred to as backgrounds.Backgrounds from five sources are known to produce two-lepton DVs which satisfy the preselection criteria.1. DVs from particle interactions with detector material.2. Decays of metastable SM particles.3. 푍 → ℓℓ decays with a random crossing.4. Cosmic-ray muons.5. DVs from random crossings of lepton tracks.The SR selection is designed to retain high signal efficiency and suppress the first four types of backgroundto negligible levels, with random crossing remaining the only background that must be estimated.7.5.1 Material interactions푒푒 DVs have the most background from particle interactions with detector material, both from active layersand support structures. Many of the material interactions that produce 푒푒 DVs have a low reconstructedDV mass and are removed by requiring that 푚DV is at least 2GeV. However, some material interactionshave 푚DV > 2GeV, and because it is difficult to distinguish between vertices from material interactions andHNL signal decays, a material veto is used. The material veto is based on a pair of three-dimensional mapsof the ID material [125]. The first map, which extends in radius to 푟DV < 150mm, is constructed fromlow-mass vertices in data (with selections to remove low-mass SM resonances). The second map, whichextends in radius from 150mm < 푟DV < 300mm, is reconstructed using vertices in simulation, to createa more complete map than statistics will allow in data. Both maps extend out to |푧 | = 300 mm and so thematerial veto also requires that the DV has |푧 | < 300mm.7.5.2 Metastable SM particlesCertain heavy-flavour SM particles produced in LHC 푝푝 collisions have long enough lifetimes that somedecay within the SR beyond 4mm. B-hadrons can have decay lengths of a few mm when they are highlyboosted or in the tail of the exponential decay distribution. These particles have masses of the order 5–6GeV,thus encroaching on the signal region. 퐽/휓 mesons have masses centred at 3.1GeV and can be displacedwhen other heavy-flavour particles decay to 퐽/휓.These contributions are removed from the signal region using dedicated cuts on푚DV and 푟DV. Since thesebackgrounds are not expected to have an associated prompt lepton, cuts are designed by studying the invertedprompt lepton VR and removing regions with more OS DVs than SS DVs. For 휇휇 DVs, 푚DV > 5.5 GeVis required. The heavy-flavour contamination is smaller for 푒휇 and 푒푒 DVs, allowing looser requirementsthat exploit correlations between 푟DV and 푚DV. The selections that are applied are described in table 7.7 andseen graphically in fig. 7.8.907.5. Backgrounds0 50 100 150 200 250 300 [mm]DVr012345678910 [GeV]DVm051015202530Opposite-sign minus same-sign DVsHeavy-Flavor DecayBackground VetoATLAS -1 = 13 TeV, 139 fbsValidation Region DVsµµ(a) 휇휇 DVs0 50 100 150 200 250 300 [mm]DVr012345678910 [GeV]DVm051015202530Opposite-sign minus same-sign DVsHeavy-Flavor DecayBackground VetoATLAS -1 = 13 TeV, 139 fbsValidation Regionee DVs(b) 푒푒 DVs0 50 100 150 200 250 300 [mm]DVr012345678910 [GeV]DVm051015202530Opposite-sign minus same-sign DVsHeavy-Flavor DecayBackground VetoATLAS -1 = 13 TeV, 139 fbsValidation Region DVsµe(c) 푒휇 DVsFigure 7.8: The two-dimensional distribution of 푚DV and 푟DV. Shown is the difference between the OS-and SS-vertex distributions in the VR. The 푧-axis is saturated at 30 to provide a scale that distinguishesbetween small positive (more OS- than SS-DVs) and small negative (more SS- than OS-DVs) entries. Thesolid red line represents the DV selection applied in each channel to remove backgrounds from heavy-flavourdecays [1].Table 7.7: Definition of the metastable particle veto.DV type Selection휇휇 푚DV > 5.5GeV푒푒 or 푒휇 푚DV > −7150푟DV + 7, if 2 < 푚DV < 5.5GeVelse, 푚DV > 5.5GeV7.5.3 푍 → ℓℓ decays with a random crossingStudies of the data-driven SS background estimate (section 7.5.6) revealed that 푍 → ℓℓ decays can contam-inate the SR by misreconstruction. Though the 푍 decay is prompt, the HNL signature can be mimicked ifone of the leptons from the 푍 decay is identified as the prompt lepton and the other forms a DV with a third,917.5. Backgroundsunrelated lepton. This can occur for channels where the prompt lepton and at least one of the displacedleptons have the same flavour (i.e., 휇−휇휇, 휇−휇푒, 푒−푒휇, 푒−푒푒). It is assumed that the contamination wouldproduce similar numbers of OS and SS vertices since the unrelated lepton may be of either charge and crossthe path of either prompt lepton. A 푍-mass veto is thus applied to remove these types of events from the SR.Events are discarded when the invariant mass of the prompt lepton and the displaced lepton with the sameflavor (i.e., 훼 = 훽) and opposite charge satisfies 80GeV < 푚(ℓ±훼ℓ∓훽 ) < 100GeV.297.5.4 Cosmic ray muonsAs discussed in section 7.4.3, cosmic-ray muons, which can be reconstructed as two back-to-back muons ina DV, are rejected by requiring the two displaced tracks to satisfy√(Σ휂)2 + (휋 − Δ휙)2 > 0.05 [127].7.5.5 Random track crossingsRandom track crossings (RTCs) occur when two random uncorrelated tracks cross in the inner detector soclose that the vertexing algorithm associates them to a common DV. While the probability of a two-leptonRTC is relatively low, the 푚DV of these vertices is unconstrained, making them difficult to distinguish fromthe HNL signal. The previous reducible backgrounds can be suppressed by judicious selection criteriawithout substantially impacting the signal sensitivity. Conversely, the RTC background is considered to beirreducible, and its contribution to the SR must be estimated.In this search, a data-driven approach estimates the number of background events fromRTCs in the signalregion. A full description of the data-driven estimate for RTCs using a prompt lepton shuffling method isdescribed below.7.5.6 Data-driven estimateThe RTC background is not well modelled by simulation; therefore, a simulated sample cannot be usedto estimate the number of events in the SR. Instead, two methods use data to estimate the impact of thebackgrounds which were developed and tested on data outside the SR to avoid accidental unbinding.Same-signThis background estimation method uses the number of random crossings with two same-sign (SS) tracksto estimate the number of random crossings with two opposite-sign (OS) tracks in the signal region. It isassumed that the probability for two tracks to form a random crossing vertex is independent of the charge ofthe two tracks, and therefore, the number and distributions of OS and SS DVs are similar. Inverting the OSDV requirement of the SR ensures an unbiased estimate with no HNL signal contamination.This method is statistically limited, and as a result, it is not used as the final background estimate inthis analysis. However, the SS region has been used to study the backgrounds and inform selections. Forinstance, residual contamination from heavy-flavour decays was discovered by comparing the OS and SS29The mass of the 푍 boson is 91GeV [21].927.5. Backgroundsvertices in the inverted prompt lepton VR prompting the development of the metastable particle veto (seefig. 7.8).Once suppressing the reducible backgrounds, vertices are compared in the VR to validate the OS≈SSassumption. The resulting distributions are shown fig. 7.9. Agreement between the two distributionsis generally good, indicating that the assumption is sound and that other background sources have beensuppressed. Any disagreement between SS and OS vertices in the VR is taken into account later by the DVbackground systematic (section 7.7).0 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 -1 = 13 TeV, 139 fbsValidation Region DVsµe0 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 -1 = 13 TeV, 139 fbs=10 mmNτe, cµ-µ0 5 10 15 20 25 30 35 40 45 50 [ e ]HNL2−101−10110210310Events / 2.5 GeVSR CRackgroundncertaintyataL (5 e )L (10 e )L (15 e ) -1 = 13 Te , 139 fbs=10 Nτe, cµ-µ(a) 푒휇 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 -1 = 13 TeV, 139 fbsValidation Region DVsµµ(b) 휇휇 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 -1 = 13 TeV, 139 fbsValidation Regionee DVs(c) 푒푒 DVsFigure 7.9: The 푚DV distributions of OS and SS DVs in the validation region, for (a) 푒휇, (b) 휇휇, and(c) 푒푒 DVs. These demonstrate that the SS and OS DV distributions generally agree well, in line withthe assumption that the dominant residual background for the search is that of random-crossing vertices,which is then estimated by a data-driven method. The disagreements visible here result partly from theremaining nonrandom-crossing backgrounds, which are accounted for with a systematic uncertainty (seesection 7.7) [1].937.5. BackgroundsPrompt lepton shufflingAmethod beyond the statistically-limited SS background estimate is required to obtain a smooth distributionof background events across 푚HNL. The shuffled event method creates an artificial collection of eventsby combining DVs and prompt leptons from separate events. This sample is created by combining eachOS DV in the VR with each prompt lepton found in non-VR events that contain a SS DV satisfying looserequirements: 푚DV > 1GeV, with no lepton identification criteria imposed on its displaced leptons. Foreach channel, the shuffled sample has at least 2 × 103 times the number of events in the “unshuffled” datasample, in which the DV and the prompt lepton are from the same event. As with an unshuffled event, ashuffled event is classified as 푚HNL < 20GeV (SR) or 20GeV < 푚HNL < 50GeV (CR).The increase in statistics is limited by the number of prompt leptons and random crossing DVs in thedata sample. In order to have a sufficient number of initial events to draw from, the requirements on 푚HNL,푚푙푙푙, and the 푍-mass veto are removed, and that on 푚DV is loosened to 푚DV > 2GeV. The standard selectionsamples have between 36 and 187 events in each channel, and the samples used in the shuffling with theselooser selections are more than 50 times larger. In all analysis regions with three leptons, the shuffled andunshuffled distributions in 푚HNL and 푚푙푙푙 are in good agreement, and the shuffled distribution is then usedto estimate the expected number of background events observed in the SR.The shuffled-event backgroundmodel assumes the absence of correlations between the randomly crossingtracks and the prompt lepton. The validity of this assumption is checked by comparing the kinematicdistributions of shuffled events and unshuffled events in various analysis regions as described below.7.5.7 Background estimate validationBoth the SS and prompt lepton shuffling background estimation assume that the background events in theSR are dominated by random crossings of tracks combined with the association of a prompt lepton. A set oftests on the available background samples is performed to validate this claim.In the VR, it is assumed that DVs with two SS leptons have kinematic distributions similar to OS DVs,except in the low 푚DV region (below 5.5GeV) where B-hadron decays dominate. In the VR, OS and SSindeed show good agreement (fig. 7.9).It is also assumed that there is no dependence on track charge in creating random vertices; therefore, SSDVs in the VR should show no asymmetry between ℓ+ℓ+ and ℓ−ℓ− DVs. As shown in fig. 7.10, no significantasymmetry is observed in the SS DVs in the 푒휇 and 푒푒 channels. The statistics in the 휇휇 channel are limitedthough there is no physics motivation why the conclusions should differ.Finally, it is assumed that the pairing of a prompt lepton with a DV is random. Unshuffled SS eventsfrom data are compared to the statistics-enhanced shuffled event collection. Comparisons of the 푚HNLdistribution are shown for each channel in fig. 7.11. A Kolmogorov-Smirnov (KS) goodness-of-fit test isperformed to compare the shapes of the two distributions. The results of the KS test for both the 푚HNL and푚푙푙푙 distributions indicate that the original and the shuffled SS events are compatible. This suggests that thepairing of a prompt lepton with an accidental crossing of a two-lepton displaced vertex is indeed random.Altogether, these validations indicate that the SS and the prompt lepton shuffling are valid background947.5. Backgrounds0 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 Region(a) 푒휇 DVs0 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 Region(b) 휇휇 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 Region(c) 푒푒 DVsFigure 7.10: SS DVs in the VR with the metastable particle veto and material veto for 푒푒 DVs applied. SSDVs are separated by DV charge in ℓ+ℓ+ and ℓ−ℓ− DVs. The event yields are shown in the legend of eachplot. No significant differences in the two types of DVs are seen.approximation methods.957.5. Backgrounds0 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=57(a) 휇−휇휇0 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=128(b) 푒−푒휇0 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=187(c) 휇−휇푒0 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=59(d) 푒−푒푒0 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=59(e) 휇−푒푒0 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=59(f) 푒−휇휇Figure 7.11: 푚HNL distribution of SS background events, where the DV and prompt lepton are from the sameevent (gray circles) and the distribution obtained by taking SS DV and randomly shuffling each vertex with aprompt lepton from a different event in the SR (coloured triangles). A KS goodness-of-fit test indicates thatthe distributions are compatible. The shuffling factor 푓 (ratio of the number of shuffled events to the numberof original SS background events) is shown on each plot.967.6. Signal systematics7.6 Signal systematicsThe predicted abundance and distribution of signal events are susceptible to systematic uncertainties. Quan-tifying these uncertainties is essential for performing the necessary fits in the limit-setting procedure. Thissection describes the uncertainties, or systematics, identified in the analysis. Several sources of systematicsimpact the predicted signal yield, typically arising from differences between data and simulation.In addition to the standard systematics present in many ATLAS analyses, the non-standard reconstructiontechniques introduce several non-standard uncertainties. As this special reconstruction is not used widely,no combined performance groups have produced centrally available uncertainty recommendations. Eachsystematic estimates the impact of the uncertainty on the final signal selection efficiency. Some are appliedas a uniform uncertainty while others vary across one or more variables such as track 푝T or 휂.Luminosity and pileup systematics account for uncertainties in ATLAS’s measurement of the numberof 푝푝 collisions. The centrally-provided tracking systematic, derived for low-|푑0 | tracks, is applied to alltracks, while an additional uncertainty accounts for high-|푑0 | tracks and displaced vertices simultaneously.To estimate the latter, a comparison of displaced vertices in MC and data is performed. As displaced dileptonvertices are very rare, displaced 퐾0푆 → 휋+휋− vertices are used as an analog to measure DV reconstructionefficiencies. This is done under the assumption that the VSI algorithm performs similarly regardless ofwhether it uses tracks matched to hadrons or leptons. An additional lepton identification systematic derivedfor this analysis accounts for the uncertainty introduced by leptons produced some distance beyond where thestandard uncertainties remain valid. The theory and signal modelling systematics account for uncertaintiesin the cross sections and branching ratios used to scale the signal strength. A summary of the relevantuncertainties is shown in table 7.8.Table 7.8: Table summarizing systematic uncertainties impacting reconstruction efficiencies. The valuesshown in the table refer to the impacts on the signal yields for each channel. The total uncertainty is the sumin quadrature of all systematic components (the root of the sum of the squares).Uncertainty Source Maximum Selection Efficiency Uncertainty [%]Channel 휇−휇휇 휇−휇푒 휇−푒푒 푒−푒푒 푒−푒휇 푒−휇휇Integrated luminosity 2Pileup 3Filter emulation 3Standard tracking 3Displaced tracking and DV 11 21 19 20 28 9Lepton 푑0 extrapolation 5 7 7 7 6 4Trigger efficiency < 1 1 < 1 < 1 < 1 < 1Lepton reconstruction and identification 4 9 12 17 15 2푊 cross section and modeling 3HNL branching fractions and decay 5Total 8 – 33977.6. Signal systematics7.6.1 Standard systematicsStandard systematics refer to those which are calculated using centralized analysis tools provided by theATLAS combined performance groups. As these systematics are relevant to dozens of analyses, the combinedperformance groups regularly provide calibrations and associated systematic uncertainties. They are typicallymade available as imported C++ libraries.The uncertainty in the combined 2015–2018 integrated luminosity is 1.7% [75]. The uncertainty relatedto the modelling of the pileup conditions is computed using the Pileup Reweighting (PRW) Tool for Run 2ATLAS analyses. The systematic uncertainties associated with the lepton calibration, identification, recon-struction, and trigger efficiencies are implemented using the central analysis tools provided by ATLAS. Theuncertainties used are those recommended for full Run 2 analyses. Similar to the scale factors discussedabove, a study of the systematics of the LHVeryVeryLoose and LHLooseBLayerWPs indicated the LHLoose-BLayer uncertainties can be used as an estimate of the LHVeryVeryLoose ones used in the electron selection.As there are no scale factors provided without isolation requirements, theGradientWP is chosen as changingthe WP changes the systematic negligibly so we assume the uncertainties for isolation-free leptons are thesame as those from the gradient WP. Because it is possible for a prompt or displaced lepton to trigger theevent, the trigger-matched lepton is required to be Medium quality, and the systematic variation used is thatassociated with that WP.7.6.2 Theory and signal modellingThe signal strength scales with the푊 boson production cross section and푊 decay to a signal lepton flavour.This cross section times branching ratio is obtained from a direct ATLAS measurement in√푠 = 13TeV 푝푝collisions [147] which quotes a 3% uncertainty. This is applied as a systematic to the signal yields.There is also an uncertainty on the theoretical branching fraction of theHNL.This analysis uses an updatedcalculation from reference [148] that includes perturbative QCD corrections not included in MC simulation.A conservative 5% systematic uncertainty is assigned to the HNL branching fraction by comparing theupdated BR calculation to existing MC simulations.7.6.3 TrackingTo determine the impact of track reconstruction uncertainties, a study is performed to measure the impact onthe final yield. For each available signal sample, the standard event selection is applied but with a fractionof tracks randomly removed from each event. This “track-dropping probability” is determined from thetracking performance group’s central recommendations and varies across 푝T and 휂. It is derived usinglow-|푑0 | tracks. The tracking uncertainty map, used as the track-dropping probability, is shown in fig. 7.12.The ntuples produced with and without dropped tracks are processed with the signal selection frameworkand the selection efficiencies are compared.The resulting reduction in signal selection efficiency is evaluated at theDV type selection30 (see table 7.5).The difference is symmetrized about the nominal efficiency as one can easily exclude existing tracks butnot easily create additional valid tracks. No variation in impact is observed when performing this test on987.6. Signal systematics1 10 [GeV]Tp2−1−012η0123Track Reconstruction Efficiency Ratio InternalATLASUncertaintiy [%]Figure 7.12: The overall tracking uncertainty from the tracking performance group’s central recommenda-tions. The value in each bin is used as the probability that a track will be randomly removed when calculatingthe impact on the signal selection efficiency.samples with different masses, lifetimes, and decay channels. Figure 7.13 shows the combined reduction inefficiency is 2.6% at the DV type cut. A conservative estimate of 3% is chosen as the total impact of thetracking uncertainty on the final signal yield.Distributions for the kinematic variables most relevant to the analysis are plotted and justify a flatsystematic variation. No shape-dependant variation is seen in the distributions of the 푚DV, 푟DV, 휂, 푝T, and푚HNL. Example distributions can be seen in fig. 7.14, and similar behaviour is seen in the other signalmasses, lifetimes, and decay channels.7.6.4 Displaced track and DV reconstructionThe efficiency of DV reconstruction can vary between data and simulation. To estimate the effect of thesedifferences, 퐾0푆 → 휋+휋− vertices are studied. 퐾0S mesons are produced in relative abundance at the LHCand have a relatively long mean lifetime (푐휏 = 26.84mm). This allows a data/simulation comparison of awell-known DV with a mean lifetime within the range of the HNL signal samples (1–100mm).퐾0S vertices are selected from two-to-two parton scattering (dijet) simulation and data for which large-radius tracking and displaced vertexing have been used in the event reconstruction. The vertexing algorithmused is the same configuration as the custom vertexing described in section 7.3.3 except that it does not requirelepton tracks but instead considers all charged tracks. To prevent contamination from the signal region, onlyvertices from the inverted prompt lepton validation region are used as described in section 7.4.4. The relativeabundance of vertices in data and simulation (data/MC) is calculated in bins of 푝T and production radius,30The impact on the final signal yield is evaluated before the complete selection criteria are applied in order to observe a sufficientnumber of events and thus obtain a reasonably precise measurement of this uncertainty.997.6. Signal systematicsalltrigger PV4-filterquality prompt leptonno plep overlap with DV DVfiducial2-track DVOS DVDV type01234567Number of passed events1e660000002056859 20568591140585 1006581 10030811003194+0.0%232095226482-2.4%186291181634-2.5%175593171334-2.4%172206167904-2.5%168058163733-2.6%ATLAS InternalMass: 3-20 GeVLifetime: 1-100 mmChannel: + e + ee + eeeTracking systematic calculationTracks droppedNormalFigure 7.13: This cutflow shows the reduction in the number of verticeswhen randomly removing a proportionof tracks using the tracking performance group’s recommendations. The average reduction in efficiency is2.6% at the DV type cut.3− 2− 1− 0 1 2 3ηDV 01020304050607080903−10×Fraction of Vertices3− 2− 1− 0 1 2 3ηDV 0.90.9511.051.1ratioDV type cut, nominalDV type cut, w/tracks droppedATLAS Internal = 13 TeVsVSI_LeptonsMod(a) 휂0 20 40 60 80 100 [GeV]TDV p00.050.10.150.20.25Fraction of Vertices / 4 GeV0 20 40 60 80 100 [GeV]TDV p0.90.9511.051.1ratioDV type cut, nominalDV type cut, w/tracks droppedATLAS Internal = 13 TeVsVSI_LeptonsMod(b) 푝T0 2 4 6 8 10DV mass [GeV]00.020.040.060.080.10.120.140.160.180.2Fraction of Vertices / 0.5 GeV0 2 4 6 8 10DV mass [GeV]0.90.9511.051.1ratioDV type cut, nominalDV type cut, w/tracks droppedATLAS Internal = 13 TeVsVSI_LeptonsMod(c) 푚DV0 50 100 150 200 250 300 [mm]DVr00.050.10.150.20.25Fraction of Vertices / 6 mm0 50 100 150 200 250 300 [mm]DVr0.90.9511.051.1ratioMaterial LayersDV type cut, nominalDV type cut, w/tracks droppedATLAS Internal = 13 TeVsVSI_LeptonsMod(d) 푟DV0 5 10 15 20 25HNL mass [GeV]00.10.20.30.40.5Fraction of Vertices / 0.5 GeV0 5 10 15 20 25HNL mass [GeV]0.90.9511.051.1ratioDV type cut, nominalDV type cut, w/tracks droppedATLAS Internal = 13 TeVsVSI_LeptonsMod(e) 푚HNLFigure 7.14: Kinematic distributions of several relevant variables illustrating the effect of randomly removingtracks from the sample. A small reduction in total events is seen, but no clear shape dependence. Sampleshown: 휇−휇휇, 푐휏N = 10mm, 푚N = 10GeV.1007.6. Signal systematics푟DV, chosen to provide coverage of the HNL signal distributions. These bins are scaled, so the data/MCratio of vertices produced near the interaction point is unity. This is done under the assumption that thereconstruction of less-displaced vertices is more robust and that prompt tracking uncertainties are quantifiedby the tracking systematic. The uncertainty is applied to each vertex as a per-event systematic variation.This is shown graphically in fig. 7.15.1.001.001.040.990.960.850.830.790.780.780.800.840.800.840.791.001.011.071.051.000.940.950.900.880.840.930.890.850.830.911.001.071.071.061.071.060.940.920.950.910.990.941.020.980.921.000.941.001.011.000.980.960.940.870.940.880.980.920.860.801.001.051.111.101.071.071.020.990.950.930.970.981.031.000.901.001.001.071.101.141.111.061.051.011.051.020.981.041.000.991.001.001.101.171.241.191.181.041.091.091.051.101.061.041.171.001.001.001.141.191.121.231.150.941.080.841.181.061.311.021.001.001.001.001.281.111.471.400.951.071.151.351.011.240.8750 100 150 200 250 300) [mm]DVrDisplaced vertex radius (5101520253035 [GeV]TDisplaced vertex p00.20.40.60.811.21.41.61.82 ATLAS -1 = 13 TeV 139 fbsnormalizationbinsData/MC ratioFigure 7.15: The dominant signal uncertainty is due to differences in the reconstruction of displaced verticesand tracks between data and MC produced with Pythia8.186. Only events in the VR are observed. Theuncertainty is evaluated by comparing 퐾0푆 → 휋+휋− event yields in bins of 푝T and 푟DV. The data/MC ratiois normalized to the bin nearest the IP, where the tracking and vertex reconstruction algorithms are expectedto be most robust. Higher-푝T vertices are grouped in larger low-푟DV “normalization bins” since fewerdisplaced vertices populate bins near the IP. The highest-푝T bin contains all vertices with 푝T > 35GeV. Thesymmetrized difference from 1.0 is applied to each signal vertex as a per-event systematic variation [1].7.6.5 Filter emulation efficiencyA DRAW filter is applied to data events before they are selected for secondary reconstruction (see section 7.2.4).An emulator is used on both MC and data to apply a filter emulation as close as possible to the real one.Due to differences mentioned below in the objects used by the DRAW filter and the emulated filter, thereis a mismatch in the signal efficiency. The subtle difference arises from the filtering pipeline, as seen infig. 7.16. The detector simulation outputs samples which have only undergone the specialized reconstruction,including LRT and with updated conditions. The full collection of tracks, including LRTs, is then used toproduce physics objects such as electrons and muons. Each event passes through the filter emulator, whichapplies the same filter criteria as in the RAW→ DRAW_RPVLL step but on these slightly different objects. Onthe other hand, real data is first reconstructed using standard physics objects in the RAW→ DRAW_RPVLL step.1017.6. Signal systematicsData events passing this filter step continue to the secondary reconstruction step, which crucially overwritesthe standard reconstruction objects. Data events then also pass through the filter emulator using the finalelectrons and muons constructed from both LRT and standard tracks. Effectively, data events are filteredtwice, and MC events are filtered once, suggesting that the acceptance for data is always strictly less than forMC.Uses standard physics objects (e.g. muons)DRAW_RPVLLData RAW DRAW Filter DAOD_RPVLLLarge-radius tracking + reconstructionFilter Emulator ntupleUses overwritten physics objects constructed with large-radius tracksMC RAW DAOD_RPVLL Filter emulator ntupleLarge-radius tracking + reconstructionCollections overwritten after LRT is runFigure 7.16: Real and simulated data are processed differently in the DRAW pipeline. MC has only filteremulator applied to LRT objects. Data has a filter applied to standard objects as well as a filter emulatorapplied to LRT objects. This introduces a discrepancy in the signal acceptance between data and MC.It is possible to estimate the size of this effect on the signal acceptance by using only simulated data.First, a subset of the MC events are reconstructed in two different pipelines, one where LRT is enabled(DAOD_RPVLL) and one where it is not (AOD). Events are matched between the the two pipelines and finalyields are calculated for events which pass both filters (true positive) and those which pass the second butnot the first (false positive), estimating the degree of undercounting of data events. A conservative estimateof 3% is applied as a systematic to account for this discrepancy.7.6.6 Lepton 푑0 extrapolationThe use of displaced leptons in secondary vertices introduces an additional uncertainty which is not capturedusing prompt lepton reconstruction uncertainties. In particular, the lepton identification efficiency is reducedwhen the lepton has a high impact parameter, |푑0 |. This is expected to differ in simulation and data, butunfortunately, no pure sample of high-|푑0 | leptons are available in data to derive such a systematic. Thefollowing study uses only MC samples to estimate the uncertainty from lepton displacement.To estimate this uncertainty, the effect of applying the lepton ID criteria to HNL signal DVs is explicitlymeasured. Events from each푚N–푐휏N point are taken after applying the full preselection, so they containDVsof the specified lepton type (up to 휇휇, 푒푒, or 푒휇 DV as shown in the selection cutflows in fig. 7.7). The leptonquality requirements are then applied to each lepton in the DV; Medium for muons, and LHVeryVeryLoosefor electrons.1027.7. Background systematicsFor each lepton type, the set of all reconstructed leptons is divided by the set of quality-selected leptonsin bins of |푑0 |. These bins are normalized to the 0–3mm |푑0 | bin, where the ID efficiency in data and MCis expected to be most similar. The difference from one is symmetrized and used as the 푑0 extrapolationuncertainty. Using the ratio of the histograms, effects from other selection efficiencies such as vertexing andtracking are factored out of this systematic. Figure 7.17 shows the calculated systematics in bins of |푑0 | .00.20.40.60.811.21.4# muons relative to first bin+overflow0 10 20 30 40 50 60|d0| [mm]0.80.911.1systematic 1.000 0.984 0.976 0.970 0.962 0.945 0.949All displaced muonsMedium displaced muonsATLAS Simulation Internal = 13 TeVs(a) 휇−휇휇00.20.40.60.811.21.4# electrons relative to first bin+overflow0 10 20 30 40 50 60|d0| [mm]0.80.911.1systematic 1.000 0.980 0.951 0.944 0.934 0.934 0.944All displaced electronsVeryVeryLoose displaced electronsATLAS Simulation Internal = 13 TeVs(b) 푒−푒푒Figure 7.17: The displaced lepton ID systematic is derived by dividing all reconstructed leptons by all leptonsthat pass quality selection in bins of |푑0 |. The systematic is calculated in relation to the prompt, 0–3mm bin.Displaced muon ID (a) is less affected than displaced electron ID (b).For each signal vertex, the uncertainty for each lepton depends on its type and its |푑0 |. Since each vertexconsists of two leptons, the systematic for each is multiplied, and the product is used as a systematic forthat event. In many signal vertices, most leptons have small |푑0 |; therefore, the lepton 푑0 extrapolationuncertainty is often negligible.The displacement and associated uncertainty can be substantial for signals with lower mass and higherlifetime. For muon channels, the average impact on the selection efficiency is 2.0% and the maximum, 5.5%.For electron channels, the average impact on the selection efficiency is 2.6% and the maximum 6.9%. ThemuonMediumWP definition is the same as is used for prompt muons, so the displacement effect is relativelysmall. However, electrons are identified using a likelihood trained with 푑0 as a discriminating variable.Since the custom electron quality definition used in this analysis, LHVeryVeryLoose, has no maximum-푑0requirement, the 푑0 extrapolation uncertainty for electrons can depend quite strongly on displacement.7.7 Background systematicsSystematic uncertainties in the background model, taken to be fully correlated between the CR and the SR,are evaluated for two sources. The first estimates the uncertainty from the assumption that non-randombackgrounds are negligible and is estimated from differences between the 푚HNL distributions of shuffledevents created from SS and OS DVs. This uncertainty varies between 5% for the 푒−푒휇 channel and 79% forthe 휇−휇휇 channel.1037.8. Statistical methods and resultsThe second uncertainty accounts for statistical fluctuations in the 푚HNL distribution of the shuffledsample due to the finite number of prompt leptons used. The limited number of prompt leptons used in theshuffling will introduce unphysical bumps in the kinematic properties of the shuffled DVs. The uncertainty isestimated from the differences between the 푚HNL distributions for shuffled events of two types: in type 1 (2),the combined DV and prompt lepton originate from events in identical (different) DV channels (푒푒, 휇휇, 푒휇).This uncertainty is largest for the 휇−휇푒 channel, reaching 5%. The background systematics for each channelare summarized in table table 7.9. The total uncertainty is the quadrature sum of the two contributions. Theuncertainties are treated as uncorrelated among the different channels.Table 7.9: The relative systematic uncertainties on the background estimate, estimated by creating shuffledevents from SS DVs or from prompt leptons taken from events with different DV channels [1].Channel Relative Uncertainty (%)DV Prompt ℓ Total푒−푒푒 35 < 1 35휇−푒푒 27 < 1 27푒−푒휇 2 1 2휇−휇푒 5 5 7푒−휇휇 70 2 70휇−휇휇 79 3 797.8 Statistical methods and resultsAfter finishing the analysis procedure, estimating the uncertainties and computing the expected sensitivity,then checking our assumptions by unblinding the CR, the SR is unblinded. Each MC signal samplecorresponds to specific values of |푈훼 |2 vs. 푚N , for which the efficiency is evaluated. A hypothesis test for agiven model is performed at each point with 104 pseudoexperiments. The unblinded data shows no excess inany channels above the expected backgrounds. Exclusion limits are set for each theoretical HNL scenario.The statistical method used to interpret the observed data follows the standard ATLAS recommendations andis summarized below. A detailed presentation of the statistical foundations including the profile likelihoodratio and the “modified frequentist” CLs method can be found in references [166, 168, 169].7.8.1 Statistical methodsThe most powerful test statistic for discrimination between the two hypotheses is the likelihood ratio [5,170]. In the following definitions, the signal strength parameter 휇 is the parameter of interest (POI) and thesystematic uncertainties are encoded as nuisance parameters (NPs) represented with the vector 휃. Testingthe different values of the signal strength parameter 휇 is done using a likelihood function 퐿 (휇, 휃).1047.8. Statistical methods and resultsA binned likelihood is represented as퐿 (휇, 휃) =∏푖∈binsPois (푛푖 |휇푆(휃) + 퐵(휃))︸ ︷︷ ︸observed events·∏푗∈systGaus(휃 푗 |휃0푗 ;휎휃 푗 )︸ ︷︷ ︸systematics. (7.8)The probability distribution function of the observed events is modelled as a Poisson distribution, and that ofthe nuisance parameters is modelled as a Gaussian distribution. In this notation, 푛푖 is the observed numberof events in bin 푖, and 푗 NPs represent the systematics. 휇푆(휃) + 퐵(휃) is the expected number of signaland background events, with the signal yield scaled by the parameter 휇, where 휇 = 1 would represent theexpected cross section. 휃0푗 is the central value of systematic uncertainty 푗 , and 휎휃 푗 is its width. The nuisanceparameters broaden 퐿 reflecting the loss of information about 휇 due to systematic uncertainties.The profile likelihood ratio (PLR) is휆(휇) = 퐿 (휇,ˆˆ휃휇)퐿 ( 휇ˆ, 휃ˆ휇)(7.9)where ˆhats represent fitted values. In the numerator, 휇 is the fixed signal strength (e.g., 휇=0 in the backgroundhypothesis) and ˆˆ휃휇 is the best-fit value of the NPs for fixed 휇. In the denominator, the signal strength 휇ˆ and휃ˆ휇 are fit simultaneously. These values, which maximize each likelihood function, are known as maximumlikelihood estimates (MLEs).In this formulation, 휆 takes a value between 0 and 1, with higher values representing better agreementbetween the observed data and the hypothesized value of 휇. The next technique is to take the negativelogarithm of the likelihood ratio as the test statistic as minimizing the log-likelihood is equivalent tomaximizing the likelihood while being easier to compute. The one-sided profile likelihood test statistic usedfor this analysis is defined as푞휇 =−2 ln휆(휇) 휇ˆ ≤ 휇0 휇ˆ > 휇. (7.10)In this definition, higher values of 푞휇 correspond to increased incompatibility between observed data andhypothesized 휇.The 푝-value quantifies the level of disagreement:푝휇 =∫ ∞푞obs푓 (푞휇 |휇)푑푞휇 . (7.11)In frequentist statistics, a model is rejected if this value is less than some threshold 훼 (e.g., 95% confidencelimits are set using a threshold of 훼 = 0.05). The CLs method aims to reduce the ability to reject a model inthe case where an experiment has very little sensitivity to the model. The CLs quantity is defined asCLs ≡ 푝푆+퐵1 − 푝퐵 (7.12)1057.8. Statistical methods and resultsand takes the place of the 푝-value such that the signal+background (푆+퐵) model will be rejected if CLs < 훼.The reader is directed to reference [169] for a clear description of the CLs method’s motivations.For low-background analyses such as this, it is useful to perform the integrals of eq. (7.11) numericallyusing “toy” techniques. In this analysis, distributions of the test statistic (eq. (7.10)) are created usingrandomly-generated pseudoexperiments (toys). The background (퐵) hypothesis is tested by generating toysfrom the likelihood distribution for 휇 = 0. The 푆 + 퐵 hypothesis is tested by generating toys with a specificvalue of 휇.By calculating the 푝-values for a range of 휇, the observed upper limit 휇up is determined where CLs(휇up)drops below 0.05. The CLs prescription is applied to each model in the 푚N–푐휏N plane for each channel.Those models for which 휇up < 1 are excluded. Limit contours are then obtained by performing a cubicspline interpolation between the generated 푚N–푐휏N points. Expected limits are obtained by performing thesame procedure but instead setting the observed statistic to be the median of the 퐵 distribution. ±휎 and ±2휎bands are also shown by varying the expected value assuming 퐵 is Gaussian distributed.7.8.2 ResultsLimits are set at 95% confidence level (CL) on |푈 |2 vs. 푚N for each HNL model, using the CLs prescriptiondescribed above and implemented in the TRExFitter package [163–165]. Histograms of the푚HNL distributionin two bins (0–20GeV, 20–50GeV) are used as inputs to TRExFitter. The background histograms areconstructed using the data-driven shuffled background estimate described in section 7.5.6 and scaled bya separate unconstrained normalization factor for each channel. The background normalization used togenerate the toys is taken as that obtained by normalizing the OS shuffled backgrounds to the SS data in theCR. The signal histograms are generated from simulation and are assigned a single floating signal strength휇 for all relevant channels, weighted according to each model (section 7.2.1). The inputs to the fit are theOS-event yields observed in the SR and CR. The inclusion of the CR in the fit constrains the predictedbackground yield in the SR.Table 7.10 shows the post-fit estimated and observed yields in the SR and CR for all channels. Theseyields are consistent with the estimated backgrounds, indicating no excess signal. The observed yields in theCR are consistent with the CR background estimates. The pre-fit and post-fit yields are shown in fig. 7.18.All systematic uncertainties are included in the fit by using nuisance parameters, whose post-fit values donot show any significant pull or constraint. To visualize the distribution of predicted and observed yields, amore finely-binned display of the unblinded data is shown in fig. 7.19.The various channels are combined in different ways to set limits for each of the four models presentedin section 7.1. The Majorana limit and the Dirac limit of each model are treated separately. The observed95% CL contour plots are shown in fig. 7.20 for all eight interpretations as well as the observed and expectedlimits for the 2QDH NH model with one- and two-sigma uncertainty bands. For a signal at a given 푚N–푐휏Npoint in the plane, the expected event yield depends on the cross section and branching ratio predicted byeach model, causing the limit contours of each to be different.1067.8. Statistical methods and results10−1100101102103EventsATLASDirac, 2QDH (NH), 10 GeV, 10 mm√s = 13 TeV, L = 139 fb−1DataHNL Signal MCBackgroundUncertaintyµ−µµ µ−µe µ− ee e− ee e− eµ e−µµSR CR SR CR SR CR SR CR SR CR SR CR−2σ−σ0σ2σSignificance(a)10−1100101102103EventsATLASMajorana, 2QDH (NH), 10 GeV, 10 mm√s = 13 TeV, L = 139 fb−1DataHNL Signal MCBackgroundUncertaintyµ−µµ µ−µe µ− ee e− ee e− eµ e−µµSR CR SR CR SR CR SR CR SR CR SR CR−2σ−σ0σ2σSignificance(b)10−1100101102103EventsATLASDirac, 2QDH (NH), 10 GeV, 10 mm√s = 13 TeV, L = 139 fb−1DataBackgroundUncertaintyHNL Signalµ−µµ µ−µe µ− ee e− ee e− eµ e−µµSR CR SR CR SR CR SR CR SR CR SR CR−2σ−σ0σ2σSignificance(c)10−1100101102103EventsATLASMajorana, 2QDH (NH), 10 GeV, 10 mm√s = 13 TeV, L = 139 fb−1DataBackgroundUncertaintyHNL Signalµ−µµ µ−µe µ− ee e− ee e− eµ e−µµSR CR SR CR SR CR SR CR SR CR SR CR−2σ−σ0σ2σSignificance(d)Figure 7.18: Summary plots for the 2QDH (NH) (two quasi degenerate HNLs, normal neutrino masshierarchy mixing, 푥푒 = 0.06, 푥휇 = 0.48, 푥휏 = 0.46) model in the Dirac-limit (a,c) and Majorana-limit (b,d).Shown are pre-fit plots (a,b) with background and HNL signal MC stacked, and post-fit plots (c,d) in whichthe pre-fit signal contribution is overlaid as a dashed line (post-fit signal contribution is zero). Figure from [1]supplemental material.1077.8. Statistical methods and resultsTable 7.10: Yields of estimated post-fit background events and of observed events in the signal and controlregions for all final states. The background yield uncertainties include both systematic and statisticaluncertainties. The last two rows show the 1SFH Dirac-limit, LNC configuration ℓ±훼–ℓ∓훼ℓ±훾 [1].Channel Signal region Control regionBackground Observed Background Observed푒−푒푒 0.4 ± 0.3 2 3.6 ± 1.8 2휇−푒푒 0.2 ± 0.1 1 1.8 ± 1.3 1푒−푒휇 0.9 ± 0.4 0 4.1 ± 1.9 5휇−휇푒 2.8 ± 0.8 2 12.2 ± 3.2 13푒−휇휇 1.2 ± 0.9 1 2.8 ± 1.6 3휇−휇휇 2.2 ± 1.4 2 8.7 ± 2.9 9푒±–푒∓휇± 0.6 ± 0.3 0 2.4 ± 1.4 3휇±–휇∓푒± 1.9 ± 0.6 0 8.1 ± 2.6 101087.8. Statistical methods and results0 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 -1 = 13 TeV, 139 fbs=10 mmNτ, cµµ-µ(a) 휇−휇휇0 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 -1 = 13 TeV, 139 fbs=10 mmNτ, cµµe-(b) 푒−휇휇0 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 -1 = 13 TeV, 139 fbs=10 mmNτ-ee, cµ(c) 휇−푒푒0 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 -1 = 13 TeV, 139 fbs=10 mmNτe-ee, c(d) 푒−푒푒0 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 -1 = 13 TeV, 139 fbs=10 mmNτ, cµe-e(e) 푒−푒휇0 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 -1 = 13 TeV, 139 fbs=10 mmNτe, cµ-µ(f) 휇−휇푒Figure 7.19: The 푚HNL distribution in the signal (SR) and control (CR) regions for the observed data, theshuffled-event-model background normalized by the two-bin fit described in the text with its uncertainty, andsimulated signals with a proper decay length 푐휏N = 10 mm [1].1097.8. Statistical methods and results2 4 6 8 10 12 14 16mN [GeV]10−710−610−510−410−310−2(|Ue|2,|Uµ|2 ,|Uτ|2)=|U|2 (x e,xµ,xτ) ATLASDirac√s = 13 TeV, L = 139 fb−12QDH (NH):|U |2(0.06,0.48,0.46)2QDH (IH):|U |2(0.33,0.33,0.33)1SFH: |U |2(1,0,0)1SFH: |U |2(0,1,0)(a) Dirac limit2 4 6 8 10 12 14 16mN [GeV]10−710−610−510−410−310−2(|Ue|2,|Uµ|2 ,|Uτ|2)=|U|2 (x e,xµ,xτ) ATLASMajorana√s = 13 TeV, L = 139 fb−12QDH (NH):|U |2(0.06,0.48,0.46)2QDH (IH):|U |2(0.33,0.33,0.33)1SFH: |U |2(1,0,0)1SFH: |U |2(0,1,0)(b) Majorana limit2 4 6 8 10 12 14 16mN [GeV]10−710−610−510−410−310−2(|Ue|2,|Uµ|2 ,|Uτ|2)=|U|2 (x e,xµ,xτ) ATLASDirac, 2QDH (NH)√s = 13 TeV, L = 139 fb−1obs 95% CLexp 95% CL±1σ±2σ(c) Dirac limit2 4 6 8 10 12 14 16mN [GeV]10−710−610−510−410−310−2(|Ue|2,|Uµ|2 ,|Uτ|2)=|U|2 (x e,xµ,xτ) ATLASMajorana, 2QDH (NH)√s = 13 TeV, L = 139 fb−1obs 95% CLexp 95% CL±1σ±2σ(d) Majorana limitFigure 7.20: Summary of the observed 95% CL contours for the different HNL models in Dirac limit (a) andMajorana limit (b). The observed and expected 95% CL contours are shown for the 2QDH (NH) model inthe Dirac (c) and Majorana (d) limits. The green and yellow bands show the one and two standard deviation(휎) spreads for the expected limits [1].1107.9. Discussion7.9 DiscussionThe limits obtained by this search supersede those obtained in the previous ATLAS search for HNLs [122].The previous search, which reported results for both prompt and displaced HNL decays, only analyzed thedisplaced muon decays using the |푈휇 |2 mixing model. That search excluded models with mixing anglesbetween 10−3 < |푈휇 |2 < 10−6 for masses 4GeV < 푚N < 10GeV. The present search extends the |푈휇 |2sensitivity by nearly an order of magnitude to 10−7 in some mass ranges and substantially extends the HNLmass reach in both directions, setting limits on 2.5GeV < 푚N < 14GeV. This search set limits on the |푈푒 |2mixing model using displaced decays for the first time in an ATLAS publication.Three particularly novel techniques are used in this analysis:• The interpretation of the measured data is performed for the first time in any experiment using realisticHNL mixing models as well as the traditional single-flavour benchmark models.• The reconstruction of the HNLmass by way of four-momentum conservation presented a new variablewith which to bin the yields.• The background from random track crossings is estimated using an event shuffling method.The unusual shape of the exclusion limits is caused by the following. According to eq. (7.6), high-massHNLs have a very short proper decay length, and the decay vertices are likely to fail the minimum 푟DVrequirement, limiting sensitivity beyond 푚N > 14GeV. At 푚N < 2GeV, the proper decay length is so longthat too few HNLs decay within the ID to provide sufficient signal sensitivity. The “pinched” shape between4–6GeV is due to the strict cuts imposed to exclude backgrounds from SM metastable particle decays.The 95% confidence levels are primarily limited in their sensitivity by low event yields and associatedPoisson statistical uncertainties. There is very little change between the limits gained from the completeanalysis and results obtained using only the statistical uncertainties. Fortunately, this suggests that Run 3 andhigh-luminosity LHC datasets will continue to improve the analysis sensitivity as more data is collected.In addition to more data, further refinements to the analysis could be made. For example, even afterstatistical enhancement, the background estimation is limited by large systematic uncertainties. A betterbackground estimate and more recorded data could allow the use of a more finely-binned푚HNL discriminant.The vertex reconstruction uncertainty, the largest of the signal systematic uncertainties, could be substantiallyreducedwith bettermodelling of the detector response to displaced tracks and vertices (e.g., improvedmaterialmaps and detector conditions). Future searches could improve signal sensitivity by including semi-leptonicfinal states — an HNL process in which the virtual푊 boson decays into a pair of hadrons instead of leptons.Perhaps the largest improvement to the analysis procedure will be made by running the optimized LRTtracking in the default reconstruction stream. As discussed in section 6.7, optimizing the LRT algorithmimproves the vertex reconstruction efficiency and allows the entire recorded dataset to be processed, asopposed to the 10% accessed using the DRAW filters. Not only would this increase the general signal sensitivity(nearly doubling the acceptance), but it would also allow for the improvedmodelling of background processes.For example, instead of the metastable particle veto described in section 7.5.2, mesons decaying at large1117.9. Discussion푟DV could be modelled and explicitly included in the background estimate. This would, in turn, increase thesignal sensitivity, particularly at low 푚DV, removing the pinched feature in the exclusion limit contours.A recent publication from the CMS collaboration places limits on only the 1SFH mixing scenario using138 fb−1 of√푠 = 13TeV 푝푝 collision data with results in those channels comparable with ATLAS [171].CMS, however, uses a different track reconstruction workflow which effectively does not distinguish betweenstandard and displaced tracks. This enables the modelling of SM backgrounds, which improves the signalsensitivity by allowing looser final selection. A notable consequence is in the low mass range limits setby CMS. The contours are not closed as they are in ATLAS, and the pinched feature is absent. Thesensitivity is also slightly increased at high mass ranges extending the exclusion limits by approximately1GeV, presumably due again to looser selection criteria.112Chapter 8ConclusionNow, we’ve basically got it all worked out, except for small stuff, big stuff, hot stuff,cold stuff, fast stuff, heavy stuff, dark stuff, turbulence, and the concept of time.–Zach Weinersmith, Science: Abridged Beyond the Point of UsefulnessThe StandardModel of particle physics is incredibly successful at describing nearly all observed physicalphenomena. Still, some conspicuous holes are present in our understanding, suggesting that physics beyondthe Standard Model is yet to be discovered. The mystery of neutrino masses and oscillations is one such gapthat requires imaginative theory and careful experimentation to address. Many theories that address thesegaps predict metastable particles, which exist for finite periods before decaying into known matter. Thesephenomena are sought at colliders like the LHC and observed with detectors like ATLAS, where specializedalgorithms are used to identify long-lived particles.The search for Heavy Neutral Leptons (HNLs) presented in this dissertation used 139 fb−1 of 푝푝 collisiondata gathered by the ATLAS detector at the LHC. No excess of signal events was observed in the region ofphase space explored. Exclusion limits are set for models with HNLs with mixing angles between 10−3–10−7and masses between 2.5–14GeV, extending the limits set by the previous ATLAS analysis. These limits arecomparable to, and consistent with, the recent CMS search for displaced HNLs. For the first time, limits arepresented for realistic HNL mixing models motivated by neutrino flavour oscillation data.Finding no new phenomena is typical of such a search in high-energy physics, yet with every null resultwe continue to accrue knowledge about our universe, which in turn helps theorists refine their imaginationswith real-world measurements. This displaced vertex search complements other experiments searching forHNLs by probing a region of masses and coupling strengths yet to be investigated. Long-lived particleanalyses are challenging as many standard assumptions and algorithms used within the collaboration mustbe altered.The work in this dissertation is centred around the use and performance of ATLAS’s large-radiustracking (LRT) algorithm, the use of which was crucial in the search for displaced HNL vertices among othersearches. However, in conducting the analysis, it became clear that the configuration of the LRT algorithmwas producing excessive numbers of fake tracks and limiting the signal sensitivity. The recognition that sucha limitation impacted many current and future analyses prompted us to undertake a campaign to improve theuse of LRT in future studies.The refinements made to the LRT algorithm will deliver considerable benefits. By drastically reducingthe rate of fake tracks at the expense of a small number of signal tracks, the LRT signal sensitivity willincrease by 400% for future analyses. A DNN discriminant was developed, which, if enabled, can further113Chapter 8. Conclusionenhance this improvement. By increasing the LRT track purity, the displaced vertexing algorithm produceshigher-quality signal vertices and far fewer fake vertices.Perhaps most importantly, the reduction in the computational cost of the LRT algorithm has allowedfor its inclusion in the standard reconstruction pipeline. It can hardly be overstated how much this changewill simplify future LLP analyses. Until now, ATLAS LLP searches that use tracking information wererestricted to analyzing 10% of the complete dataset by selecting events with filters which required substantialdevelopment time and introduced discontinuities in the kinematic distributions. Including LRT in thedefault reconstruction removes the need for filters, making continuous prompt-to-displaced analyses possible,allowing analyses to develop well-informed control and validation regions, and amplifying signal sensitivity.The next iteration of the displaced HNL analysis will use the improved data pipeline enabling themodelling of backgrounds from metastable particle decays, improving the sensitivity to low-mass HNLs.Because the low number of signal events limits the sensitivity of the present analysis, the reach of the HNLsearch will benefit from the inclusion of data from Run 3 of the LHC. Moreover, the analysis softwarepipeline will be substantially simplified, reducing development time, complexity, and chances for humanerror.This dissertation comes to a close at a notable moment in the ATLAS collaboration. Two significantevents are taking place the same week that these words are written. On July 4th 2022, CERN was alive withcelebrations of the tenth anniversary of the Higgs boson discovery — a massive achievement in physics anda guiding force in the design of the LHC. The following day, the first√푠 = 13.6TeV collisions of protonswere recorded in Run 3, breaking the previous record and further advancing the energy frontier. 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Lister, Alison
Using displaced tracks to search for sterile neutrinos in the ATLAS detector
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