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Search for long-lived neutral particles in final states with a muon and multi-track displaced vertex… Loh, Chang Wei 2013

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Search for Long-Lived Neutral Particles in Final States with a Muon and Multi-Track Displaced Vertex with the ATLAS Detector at the Large Hadron Collider  by  Chang Wei Loh B.Sc. (Physics), Universiti Malaya di Kuala Lumpur, Malaysia, 2006  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES (Physics)  The University Of British Columbia (Vancouver) April 2013  c Chang Wei Loh, 2013  Abstract This work presents the result of a search for a new long-lived neutral particle decaying into a muon and charged hadrons in proton-proton collisions at a centre-of-mass energy of 7 TeV with a total integrated luminosity of 4.4 fb−1 , using the ATLAS detector located at the Large Hadron Collider (LHC). Many extensions to the current Standard Model of particle physics predict the existence of such new particles, including the neutralino in an R-parity violating supersymmetry scenario. In this search, a set of selection criteria has been established to be sensitive to this kind of signal, in addition to evaluating the background in a data-driven manner. No excess of events above the expected background is observed with the collected data and limits are set on the squark pair production cross section, multiplied by the branching ratio for a squark to decay, via a long-lived neutralino, to a muon and charged hadrons, as a function of the neutralino lifetime.  ii  Preface The ATLAS experiment has over 3000 members and a variety of physics programs, which includes the displaced vertex group. The displaced vertex channel search (muon and multi-track) was initiated from a discussion in February 2010 by four members: Abner Soffer (professor), Claus Horn (postdoctoral researcher), Nick Barlow (postdoctoral researcher) and the author. The publication with the 2010 data can be found in [i], with the ATLAS internal note in [ii]. The author was also involved in the initial phase of the vertexing algorithm in 2010, together with Claus Horn, Nick Barlow and Arik Kriesel (postdoctoral researcher). This framework was used for the 2011 data, albeit with some modifications to its core. The author was also involved in the design of the displaced vertex selection criteria which were used in the 2010 data, and were still largely used for the 2011 data with further improvements [iii] [iv]. The author has also introduced several new ideas for the displaced vertex community: • a data-driven particle-material interaction background estimation (for the data collected in 2010) [i],  • the Ks + 1 approach (for the data collected in 2010) [ii]. For the 2011 data, this was implemented by Nick Barlow in a different context (see Section 6.2),  • a data-driven random combination fake vertex background estimation (for the data collected in 2011) (see Section 6.1.1),  • a method to search for potential new physics with pp → V 0 +V 0 + X + ISR (see Section 8.2).  [i] The ATLAS Collaboration, “Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS,” Phys. Lett. B, vol. 707, no. 5, pp. 478 – 496, 2012. [ii] The ATLAS Collaboration, “Search for Heavy Medium-Lived Particles at ATLAS,” ATLAS iii  Note, ATL-PHYS-INT-2011-076, 2011. [iii] The ATLAS Collaboration, “Updates of search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS”, ATLAS Note, ATL-COM-PHYS-2012-785, 2012. [iv] The ATLAS Collaboration, “Search for long-lived, heavy particles using a muon and multitrack displaced vertex, in proton-proton collisions at ps = 7 TeV with the ATLAS detector,” ATLAS Note, ATL-COM-PHYS-2012-1090, arXiv:1210.7451 (accepted by Phys. Lett. B).  Hereafter, we use h¯ = c = 1.  iv  Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ii  Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  iii  Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  v  List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  ix  List of Abbreviations and Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xii  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  xv  Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi 1  2  3  The Standard Model and Beyond . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.1  The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  1  1.2  Supersymmetry and R-Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  5  The ATLAS Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12  2.1  The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  12  2.2  Conventions in ATLAS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16  2.3  Subsystems : Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  16  2.4  Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  18  2.5  Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21  2.6  Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  22  2.7  Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  23  Physics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  25  3.1  25  Track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  v  4  3.1.1  Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  25  3.1.2  Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  27  3.2  Muon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  29  3.3  Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  29  3.4  Primary Vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  30  Displaced Vertex Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  33  4.1  Datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  33  4.2  Displaced Vertex Finder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  36  4.2.1  RPVDispVrt Vertex Finder . . . . . . . . . . . . . . . . . . . . . . . . . .  36  Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  42  4.3.1  Invariant Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  42  4.3.2  pT -corrected Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  43  4.3.3  Muon+Jets Invariant Mass . . . . . . . . . . . . . . . . . . . . . . . . . .  44  Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  45  4.4.1  Event Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  45  4.4.2  Muon Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46  4.4.3  Vertex Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  46  Data vs. MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  49  Total Signal Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  55  5.1  Efficiency Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  57  5.2  Efficiency vs. cτ  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  58  5.3  Systematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  62  Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  68  6.1  Region 0 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . .  69  6.1.1  Justification of the ABCD Method . . . . . . . . . . . . . . . . . . . . . .  71  Regions 1-8 Background Estimation . . . . . . . . . . . . . . . . . . . . . . . . .  79  6.2.1  The Constraints in the Likelihood . . . . . . . . . . . . . . . . . . . . . .  83  Search Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  86  7.1  Limits on New Particle Production . . . . . . . . . . . . . . . . . . . . . . . . . .  90  Going Forward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  92  8.1  Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  92  8.2  pp → V0 +V0 + ISR + X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  93  4.3  4.4  4.5 5  6  6.2  7  8  8.2.1  Data vs MC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi  97  9  Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105  Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Appendix A pT -corrected Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Appendix B Event Display Legend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115  vii  List of Tables 1.1  Examples of mesons and baryons. . . . . . . . . . . . . . . . . . . . . . . . . . .  4  1.2  SUSY particle content. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  6  1.3  Long-lived particle searches from other experiments. . . . . . . . . . . . . . . . .  10  2.1  The LHC proton beam parameters and at the ATLAS collision point. . . . . . . . .  13  3.1  Criteria imposed in NEWT and the second pass in RPVDispVrt. . . . . . . . . . . .  28  3.2  Secondary track reconstruction efficiency, fake rate, optimisation factor ε (1 − f )  and average reconstructed track multiplicity per event for different cut values of |d0 |. 28  4.1  Signal MC samples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  34  4.2  Layers in the beam pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  41  6.1  Comparing the expected background yield using the method described in this Section and the observed number of DV (Ntrk ≥ 5) in various data streams. . . . . . . .  viii  85  List of Figures 1.1  The elementary particles in the Standard Model. . . . . . . . . . . . . . . . . . . .  2  1.2  The Higgs bare mass receives a top loop correction. . . . . . . . . . . . . . . . . .  5  1.3  In supersymmetry, the Higgs bare mass receives a top and stop loop correction. . .  7  1.4  Possible RPV diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8  1.5  Proton decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  9  1.6  χ10  9  1.7  Production of a neutralino and its decay products. . . . . . . . . . . . . . . . . . .  11  2.1  The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  14  2.2  Total integrated luminosity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  15  2.3  ATLAS detector overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  17  2.4  Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  19  2.5  η coordinate on the positive z-axis of the ATLAS Inner Detector. . . . . . . . . . .  20  2.6  Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  21  2.7  Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  22  3.1  Track parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  26  3.2  Impact parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  26  3.3  2011 data — Event with a Z → µ µ candidate and 20 reconstructed primary vertices. 31  → µud decay. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  3.4  Cross sections of SM physics for various electroweak and top physics. . . . . . . .  32  4.1  Simulation of a signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  34  4.2  (zDV , rDV ) and η distributions of the displaced vertices from the neutralino decays.  35  4.3  Invariant mass distribution constructed from 2 tracks. . . . . . . . . . . . . . . . .  37  4.4  Distributions on b-decays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  37  χ2  4.5  The  per degree of freedom after Stage 3. . . . . . . . . . . . . . . . . . . . . .  39  4.6  Vertex residual and pull distributions after Stage 3. . . . . . . . . . . . . . . . . .  40  4.7  Beam pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  41  4.8  The invariant mass mDV , pT -corrected mass and mµjet distributions. . . . . . . . . .  42  4.9  The boost invariant plane and the missing momentum. . . . . . . . . . . . . . . .  43  ix  4.10 MET spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  44  4.11 Ntrk and mDV distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  47  4.12 Material map. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  48  4.13 Simulation of the distance of the muons to the reconstructed  χ10  DV. . . . . . . . .  49  4.14 Triggered muon φ vs. η for the data and MC. . . . . . . . . . . . . . . . . . . . .  50  4.15 ∆φ vs. ∑ η for events with at least 2 muons, comparing data and MC. . . . . . . . 4.16 The spectra of the mDV and rDV in data vs. MC. . . . . . . . . . . . . . . . . . . .  51 52  4.17 Data vs. QCD distributions in mDV and rDV . . . . . . . . . . . . . . . . . . . . . .  53  4.18 Data vs. non-QCD distributions in mDV and rDV . . . . . . . . . . . . . . . . . . .  54  Signal vertex efficiency rDV vs. |zDV |. . . . . . . . . . . . . . . . . . . . . . . . .  58  The method to obtain average signal efficiency. . . . . . . . . . . . . . . . . . . .  59  5.3  The vertex selection and event-level efficiency. . . . . . . . . . . . . . . . . . . .  60  5.4  Event efficiency εevt vs. cτ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  60  5.5  Relativistic boost β γ versus η and the exponential lifetimes. . . . . . . . . . . . .  61  5.6  Vertex finding efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  61  5.7  Trigger efficiency vs. pT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  63  5.8  Trigger efficiency vs. d0 and z0 . . . . . . . . . . . . . . . . . . . . . . . . . . . .  64  5.9  Nominal signal εevt and tracks-killed εevt . . . . . . . . . . . . . . . . . . . . . . .  64  5.1 5.2  5.10 The η distributions of the cosmics and signal sample before and after the reweighting. 65 5.11 Muon d0 data/MC ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  66  5.12 The event selection efficiency and the total uncertainties. . . . . . . . . . . . . . .  67  6.1  Labels for different regions of the detector in terms of (|zDV |, rDV ), used for back-  ground estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  68  6.2  The ABCD box notation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  70  6.3  The ABCD box result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  71  6.4  Vertex mass distributions constructed from randomly combining the tracks in an event. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  72  6.5  Illustration interpreting the reweighting framework. . . . . . . . . . . . . . . . . .  74  6.6  The invariant mass distribution for the EF_mu40_MSonly_barrel(_medium) control (inverted) sample and JetTauEtmiss, before and after the reweighting. . . . . . . .  75  6.7  Tracks pT , η and MET before and after reweighting. . . . . . . . . . . . . . . . .  76  6.8  The invariant mass distribution before and after reweighting. . . . . . . . . . . . .  77  6.9  The expected yield of the JetTauEtmiss sample before and after reweighting compared to the number of observed DV. . . . . . . . . . . . . . . . . . . . . . . . . .  77  6.10 The invariant mass distributions before and after reweighting for various |d0 | cuts. .  78  x  6.11 Results from the ABCD method on the control sample and signal sample (without re-tracking). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  79  6.12 Gaussian + polynomial fits to the 2-track invariant mass (for Ks ) distribution of 2-track DV and 2 track combinations within 3-track DV. . . . . . . . . . . . . . .  80  6.13 Probability of DV containing random track. . . . . . . . . . . . . . . . . . . . . .  82  6.14 A method for modelling the invariant mass distribution, by summing two histograms. 82 6.15 Ratio of the number of DV, NDV in Region N to those in Region (N − 1) vs. Ntrk in  DV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  84  6.16 The number of displaced vertices, NDV vs. the number of tracks in each displaced vertex, Ntrk with an exponential fit in each Region. . . . . . . . . . . . . . . . . . .  84  6.17 Distributions of 5,≥ 6-track DV compared with PDFs. . . . . . . . . . . . . . . .  85  7.1  Vertex mass (mDV ) vs. vertex track multiplicity (Ntrk ) for displaced vertices in events. 87  7.2  Run 189822, Event 71110743. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  88  7.3  Run 189875, Event 19332017. . . . . . . . . . . . . . . . . . . . . . . . . . . . .  89  7.4  Upper limits at 95% confidence level using the CLs method, on the squark pair production cross section σ times the branching ratio BR for a squark to decay, via a long-lived neutralino, to a muon and quarks, vs. the neutralino lifetime. . . . . .  8.1 8.2  An event with a Z → µ µ candidate amongst 25 reconstructed PV in the data col-  lected in 2012. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  93  qq → V0 +V0 + ISR + X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  94  8.3  Lepton-jets and Hidden Valley models. . . . . . . . . . . . . . . . . . . . . . . . .  8.4  The normalized MET computed for each DV for the QCD sample vs (a) γd and (b) πv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  8.5 8.6  91  94 95  Minima of normalized MET given the whole set of PVs in an event for the QCD sample vs (a) γd and (b) πv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  96  / vs MET distribution for the QCD sample vs signal γd and πv . . . . . . . . . METZ  96 97  8.8  | of the QCD sample vs γd and πv . . . . . . . . . . . . . . . . . . . . . . .  cos α of the QCD sample vs γd and πv . . . . . . . . . . . . . . . . . . . . . . . . .  97  8.9  The spectra of MET and mDV for EF_e18_medium1_g25_loose triggered data. . .  99  8.7  |  cos θ ∗  8.10 The spectra of MET and mDV for EF_e18_medium1_g25_loose triggered data. . . 100 8.11 The spectra of MET and mDV for EF_xe80T_tclcw_loose triggered data. . . . . . . 101 8.12 The spectra of MET and mDV for EF_xe80T_tclcw_loose triggered data. . . . . . . 102 8.13 The spectra of MET and mDV for EF_j360_a10tcem triggered data. . . . . . . . . . 103 8.14 The spectra of MET and mDV for EF_j360_a10tcem triggered data. . . . . . . . . . 104  xi  List of Abbreviations and Symbols ALICE  A Large Ion Collider Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  ATLAS  A Toroidal LHC Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  BR  branching ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Conseil Européen pour la Recherche Nucléaire, now known as Orgnisation Eu-  CERN CMS  ropéenne pour la Recherche Nucléaire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Compact Muon Solenoid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  CR  control region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47  cτ  proper lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9  ∆R d0  ∆η 2 + ∆φ 2 between two objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 transverse impact parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25  DV  displaced vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38  E  energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16  ε  total efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  ECal  Electromagnetic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21  EF  Event Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 pseudorapidity, η = − ln tan θ2  η FCal HCal HH ID Ks  Forward Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21  Hadronic Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 heavy squark, heavy neutralino. This is the 1500 GeV q, ˜ 494 GeV χ10 sample. . 34 Inner Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 K-short particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 lepton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6  L  integrated luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13  LHC  Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  LHCb  Large Hadron Collider beauty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  LSP  lightest supersymmetric particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  mDV  4-momenta invariant mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42  MC  Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 xii  MCP  Muon Combined Performance group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65  MH  medium squark, heavy neutralino. This is the 700 GeV q, ˜ 494 GeV χ10 sample. 42  ML MS  medium squark, light neutralino. This is the 700 GeV q, ˜ 108 GeV χ10 sample. . . 42 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22  MSSM  Minimal Supersymmetric Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5  MuId  one of the two muon reconstruction algorithm in ATLAS . . . . . . . . . . . . . . . . . . . . 29  NDV  number of displaced vertices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83  Ntrk  track multiplicity, i.e., number of tracks in the vertex . . . . . . . . . . . . . . . . . . . . . . . . 47  NEWT  ATLAS NEWTracking framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27  φ  azimuthal angle in a spherical coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . 26  PDF  probability density function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58  pp  proton-proton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  pT pTlead  transverse momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 momentum of the leading track in the DV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72  PV  primary vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30  Q2 QCD  momentum transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33  QED  Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3  rDV  transverse distance from ATLAS origin (0, 0, 0) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39  RPC  Resistive Plate Chamber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 R-parity violating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8  RPV  RPVDispVrt the R-Parity Violating Displaced Vertex vertexing package . . . . . . . . . . . . . . . . 36 √ centre-of-mass energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 s σs  cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  SCT  Semiconductor Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18  SM SR  Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 signal region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47  SUSY  supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5  θ  polar angle in a spherical coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26  TRT  Transition Radiation Tracker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 underlying event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31  UE vs. y χ10 z0  versus or compared to . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 z rapidity, y = 12 E+p E−pz , where E and pz are the energy and z-component of the momentum of the particle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 neutralino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 longitudinal impact parameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26  xiii  zDV  z-coordinate of the displaced vertex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46  xiv  Acknowledgments Every snowboarding season in Cypress and every spring bloom of the sakura in UBC reminds me of their positive correlation with my time in ATLAS. It is time to stop, wrap up, and move on. Thanks to Canada for the wonderful Northern Lights and hospitality of the people, and a big appreciation to the conducive environment that the university and Hennings 207 has provided. It is my honour to be part of ATLAS. I wish to thank Colin Gay, for his ingenuity and physics explanations. A special gratitude for his patience at me climbing the learning curve (you know? It was hard.) and for the emacs shortcuts ! I stumbled on these people along the way — Alex Muir, Claus Horn and Gecse Zoltán. Thanks for giving me a stepping stone towards my research at CERN, for your trust and confidence in me, and for the laughs and RooFit that I need. My respect to Nick Barlow for his huge effort through our 2010 and 2011 data, laid with many hurdles. Although I do disagree with you sometimes, I can’t imagine anyone else who has done a better job than you. Thank you also for your selflessness, which I’ve sometimes forgotten what was taught in my school days, embarassingly. I wish to thank the rest of the ATLAS RPV Displaced Vertex people — Julian Bouffard, Frederic Brochu, Jesse Ernst, Adam Fischer, Vivek Jain, Hyeon Jin Kim, David Milstead, Abner Soffer and Nimrod Taiblum. I’ve learned tremendously. Lest I forget in years to come, let me mark this down — Hennings 207 has left a memory to me because of them and their laughs — Danny, Adam Cadien, Bill Mills, Sam King, Arash Khazraie, Oliver Stelzer-Chilton, Anadi Canepa, Simon Viel, Stephen Swedish, Nigel, Matthew Gignac, Kyle Boone and everyone else that I’ve mentioned. Thank you also to Reyhaneh Rezvani for showing me lots of Athena and C++ while at CERN. Friends, too long a list for here, but you know who you are — all the plays and travels that we had...great times. I needed them. I was fortunate. Xin Yi and Masrur, you were my PhD pacemakers. I needed them. It was a marathon. I am grateful again to the University of British Columbia for awarding me the Four Year Fellowship (4YF) during my PhD program. Apologies for any language abuse.  xv  To my parents, my brothers and my late grandmother, for the very first layer of foundation. Ucapan terima kasih dalam berbagai-bagai aspek dan minta maaf jikalau ada. 日日月月的寻找。 前进天地地平线 sehingga akhirnya aku sedar di mana penghujungnya. Akulah penghujungnya.  xvi  1  The Standard Model and Beyond In this Chapter, we shall give a review of the Standard Model of particle physics. Next, we shall explain some of its shortcomings, which will motivate supersymmetry as a solution to some of these problems. For more information on the Standard Model, see e.g. Refs. [1][2][3]. For more details on supersymmetry, see e.g. Refs. [4][5].  1.1  The Standard Model  The Standard Model (SM) is currently the model that codifies our understanding of all of particle physics — the basic constituents of matter and the three forces governing the interactions between the elementary particles. The three forces are the electromagnetic force, the strong force and the weak force. Figure 1.1 gives an overview of all the elementary particles in the SM. The matter particles, also known as the fermions, are spin- 12 particles. They can be categorized into three generations. Each generation is an exact copy of the others, except their masses differ. In each generation, there is an electrically charged lepton and an electrically neutral one (neutrino), and two types of quarks. Each matter particle (fermion) is associated with an antimatter particle (antifermion). For instance, the anti-electron, also known as the positron has a positive electrical charge, in contrast with the negatively charged electron. In fact, apart from the neutrinos, all fermions differ from their counterpart by the sign of their electrical charges. Currently, whether or not the neutrinos are their own antiparticles remains an open question [7]. An antiparticle is denoted with a bar ( ¯ ) and adopts the same letter symbol as its particle counterpart, e.g. u¯ which is the antiparticle of the u quark [1]. For the charged leptons, the electric charge sign is explicitly shown, instead of a bar. For example, the positron, which is the antiparticle of the electron, is represented by e+ . The interactions of fermions are mediated by gauge bosons with integer spins. The electromag1  Three generations of matter (fermions)  mass→ 2.4 MeV/c2 charge→ ⅔ spin→ ½  u  Quarks  III  1.27 GeV/c2  171.2 GeV/c2  0  ⅔ ½  ⅔ ½  0  up  name→  c  t  charm  top  photon  104 MeV/c2  4.2 GeV/c2  0  -⅓ ½  -⅓ ½  -⅓ ½  0  d  s  down  0  ½  γ  1  4.8 MeV/c2  <2.2 eV/c2  Leptons  II  b  g  1  strange  bottom  gluon  <0.17 MeV/c2  <15.5 MeV/c2  91.2 GeV/c2  0  0  0  ½  ½  1  νe νμ ντ  Z0  electron neutrino  muon neutrino  tau neutrino  Z boson  0.511 MeV/c2  105.7 MeV/c2  1.777 GeV/c2  80.4 GeV/c2  -1  -1  -1  ±1  ½  e  electron  ½  μ  ½  muon  τ  1  W±  W boson  tau  (a)  Gauge bosons  I  ? 0 0  Higgs (b)  Figure 1.1: From Reference [6]. The elementary particles in the Standard Model. The mass, electrical charge, spin, name and symbol of the particles are shown. The 3 generations of fermions are labelled I,II and III. Quarks in the same row with the up quark are also called up-type quarks, while those in the same row with the down quark are also called down-type quarks.  2  netic force is mediated by the massless photon, the strong force is mediated by the massless gluons and the weak force is mediated by the massive W ± and Z bosons. Only fermions possessing a non-zero charge associated to a force will feel its effect. All fermions except the neutrinos possess non-zero electrical charge, hence they can interact electromagnetically. The electromagnetic force can be explained using Quantum Electrodynamics (QED) [8]. The weak gauge bosons interact with all particles in the SM. The W ± bosons are the only bosons that can change one quark type into another. The unification of the electromagnetic and the weak interaction is described by the electroweak theory of Glashow-Salam-Weinberg based on an SU(2) × U(1) symmetry [9][10][11].  The four physical gauge bosons (W + ,W − , Z 0 and γ) are the consequences of the mixing between  the electroweak gauge fields (W1 ,W2 ,W3 and B) after the electroweak symmetry breaking. The relationships between the fields are [1] 1 √ Wµ1 ∓ iWµ2 , 2 = −Bµ sin θW +Wµ3 cos θW ,  Wµ± = Zµ0 Aµ  = Bµ cos θW +Wµ3 sin θW ,  (1.1) (1.2) (1.3)  where θW is the Weinberg angle and Aµ is the photon field. The weak interaction distinguishes between the left- and the right-handed fermions. The left-handed fermions ψL and the right-handed fermions ψR are defined as ψL = PL ψ =  1 1 − γ 5 ψ, 2  ψR = PR ψ =  1 1 + γ 5 ψ, 2  (1.4)  where PL and PR are the projection operators and γ 5 is related to the Dirac γ-matrices [1]. The W ± bosons only interact with the left-handed fermions but the Z boson interacts with both the left- and the right-handed fermions. The strong force is described by Quantum Chromodynamics [12]. Particles participating in the strong interaction possess colour charges. The quark (antiquarks) can interact strongly as each of them carries one colour (anticolour) charge. There are three colours: red, green and blue, and three anticolours: antired, antigreen and antiblue. The gluon carries one colour and one anticolour charge, hence gluons can interact among themselves via the strong force. Leptons, however do not possess a colour charge. Quarks cannot occur singly in nature, but will quickly hadronize and be confined into composite particles called hadrons. The narrow cone of hadrons produced from the hadronization is also known as a jet. Quark confinement is due to the self-interaction of gluons: as quark separation distance gets larger, more gluon pairs from the QCD sea are produced, which increases the strong force, since the coloured gluons tend to interact with one another. Two types of hadrons are observed in nature: mesons (bounded quark-antiquark pair), including pions and kaons, 3  Baryon Proton Neutron Lambda Meson Positive pion Positive kaon Neutral D  Symbol p n Λ0 Symbol π+ K+ D0  Quark content uud udd uds Quark content ud¯ us¯ cu¯  Table 1.1: Examples of mesons and baryons, their relevant symbols and quark contents. More examples of hadrons can be found in Ref. [14].  and (anti)baryons (three bounded (anti)quarks), including protons and neutrons. The proton is the only known stable hadron. Its lifetime has a lower bound of more than 1033 years [13]. Table 1.1 lists some examples of hadrons and their quark content. The Higgs boson, with its unknown physical mass, is the last remaining particle in the SM yet to be found. Through the Higgs mechanism [1][2], the Higgs field can generate masses to the weak bosons and the fermions. Without the Higgs, the fermions are predicted to be massless in the theory, since an explicit mass term, of the form: m (ψ¯ L ψR + ψ¯ R ψL ), where m is the fermion mass, is forbidden, as the left-handed fermion ψL and the right-handed fermion ψR carry different quantum charges. The coupling of the Higgs field φ to the fermions via an interaction term: y (ψ¯ L φ ψR + ψ¯ R φ ψL ), with y as the coupling strength, offers a way out when φ acquires a non-zero vacuum expectation value v after the electroweak symmetry breaking. The interaction term then generates a mass term of the form yv (ψ¯ L ψR + ψ¯ R ψL ), with the fermion mass proportional to the coupling strength y and v. Similarly, the Higgs coupling to the bosons Bµ via a term of the form g2 φ 2 Bµ Bµ , with g as the coupling strength, generates a boson mass term of the form g2 v2 Bµ Bµ after the electroweak symmetry breaking. The recent discovery of a new Higgs-like particle [15] with a physical mass of about 125 GeV at the Large Hadron Collider (LHC) is consistent with a light SM Higgs boson. The new particle has been observed in the two photons, ZZ and W +W − decay channels [16][17]. More data is needed for the observation of other decay channels, for example, into two tau leptons. The measurements of the relative decay rates in each decay channel will be crucial in the next stage of the experiments at the LHC, since the SM predicts precisely their rates given a specific Higgs mass [18]. However, a light Higgs mass points to a fine-tuning problem [19]. This is because to produce the observed physical mass of a light Higgs mH,physical , a precise cancellation is needed between two uncorrelated terms: the bare mass of the Higgs mH,bare , which is a fundamental parameter in the theory, and the quantum loop corrections from other SM particles, which is proportional to Λ2 ,  4  where Λ is the energy cut-off scale. Λ is taken to be the Planck scale (1019 GeV) if the SM is a valid theory up to that scale. Their relationship is m2H,physical = m2H,bare +  ∑  δ m2H ,  (1.5)  SM particles  with  ∑  δ m2H as the sum of all SM particles’ loop corrections. The loop correction can  SM particles  involve, for example the top quark t as shown in Figure 1.2. The top quark loop contains an integral  t¯ H  H yt  yt  t Figure 1.2: The Higgs bare mass receives a top loop correction. The integral of the loop is divergent and is proportional to the square of the energy cut-off scale.  of the following form [20][21], which contributes to the square of the Higgs mass: δ m2H = −2yt2  Λ  d4k  k2 + mt2 yt2 2 Λ + ..., = − 8π 2 (2π)4 (k2 − mt2 )2  (1.6)  with mt as the top quark mass, yt as the Higgs-top-top vertex coupling and k as the momentum in the loop. Since k can take very high values up to Λ, mt can be ignored and the integration is expected to contain a negative-signed quadratically divergent term with a dependency on Λ2 . The precise cancellation of 32 orders of magnitude between the square of the bare mass and the loop correction term like the one from the top loop to achieve an order of 1 TeV physical mass for the Higgs boson, suggests that the Standard Model is merely part of a deeper theory of Nature. Supersymmetry is a viable candidate for the deeper theory, because it can solve the fine-tuning problem.  1.2  Supersymmetry and R-Parity  Supersymmetry (SUSY) [4][5] is a boson-fermion symmetry. In SUSY, each SM particle is associated with a superpartner: a SM fermion has a boson superpartner and a SM boson has a fermion superpartner. Each SM particle and its superpartner has identical quantum numbers except that they differ in spin by 12 . The minimal number of supersymmetric partners needed for the SM to be supersymmetric gives rise to the Minimal Supersymmetric Standard Model (MSSM). Its particle  5  Standard Model particles and fields Symbol q ν g W± H− H+ B W3 H10 H20 H30  Name Quark Lepton Neutrino Gluon W boson Higgs boson Higgs boson B boson W 3 boson Higgs boson Higgs boson Higgs boson  Spin 1 2 1 2 1 2  1 1 0 0 1 1 0 0 0  Supersymmetric partners Interaction eigenstates Symbol Name q Squark Slepton ν Sneutrino g Gluino  W± Wino  H1− Higgsino  H2+ Higgsino  B Bino     W3 Wino  H10 H20  Higgsino Higgsino        Mass eigenstates Symbol Name q Squark Slepton ν Sneutrino g Gluino  Spin 0 0 0  ± χ1,2  Chargino  1 2  0 χ1,2,3,4  Neutralino  1 2  1 2  Table 1.2: SUSY particle content [22]. Listed are the SM particles and their corresponding superpartners as the interaction eigenstates (before electroweak symmetry breaking) and as the mass eigenstates (after electroweak symmetry breaking). In SUSY, there are 5 physical Higgs bosons in contrast with the single Higgs in the non-supersymmetric SM. The charged Higgsinos and the winos mix to form four charginos after symmetry breaking, while the neutral Higgsinos, wino and bino mix to form four neutralinos.  content is given in Table 1.2. After the electroweak symmetry breaking, the neutral bino, wino and Higgsinos mix to form four physical particles or mass eigenstates, known as the neutralinos, denoted by χi0 , with i = 1, 2, 3, 4. Furthermore, the charged Higgsinos and the winos also mix to form two mass eigenstates, known as the charginos, denoted by χi± , with i = 1, 2. A SUSY particle is denoted with a tilde (  ) and adopts the same letter symbol as its SM counterpart. For example,  the top quark t superpartner is given the symbol t. In terms of the nomenclature, the superpartner of a SM fermion receives an s- prefix followed by the name of its SM counterpart, e.g. slepton, smuon and squark. On the other hand, the superpartner of a SM boson receives an -ino suffix preceded by the name of its SM counterpart, e.g. zino, wino and photino. To date, no SUSY particles have been discovered. If they exist, these particles should be more massive than their SM counterparts. In order to achieve a mass difference between the SM particles and the superpartners, SUSY must be broken. We refer the readers to the discussion on SUSY breaking models found elsewhere [23][24]. With supersymmetry, the Higgs boson bare mass not only receives a contribution from a SM particle loop correction but also their superpartners (see Figure 1.3). In the case of the top loop in Figure 1.2, its superpartner, known as stop, gives a Higgs mass loop correction containing a positive 6  t˜  t¯ H yt  −1  H  +1  yt  H  t (a) top loop  yt∼  H  (b) stop loop  Figure 1.3: In supersymmetry, the Higgs bare mass receives a top and its superpartner, stop loop corrections. The ontribution of the integral from these loops are divergent and are proportional to the square of the energy cut-off scale. They differ in their relative sign. While the top loop has a negative sign, the stop loop has a positive sign. yt and yt are the couplings of the top and stop to the Higgs respectively.  quadratic divergence term [21]: δ m2H = +  yt Λ2 + ... 16π 2  (1.7)  where mt is the mass of the stop and yt is the coupling of the stop to the Higgs. The quadratic divergence in the loop contribution from the top can be cancelled by two scalar stops if yt2 = yt [25]. In general, a fermion loop gives a negative quadratic divergence while a boson loop gives a positive quadratic divergence. Since each SM particle is paired with a superpartner, all quadratically divergent SM particle loop corrections are cancelled by the loops of their respective superpartners, which solves the SM Higgs fine-tuning problem as described in Section 1.1. In supersymmetry, each particle is associated with a multiplicative quantum number known as R-parity [26]: R p = (−1)3(B−L)+2s ,  (1.8)  with spin s, baryon number B and lepton number L. B is a quantum number assigned to all the particles: + 13 for a quark, − 13 for an antiquark and 0 for all other particles. The lepton number for all the particles are: +1 for a lepton, −1 for an antilepton and 0 for all other particles. All SM particles  have R p = +1 but their superpartners have R p = −1. This implies that if R p is conserved in an  interaction produced in a collider experiment, SUSY particles are always produced in pairs. Their decays will eventually produce two stable lightest supersymmetric particle (LSP), which cannot decay any further since decays to any other SUSY particles are kinematically forbidden and decays to SM particles are also forbidden due to the conservation of R-parity. The stable LSP is a dark matter candidate if it is neutral and weakly interacting such as the neutralino χ10 [27]. Dark matter constitutes 25% of the energy-matter in the Universe [22] and could potentially be some new non-  7  SM particles that have yet to be identified in a collider. If R p is not conserved, the neutralino can decay through the R-parity violating (RPV) λi jk , λi jk or λi jk terms as shown in Figure 1.4, where the indices i, j, k = 1, 2, 3 refers to the fermion generations. If RPV is allowed, the dark matter candidate must originate from other sectors in an extended version of the MSSM [28]. Also, in an RPV scenario, the proton can decay rapidly, for  νi  qj  νi  j  j  λijk  i  λijk  λijk k  k  qk  i  qj  νi  qj  qj  νi λijk  λijk  λijk  qk  qk  qk  qj qi λijk  qk Figure 1.4: Possible RPV diagrams with a SUSY particle ( ,ν or q) decaying into Standard Model particles via an RPV λ , λ or λ term. The indices i, j, k = 1, 2, 3 refers to the fermion generations. Each of these diagrams constitute an interaction vertex. For RPV vertices, the product of R p of the particles involved in each vertex is always equal to -1. Thus, these vertices are forbidden in an R-parity conserving scenario, where the vertices involve two SUSY particles and one SM particle, which yields a product of R p to be +1.  instance p → e+ π 0 , where π 0 is the neutral pion, via the λ and λ RPV terms. This is shown in Figure 1.5. The decay width can be estimated as [21] Γ p → e+ π 0 ∼  | λ11k λ11k |2 5 mproton , m4  (1.9)  dk  where mproton is the proton mass and md is the squark mass. Insisting on R-parity conservation would solve the problem of rapid proton decay. Another alternative is to replace the conservation of R-parity with the conservation of baryon triality [29], which forbids the RPV λ term and hence, rapid proton decay will not occur. In fact, this means that the strong constraint on the couplings 8  u  u  u  u ¯ λ11k  p  π0  λ11k ¯q k  e+  d  Figure 1.5: A diagram of a proton decaying to a pion (π 0 ) and a positron (e+ ) via the R-parity violating λ11k and λ11k terms, mediated by a virtual squark. k is the fermion generation index.  λ λ from the experimental results on proton decays [13] can be evaded. As such, the possibility of an R-parity violating scenario as a viable Beyond Standard Model candidate cannot be ruled out. From low energy experiment results [30][31][32], the current bound for the R-parity violating coupling λ21k is less than 0.06 with a superpartner mass of 100 GeV. Our search for the χ10 → µud  decay via a λ211 coupling in this work, where u and d are the up and down quarks respectively,  complements these results by probing the coupling in the range 10−6 < λ211 < 10−4 . A diagram of such a decay is shown in Figure 1.6.  u χ01  µ∗  λ211  d¯  µ Figure 1.6: A diagram of the decay χ10 → µud via a λ211 coupling, mediated by a virtual smuon (µ ∗ ). u and d¯ are the up and anti-down quarks respectively. The neutralino-smuon-muon coupling is an interaction from the R-parity conserving sector of SUSY.  The χ10 → µud decay has a lifetime given by [33] cτ ∼  mµ 4 λ  2 5 211 mχ10  9  ,  (1.10)  Experiment CDF D0/ CMS ATLAS  this work  Decay type X → bb¯ X → γ + invisible X → bb¯ X → ¯b X→ ¯ X → γ + invisible X → bb¯ X → µud  Mass [ GeV] 20 – 65 70 – 160 10 – 40 70 – 200 20 – 400 140 – 250 20 and 40 108 and 494  Lifetime [mm] < 50 <9 25 – 100 < 104 < 104 20 – 250 102 – 103 < 103  Publication [34] [35] [36] [37] [38] [39] [40] [41]  Table 1.3: Long-lived particle searches from previous experiments and our work. Here, we list the decay type, the mass range and the corresponding lifetime from each study. We have used a general symbol X to represent the various neutral long-lived particles used in each study.  where mχ 0 and mµ are the masses of the neutralino and the virtual slepton. In our chosen λ211 1  coupling range and neutralino masses, the χ10 can be long-lived. This implies that it can decay some distance away from its production source. Such a decay can be observed as a displaced vertex in an experiment, where particles, in this case the muon and hadrons from the hadronization of the quarks are seen to be emitted from a common point in space called a vertex, which is also the decay position of the χ10 . In this work, we aim to search for long-lived neutralinos χ10 → µud decay  channel via displaced vertices formed by a muon and hadrons produced from the hadronizations of the quarks. Figure 1.7 shows a diagram of the production of the neutralinos from squarks, and another diagram showing what can be observed experimentally. We wish to point out that our long-lived χ10 → µud search has not been done previously at the  Large Hadron Collider nor at any other experiment, as far as we know. In Table 1.3, we compare our search with previous experiments. Our search will focus on a neutralino decay length of less than 103 mm for a mass range of 100 - 500 GeV. We expect the decay products to have momenta of  30 GeV (contribution from the neutralino mass to the decay products). To reconstruct the signal displaced vertex, we have developed an algorithm with a high vertex  reconstruction efficiency and vertex position resolution, while minimising the number of fake vertices from combination of unrelated tracks in an event (more details in Section 4.1 and 4.2). To discriminate between signal and backgrounds, we have used several variables including the invariant mass and the number of tracks in the displaced vertex, with their cut values optimised with the significance (more details in Section 4.4).  10  u µ  q q  χ01  q  µ∗  d  µ∗  u  g χ01 q  q q  µ d  (a) muon hadrons from the u jet  displaced vertex from a neutralino decay  hadrons from a quark jet  hadrons from the d jet  flight direction of a neutralino  squark production vertex hadrons from a quark jet  displaced vertex from another neutralino decay  (b)  Figure 1.7: (a) The production of neutralinos, with each of them decaying to µud. (b) Displaced vertices from the neutralino decays as observed experimentally. Each displaced vertex is formed from a muon and charged hadrons produced from the hadronizations of the u and d quarks.  11  2  The ATLAS Experiment 2.1  The Large Hadron Collider  Initiated at the Lausanne Workshop in 1984, the Large Hadron Collider (LHC) [42] is a proton√ proton (pp) collider, designed for a centre-of-mass energy s = 14 TeV, placed at ∼ 100 m below the surface of CERN with a circumference of about 27 km, at the Franco-Swiss border near Genève  (see Figure 2.1). On 20 November 2009, the LHC started to collide proton beams at a centre-of√ mass energy s = 900 GeV. In 2010 and 2011, the LHC had produced pp collisions at √ s = 7 TeV. In 2012, the proton beam energy was raised to 4 TeV from 3.5 TeV, to produce proton√ proton collisions at s = 8 TeV. There are four main detectors placed around the LHC ring: ATLAS [43], ALICE [44], CMS [45] and LHCb [46]. ATLAS and CMS are multi-purpose experiments, with design geared towards the search for the Higgs boson, as well as for other new physics beyond the Standard Model. ALICE is dedicated to studying the nature of the quark-gluon plasma while LHCb is designed to study bphysics. This work has been performed with the ATLAS experiment. At the LHC, the proton beams are collided in the form of bunches with each bunch containing about 1011 protons, at a frequency of 20 MHz, i.e. 20 million collision events per second. Figure 2.2 shows the total integrated luminosity for 2010, 2011 and 2012 delivered by the LHC and recorded by ATLAS. The total integrated luminosity L is a parameter which is needed in the calculation of a cross section σs of the production of a signal, since they are related by σs =  Nobs − Nbkg , εL  (2.1)  where Nobs is the number of observed events in the data, Nbkg is the number of background events expected, ε is the total signal efficiency and L is the total integrated luminosity. Cross sections are  12  commonly expressed in units of barns (1 b = 10−24 cm2 ). The total integrated luminosity is the integral over time of the instantaneous luminosity L : L = L =  L dt, and L can be expressed as [42]  Nb2 nb frev γF , 4πεn β ∗  (2.2)  where: • Nb is the number of protons per bunch; • nb is the number of bunches per beam; • frev is the revolution frequency of the beam; • β ∗ is the distance from the proton-proton interaction point (focus point) to the point where the beam width is twice as wide as the focus point;  • γ is the relativistic gamma factor of the protons; • εn is the beam normalized transverse emittance with the transverse emittance ε = 1γ εn being the spatial and momentum phase space area that contains 95% of the protons in a beam;  • F = √1  1+φ 2  , where the Piwinski angle, φ =  θ c σz 2σ ∗  with θc as the beam-crossing angle (the  beams do not collide head-on), σz as the RMS beam size in the z-direction and σ ∗ as the  RMS beam size in the transverse direction. In 2011, the instantaneous luminosity at its peak was 3.6 ×1033 cm−2 s−1 = 3.6 nb−1 s−1 . In Table  2.1, we give a summary of the LHC proton parameters.  Proton energy [TeV] Number of protons per bunch Nb Number of bunches nb pp crossing frequency [MHz] Peak instantaneous luminosity L [cm−2 s−1 ] Beam transverse size σ ∗ [µm] Bunch length σz [cm] Beta function at the interaction point β ∗ [m] Normalized transverse emittance εn [µm] Crossing angle θc [µrad]  Design 7 1011 2808 40 1.0 × 1034 16 8 0.55 3.5 280  2011 3.5 1011 1380 20 3.6 × 1033 26 10 1.0 2.4 240  2012 4 1011 1380 20 5.4 × 1033 19 10 0.6 2.4 290  Table 2.1: The LHC proton beam parameters and at the ATLAS collision point [49].  13  LHC PROJECT  Point 5  P M4 5  P X5 6 P M5 4  TX4 6 UJ 4 6  UX4 5 UJ 4 4  R A4 3  UJ 4 3  R Z3 3  UA4 3  UJ 4 7  UJ 5 3  RE 48 RE 52  UP 5 3  P M5 6  R Z5 4  Point 6  UJ 5 6 UL 54  RR 53  UJ 5 7 UXC5 5  US 4 5  US C5 5  UW 4 5  RE 42  PZ 33  R A4 7  UA4 7  UL4 6 UL4 4  P o in t 3 . 3  UNDERGROUND WORKS  P X4 6  P Z4 5  Point 4  TU5 6  UJ 5 6 1  TD 62  P M6 5  R A6 3 UJ 63  TX6 4  UA6 3 UJ 6 4  UX6 5 UJ 6 6  UL6 4  RE 32  UW 6 5  US 6 5  P M3 2 TZ3 2  P Z6 5  UJ 62  RE 58 RE 62  UJ 3 3  UJ 3 2  P X6 4  UP 62  UL5 6  CMS  RE 38  UD 62  RR 57  UL6 6 UA6 7 UJ 6 7  R A6 7  UJ 6 8 TD 6 8  P o in t 3 . 2  UD 6 8  N  UP 68 RE 68  RE 28  Point 7 UJ 2 7  Point 2  UA2 7 P GC2 UL 26  R A2 7  UP 2 5  P M2 5 US 2 5  UJ 2 6 P X2 4  UJ 7 6  Point 8  SPS UA2 3 UJ 23  UJ 2 4  RR7 3  TZ7 6 UW 2 5  UL 24  UX2 5  ALICE  RE 72  P M7 6  P o in t 1 . 8  R A2 3 RE 22  RH2 3  PM 18  RE 18  UJ 2 2  PMI 2  UL1 4 UJ 1 4  TI 1 8  UJ 1 6  UX1 5 US A1 5  P Z8 5 UL 84 UA8 7 TI 8  US 1 5 UJ 1 3 RE 12  RR1 3  TI 1 2  UJ 12 R T1 2  ATLAS  UJ 88  UJ 8 7  RR7 7  UA 83 UJ 8 2 UJ 83  US 85  TJ 8  P X1 4  RT 18  P X8 4  LS S 4  P X1 5  R R 1 7 UJ 1 7 UL1 6  TI 2  UW 8 5  PGC 8  P M1 5 P X1 6  UJ 1 8  RE 78 RE 82  PM 85  TT 40  Point 1  UL 86  R A8 3 UJ 8 4  RE 88  RH 87  RA 87  UJ 86  TX8 4 UX 85  LHC 'B'  Existing Structures LHC Project Structures  ST-CE/JLB-hlm 18/04/2003  Figure 2.1: The Large Hadron Collider and its 4 main experiments [47][48]. Note, the Figures are not in the same geographical alignment. As a guide, CMS at Point 5 in the bottom Figure corresponds to the right-most Point in the top Figure. ATLAS at Point 1 lies near the Franco-Swiss border (dotted line) in the top Figure. LHCb at Point 8 is the nearest to the large white structure in the foreground, i.e. the Genève International Airport.  14  50  ATLAS Online Luminosity  Total Integrated Luminosity [fb -1]  Total Integrated Luminosity [pb-1]  60  s = 7 TeV  LHC Delivered ATLAS Recorded  40  Total Delivered: 48.1 pb-1 Total Recorded: 45.0 pb-1  30 20 10 0 24/03  19/05  14/07  7  ATLAS Online Luminosity  6 5 4  ATLAS Recorded Total Delivered: 5.61 fb-1 Total Recorded: 5.25 fb-1  3 2 1 0 28/02  08/09 03/11 Day in 2010  30/04  (a) 2010 Total Integrated Luminosity [fb -1]  s = 7 TeV  LHC Delivered  30/06  30/08 31/10 Day in 2011  (b) 2011 25 20 15  ATLAS Online Luminosity  s = 8 TeV  LHC Delivered ATLAS Recorded Total Delivered: 18.6 fb-1 Total Recorded: 17.4 fb-1  10 5 0 27/03 27/04 28/05 28/06 29/07 29/08 29/09 30/10 Day in 2012  (c) 2012  Figure 2.2: The total integrated luminosity delivered by the LHC and recorded by ATLAS in (a) 2010, (b) 2011 and (c) 2012.  15  2.2  Conventions in ATLAS  ATLAS uses a Cartesian right-handed coordinate system, with nominal collision point at the origin (0, 0, 0). The x-axis points to the centre of the LHC ring, the y-axis points towards the Earth surface and the z-axis points along the anti-clockwise beam direction. The collisions of the protons are contained in a 30 mm radius cylindrical beam pipe, with its central axis being the z-axis of the ATLAS coordinate system itself. r is defined to be the distance from the z-axis. φ is the azimuthal angle (the angle in the x − y plane measured with respect to the x-axis) and θ is the polar angle. The pseudorapidity is defined to be  η = − ln tan  θ 2  ,  (2.3)  and is often used instead of θ to express the polar coordinate of a physics object or a subdetector. The x − y plane or equivalently, the r − φ plane is also called the transverse plane. The transverse  momentum of a particle, denoted as pT , is the momentum component of the particle in the transverse plane. The energy of a particle is denoted as E. The variable ∆R is defined to be the Euclidean  spatial distance between two physics objects in the η − φ space: ∆R = ∆η ⊕ ∆φ , where a ⊕ b =  2.3  (2.4)  √ a2 + b2 .  Subsystems : Overview  ATLAS is comprised of three main subsystems — the Inner Detector, the Calorimeter and the Muon Spectrometer. We show an overview of ATLAS and an x-y plane view in Figure 2.3, with a summary of the propagation of various particles through the detector.  16  Figure 2.3: Top: From Ref. [43]. The ATLAS detector cut-away view. Bottom: Summary of the various particles and their propagation through the detector, viewed from part of the x − y plane.  17  2.4  Inner Detector  The Inner Detector (ID) [50] is used to measure the momentum of charged particles to as low as a transverse momentum of 250 MeV. The ID, which covers a pseudorapitidy range |η| < 2.5, is 2.1  m in diameter, 6.2 m in length and is immersed in a 2 T solenoidal magnetic field from an NbTi superconductor to provide magnetic deflection in the r − φ plane. The barrel (end-cap) section of  the ID covers a pseudorapidity range |η| < 1.1 (1.1 < |η| <2.5). The ID is comprised of three  subdetectors (see Figure 2.4): the Pixel subdetector, the Semiconductor Tracker (SCT) and the  Transition Radiation Tracker (TRT). Figure 2.5 shows the η coordinate on the positive z-axis of the ID. The momentum resolution is measured with the ID to be  σ pT pT  = 0.05% · pT ⊕ 1%. This is an  important parameter as it affects the mass resolution of the displaced vertex, since  σm2 m2  ∝  σ pT pT ,  where  m is the invariant mass of the vertex. The Pixel subdetector has 80.4 million silicon sensors, grouped into 3 layers in both the barrel and the two end-caps, to provide on average 3 hits per track. The three layers in the barrel of the Pixel subdetector are located at a radial distance of 50.5 mm, 88.5 mm and 122.5 mm, and the three disks for each of the two end-caps are positioned at a distance of 495 mm, 580 mm and 650 mm from the detector centre. The Pixel subdetector is the innermost subdetector of ATLAS with a resolution of 10 µm in r − φ for both the barrel and end-caps, a resolution of 115 µm in z for  the barrel, and a resolution of 115 µm in r for the end-caps. The innermost layer is of importance  as the resolution of the transverse impact parameter is proportional to the resolution of this layer. More details on the impact parameter can be found in Section 3.1. The Pixel subdetector has a noise rate of 1 in 107 hits, where the rate is defined as the number of recorded Pixel hits in a random non-collision event, which can be due to noise in the electronics, divided by the number of Pixel sensors. In one pp collision event, the average occupancy fraction is 1%, where the rate here is defined as the number of Pixel hits in a collision event divided by the number of Pixel sensors. Located after the Pixel subdetector, the SCT subdetector consists of 6.3 million silicon sensors, where each of them are two single-sided back-to-back silicon strips. The sensitive layers of the SCT barrel are located at radii 300 mm, 371 mm, 443 mm and 514 mm, while the SCT end-caps contain nine disks each, which are placed at 839 < |z| < 2740 mm. In total, the SCT provides up to  8 hits per track. The SCT has a resolution of 17 µm in r − φ for both the barrel and the end-caps, and a resolution of 580 µm in the the r-direction in the barrel and in the z-direction in the end-caps. The noise rate in the SCT is < 5 × 10−4 .  Located after the SCT, the TRT is comprised of 3.2 × 105 proportional drift tubes, also known  as straws. Each straw has a diameter of 4 mm and contains a gold-plated tungsten anode wire in the centre, surrounded by a gas mixture of 70% Xe + 27% CO2 + 3% O2 . The TRT barrel region covers a radial distance of 560 < r < 1100 mm with 73 straw planes, while the end-caps are located  18  Figure 2.4: Top: Inner Detector end-cap. Bottom: Inner Detector barrel. The radial position R of each layer of the Pixel, SCT and TRT subdetectors are shown. The beam pipe is shown with its centre at R = 0 mm.  at 850 < |z| < 2710 mm with 160 straw planes, capable of giving on average 30 TRT hits per track.  The TRT has an r − φ resolution of 130 µm. The TRT straws are interspersed with polypropylene-  polyethylene as the transition radiation materials for electron identification capabilities [51]. This transition radiation is produced when a charged particle traverses between two materials with different dielectric constants.  19  ID end-plate  3512  Cryostat Solenoid coil PPF1  R1150  712  Radius(mm)  R1066  848  PPB1  2710 R1004  TRT(end-cap)  TRT(barrel) 1  R563 R514 R443 R371 R299  R122.5 R88.5 R50.5 0  2  3  4  5  6  7  8  9 10 11 12  1  2  3  Cryostat 4  5  6  7  8  R644 R560  SCT(barrel)  SCT (end-cap)  R408  R438.8  Pixel support tube  R337.6  Pixel PP1  R275  R229  Beam-pipe  Pixel  R34.3 1299.9 934 749 400.5 580 1399.7 495 650 853.8 1091.5  0  1771.4  2115.2  2505  2720.2  z(mm)  Envelopes Pixel  Pixel  R122.5 R88.5  R149.6 R88.8  R50.5  SCT barrel  255<R<549mm |Z|<805mm  SCT end-cap  251<R<610mm 810<|Z|<2797mm  TRT barrel  554<R<1082mm |Z|<780mm  TRT end-cap  617<R<1106mm 827<|Z|<2744mm  0 0  400.5  495  580 650  45.5<R<242mm |Z|<3092mm  Figure 2.5: η coordinate on the positive z-axis of the ATLAS Inner Detector. The radial positions of the subdetector layers are denoted as RX, where X is the radial distance in units of mm.  20  2.5  Calorimeter  The calorimeter [52] is used to measure the energy of the incoming particles. It consists of three subsystems (see Figure 2.6): Electromagnetic Calorimeter (ECal), Hadronic Calorimeter (HCal) and the Forward Calorimeter (FCal).  Figure 2.6: From Ref. [43]. The ATLAS calorimeter system. The electromagnetic calorimeter is a lead/liquid argon (LAr) sampling calorimeter, and is placed nearer to the collision point than the hadronic calorimeter (Tile and HEC). The forward calorimeter labeled as FCal, is capable of performing electromagnetic and hadronic measurements.  The ECal, with a radius of 1.4 – 2 m from the beam line, is used to measure the energy of the photons and electrons. It is a lead/liquid argon sampling calorimeter with the lead stacks making an accordion-shaped geometry for a full φ coverage. The total thickness of the ECal is ∼ 22 − 33  radiation lengths (X0 ) in the barrel and > 24 X0 in the end-caps. The barrel of ECal covers |η| < 1.475 and the two end-caps cover 1.375 < |η| < 3.2. The energy resolution is measured to be σE E  =  10% √ E  ⊕ 0.7%.  The HCal is used to measure the energy of the hadrons. This subdetector starts at 2 m from the beam line, extending to 4 m and is comprised of two subdetectors — plastic scintillator tile calorimeter (Tile) with steel absorber for |η| < 1.7 and copper/liquid argon hadronic end-cap  calorimeter (HEC) for 1.5 < |η| < 3.2. The HCal provides ∼ 10 nuclear interaction lengths of  material1 . The energy resolution is measured to be  σE E  =  50% √ E  ⊕ 3%.  The FCal covers 3.1 < |η| < 4.9 region and is comprised of three 45 cm thick modules. One of 1 The  ECal provides another ∼ 2 interaction lengths of material.  21  the modules is a copper/liquid argon type for electromagnetic measurements, while the other two are tungsten/liquid argon type for hadronic measurements. Liquid Ar is used for its capability to cope with the high radiation. The energy resolution is measured to be  2.6  σE E  =  100% √ E  ⊕ 10%.  Muon Spectrometer  The Muon Spectrometer (MS) [53] is designed to achieve a resolution of 10% for a 1 TeV pT muon, better than 4% for 10 < pT < 500 GeV and can measure muons with pT as low as 3 GeV. The resolution can be of importance in a trigger when deciding if some muon passes the trigger threshold. The 4 subdetectors (see Figure 2.7) of the MS cover a region of |η| < 2.7 and are  surrounded by an air-core toroid magnetic system (to minimize multiple scattering), providing 0.2 - 2.5 T (0.2 - 3.5 T) in the barrel (end-caps) in the r − η plane.  Figure 2.7: From Ref. [43]. The Muon Spectrometer (MS) and the air-core toroid magnetic system. The MS is comprised of four systems: the Monitored Drift Tubes (MDT) and the Resistive Plate Chambers (RPC) for the barrel region, and the Cathode Strip Chambers (CSC) and the Thin Gap Chambers (TGC) for the end-cap region.  Two of the subdetectors are employed for precision momentum measurement —- Monitored Drift Tubes (MDT) for the barrel and end-caps (|η| < 2.7) and Cathode Strip Chambers (CSC) for the end-caps (2.0 < |η| < 2.7). The other two subdetectors are also employed for momentum mea-  surement but more importantly for the Level 1 trigger (see Secion 2.7)— Resistive Plate Chambers 22  (RPC) in the barrel (|η| < 1.05) and Thin Gap Chambers (TGC) in the end-caps (1.05 < |η| < 2.7,  but |η| < 2.4 for triggering). Details on trigger can be found in Section 2.7. The coverage of the  RPC is about 80%, and as such, determines the maximum muon trigger efficiency in the barrel region. The RPC coverage is not complete, as the barrel region has to accommodate the services for the calorimeters, detector feet and magnet support. The MDT consists of 30 mm diameter aluminium drift tubes of length 1 – 6 m, each filled with 93/7 Ar/CO2 gas mixture with a gold-plated tungsten-rhenium anode wire in the centre. The CSC is a multiwire proportional chamber with a 5 mm gas gap between two cathode strips and a set of anode wires in the middle, with a 2.5 mm separation between the anodes. The CSC uses an 80/20 Ar/CO2 gas mixture. The RPC uses a 94.7/5/0.3 C2 H2 F4 /iso-C4 H10 /SF6 gas mixture with a gas gap of 2 mm between two bakelite plates, with one acting as an anode and the other as a cathode. The TGC is a multiwire proportional chamber with a 2 mm anode-anode distance, 1.4 mm anode-cathode distance and a 2.8 mm cathode-cathode distance, with a 55/45 CO2 /C5 H12 gas mixture. The MS chamber positions are aligned via an optical system to monitor for any displacements by the magnetic field and temperature changes. The system can achieve a 10 µm precision of position measurement. The region where a muon track can be missed corresponds to |η| < 0.08,  where there is a gap in the spectrometer for power cable services to the ATLAS detector. Another efficiency drop is at |η| ∼ 1.2 for cables and cooling system installation. At φ ≈ −1.2 rad and  φ ≈ −1.9 rad, the support feet of the whole ATLAS detector is installed, which also lowers the muon efficiency in this area.  2.7  Trigger and Data Acquisition  The protons are collided at a rate of 20 MHz. Recording 20 million events per second is not sustainable since each collision event on average requires ∼ 1.5 MB of disk space for storage.  ATLAS has aimed to store only 400 events from the 20 million events per second for offline physics studies, by introducing a 3-level trigger system decision maker [43] to sift out interesting events containing high pT physics objects: • Level 1 (L1) — 2.5 µs decision time per event. L1 uses the calorimeters, RPC and TGC to  decide on the possibilities of any high pT jets, τ leptons, missing energy, photons, electrons  or muons in an event. Any regions in the detector identified to contain these objects are called Regions of Interest (RoI). For a muon trigger, the detector hits in the RoI are used to compute the deviation between each of them with an infinite momentum trajectory. A Look-Up Table is then used to obtained the pT of the muon in the RoI corresponding to the computed deviations [54]. Events are passed to Level 2 at a rate of 75 kHz. 23  • Level 2 (L2) — 40 ms decision time per event. RoI information from L1 is examined in detail with full granularity. At L2, the Inner Detector (ID) information can be used to reject, for example, events triggered by fake muons. For muon triggers at L2, the muFast algorithm [55][56] reconstructs muon candidates in the Muon Spectrometer (MS). The muComb algorithm [55][57] then performs a combination from the muFast output with tracks from the ID to obtain a full ID-MS combined muon track. Events are passed to the Event Filter level at a rate of 3.5 kHz. • Event Filter (EF) — a software-based decision maker with a 4 s decision time per event. Events are recorded at a rate of 400 Hz. The EF can examine an event based on the entire detector input. If an event passes this level, it will be recorded for further physics studies. Various triggers are employed in ATLAS to keep the data recording rate under control. Data from events that pass L1, L2 and the EF of any trigger in ATLAS are distributed to a worldwide LHC Computing Grid [58]. The data are kept in different data streams corresponding to the chain of triggers it passed. Three main data streams are of interest to us — Muons, Egamma and JetTauEtmiss. The naming is meant to indicate the relevant triggered physics objects. In this work, we have used the EF_mu40_MSonly_barrel and EF_mu40_MSonly_barrel_medium triggers. In order for them to fire, both these triggers require the event to contain a muon with a pT > 40 GeV in the barrel of the Muon Spectrometer (| η |< 1.07) which is identified at the EF  level. These two triggers differ at L1, where the EF_mu40_MSonly_barrel will fire if the muon has  pT > 10 GeV based on the Look-Up Table, while the the other trigger will fire if the pT > 11 GeV. Events passing MSonly triggers at L1 are not processed at L2, but are processed directly at the EF level instead. This can provide a higher efficiency for muons produced from long-lived particles decaying at a distance from the pp interaction point, since at L2, the muComb algorithm assumes the muon originates near the nominal pp interaction point, which is equivalent to wrongly assuming an imaginary track hit at the interaction point, thus reconstructing a bad quality muon track that would be rejected as a fake muon.  24  3  Physics objects In this Chapter, we shall describe the identifications of various physics objects, including tracks, muons, jets and primary vertices. More details on their reconstructions can be found in [59][60][61][62].  3.1 3.1.1  Track Parameters  The trajectories of charged particles are reconstructed as tracks in the Inner Detector. Due to the magnetic field direction in the Inner Detector to be parallel to the z-axis, the charged particle experiences a magnetic force in the x − y plane, hence constantly changing the momentum direction in  this plane. However, the z-component of its momentum is not affected by the magnetic field. The  charged particle is said to be following a helix trajectory. Details on the parameterization of the helical track can be found in Ref. [63]. Figure 3.1 summarizes the 5 parameters used to parameterize a track [64], measured at a point Q on the helix trajectory of the track, with respect to a reference point R. The 5 parameters of a track are [65]: • transverse impact parameter d0 — the distance of closest approach to R in the x − y plane, which defines point Q. In other words, the smallest distance between the trajectory and R is at point Q; • longitudinal impact parameter z0 — the z-component of the vector RQ; • azimuthal angle φ ∈ [−π, π], tan φ =  py px  with px , py as the x- and y-component of the track  momentum at P;  25  R  Q  Figure 3.1: Track parameter d0 , z0 , φ , θ and p with a reference point R and a point Q on the trajectory of the particle. ex ,ey and ez are the unit vectors along the x-, y- and z-direction.  • polar angle θ ∈ [0, π], tan θ = momentum at P and pT = •  q p  pT pz  with pT , pz as the transverse and z-component of the track  p2x + p2y = p sin θ ;  as the charge divided by total momentum of the track.  The local coordinate system is defined such that the decay position of a particle, e.g. the displaced vertex is the origin of the system. If a track is produced at a production vertex ProdVtx(Lx , Ly , Lz ) (see Figure 3.2),  Figure 3.2: Impact parameter d0 with respect to the ATLAS origin (0, 0, 0). The daughter particle, which forms the track, was produced from the the decay of the mother at the production vertex ProdVtx(Lx , Ly , Lz ).  26  which is close to the origin (0, 0, 0), the following equations [66] are useful: d0 [Origin(0, 0, 0)] = −Lx sin φ + Ly cos φ , Lx px + Ly py z0 [Origin(0, 0, 0)] = Lz − · pz . pT 2  (3.1) (3.2)  For an arbitrary point R(rx , ry , rz ) close to the production vertex, the following equations are useful:  d0 [R(rx , ry , rz )] = −(Lx − rx ) sin φ + (Ly − ry ) cos φ , (Lx − rx )px + (Ly − ry )py z0 [R(rx , ry , rz )] = Lz − rz − pT 2  (3.3) · rz .  (3.4)  where d0 [R(rx , ry , rz )] means the transverse impact parameter with respect to the point R (rx , ry , rz ).  3.1.2  Reconstruction  Tracks are reconstructed using the ATLAS NEWTracking (NEWT) framework [59], which consists of two main reconstruction algorithms: the inside-out and the outside-in algorithm. The inside-out tracking starts by identifying three space points from silicon-only hits to form track seeds: PPP (3 Pixel hits), PPS (2 Pixel + 1 SCT hit) or SSS (3 SCT hits). A space point is defined as a coordinate in the 3-dimensional space. These track seeds are then extended to the entire silicon detector via a Kalman filter approach [67]. To remove fakes and duplicates, the Ambiguity Solver program is used in the algorithm to assign a score to each track based on its quality, including the number of silicon holes along the track and the number of common hits shared with other tracks. A hole is a detector hit which does not exist on the track, but which is expected to be there, possibly due to inefficiency of the detector. The Ambiguity Solver imposes several criteria with the assumption that these tracks originate from the interaction point [68]. Only tracks above a certain score are kept for further processing. Once the Ambiguity Solver has identified the good tracks, they are then extended into the TRT system to search for any compatible TRT hits. The outside-in algorithm is performed after the inside-out tracking algorithm. It starts by combining TRT hits which have not been used in the inside-out stage, to form track segments. These TRT segments are then extrapolated into the silicon detectors to pick up compatible silicon hits. TRT segments that are not extendable into the silicon detectors (no matching silicon hits) are stored as TRT Standalone track collections. These tracks were not used for the ATLAS RPV displaced vertex search. Tracks originating from a long-lived particle decay with large impact parameters, also known as displaced tracks, suffer from the constraints in the Ambiguity Solver, which assumes all particles  27  originate close to the pp interaction point. Displaced tracks from a long-lived particle decay have a large impact parameter |d0 | compared to prompt tracks, i.e. tracks originating from the pp interaction points. To reconstruct tracks with a large impact parameter d0 , we have developed a package  (RPVDispVrt) to perform re-tracking and vertex reconstruction in one framework. The RPVDispVrt re-tracking component conducts a second round of the inside-out algorithm, but with hits not used in any of the inside-out or outside-in algorithms during NEWT. The criteria imposed here for the Ambiguity Solver is looser than NEWT (see Table 3.1). This study was done in Ref. [68]. Table 3.2 (also see Ref. [68]) shows some d0 cut values and their corresponding secondary track reconstruction efficiency, fake rate, optimisation factor and average reconstructed track multiplicity per event. One can see that the efficiency reaches a plateau around |d0 | < 200 mm cut. The re-tracking allows us to obtain another ∼ 33% secondary track reconstruction efficiency, of which ∼ 31% comes from the loosening of the |d0 | cut.  Track pT |d0 | |z0 | Minimum number of silicon hits (not shared)  NEWTracking > 0.4 GeV < 10 mm 320 mm ≥6  RPVDispVrt second pass > 1 GeV < 300 mm < 1500 mm ≥5  Table 3.1: Criteria imposed in NEWT and the second pass in RPVDispVrt.  |d0 | cut value [mm] 50 100 150 200 250 300  Efficiency, ε [%] 21.6 28.7 20.5 31.0 31.1 31.1  Fake rate, f [%] 13.9 14.0 14.4 14.6 14.7 14.7  ε (1 − f ) 0.186 0.247 0.261 0.265 0.265 0.265  Average track multiplicity / event 14.6 19.4 21.5 22.2 22.4 22.5  Table 3.2: From Ref. [68]. Secondary track reconstruction efficiency, fake rate, optimisation factor ε (1 − f ) and average reconstructed track multiplicity per event for different cut values of |d0 |.  The processing time of NEWT is ∼ 4 seconds per event for our signal MC and ∼ 7 seconds per  event for a QCD sample. The re-tracking program adds an additional 50% to the processing time for the signal sample and 60% for the QCD sample. To achieve a tolerable event recording rate in ATLAS, the re-tracking program is only performed on events passing specific triggers and criteria [69].  28  3.2  Muon  There are two muon reconstruction frameworks in ATLAS — MuId (Muon Identification) [70] [60] and Staco (Statistical Combined) [71] [60]. Track finding in the Muon Spectrometer utilises the Hough transform method [72], which is useful when a track hit is characterized by 2-dimensional points (drift tubes in the MS lack the z-component information). Each of the frameworks reconstruct three main kinds of muons : • Stand-alone muon — The muon trajectory is reconstructed in the Muon Spectrometer (MS)  only. There is no Inner Detector (ID) track associated to it, when the MS track is extrapolated back to the beam line.  • Combined muon — The reconstructed muon has an Inner Detector track associated to its stand-alone Muon Spectrometer track. The best ID track is selected, based on the χ 2 match-  ing between the MS track and the set of ID tracks. The χ 2 is the difference between the measured track parameters in the MS and the ID, weighted by their combined errors. • Segment tagged muon — A reconstructed muon where an ID track is extrapolated into the Muon Spectrometer to search for possible MS track segment. The extrapolation takes into account the energy loss in the Calorimeter along the trajectory of the ID track. For the displaced vertex search, we have used the combined muon tracks. Loose track selections as defined by the Muon Combined Performance Group are imposed: • If | η |< 1.90, require n > 5 and noutlier < 0.9n; • If | η |≥ 1.9 and n > 5, require noutlier < 0.9n; • At least 6 SCT hits, where n = nhit +noutlier , nhit is the total number of TRT hits and noutlier is the number of TRT outliers, which is defined as the number of TRT hits associated to a track but its reconstructed trajectory did not cross the corresponding TRT sensors [73].  3.3  Jet  Jets are formed when quarks and gluons hadronize to form a collection of hadrons. The reconstruction of jets starts from the energy deposition in the calorimeter cells. Cluster seeds are identified as those cells with an energy signal > 4σ 1 above noise threshold, where noise is defined as the 11  σ = 1 Gaussian standard deviation.  29  cell energy divided by the RMS of the energy distribution measured from a set of random events. The clusters are then expanded to include all neighbouring cells with an energy signal > 2σ over noise. Finally, all other neighbouring cells of the previous neighbours containing energy signal above noise threshold are included into the clustering, to form topological clusters, also known as topoclusters. The topoclusters are then combined via the anti-kt algorithm [74] to reconstruct jets. Anti-kt uses a weighted distance measure di,min calculated for each topocluster i:  di j = minimum di =  1 1 , 2 2 pT i pT j  ∆R2i j , R2  1 , pT i  (3.5) (3.6)  di,min = minimum (di , set of all di j ) , with the resolution parameter R set to either 0.6 or 0.4 in ATLAS and ∆Ri j =  (3.7) (ηi − η j )2 + (φi − φ j )2  is a distance measure between topocluster i and j. If di,min = di , topocluster i is upgraded to a jet and is removed from the list of topoclusters. Otherwise, they are merged to form a new topocluster. Each topocluster mimics an individual particle energy deposition, and as such, is an attempt to fully contain the shower of one particle. The cluster energy is the sum of all the cells energy within the cluster.  3.4  Primary Vertex  Figure 3.3 is an event display showing 20 pp interactions in a single event containing a Z → µ µ  candidate. A primary vertex is the location in space where a pp interaction has taken place, producing a set of tracks, which are observed to be originating from that particular location. ∼ 60% of pp interactions per crossing will produce reconstructable PV.  The primary vertex (PV) reconstruction is done via a χ 2 -based iterative vertex finder method [62], where the search for vertex seeds is done along the z-direction, based on the z0 of the tracks in an event satisfying certain criteria. Tracks used to reconstruct the primary vertex have |d0 | < 4 mm and pT > 150 MeV.  In 2011, up to 25 inelastic pp interactions per bunch crossing were observed. Multiple interactions within one recorded event are known as pile-ups. Low momentum transfer (Q2 ) events dominate pp collisions at the LHC, with a cross section of ∼ 70 mb [75], in contrast with the lower  cross sections of the electroweak and top physics (see Figure 3.4). Therefore, pile-up is an issue in ATLAS, with the need to differentiate between the high Q2 hard interaction from the multiple low Q2 soft interactions in one bunch crossing. 30  Figure 3.3: 2011 data — Event with a Z → µ µ candidate and 20 reconstructed primary vertices.  N  In every event, the reconstructed primary vertices are recorded and ordered by their  ∑ pTi 2  i=1  where, N is the number of tracks associated to that PV. In ATLAS, the hard interaction is defined N  to be the PV with the highest  ∑ pTi 2 in an event. The remaining vertices in the list are regarded as  i=1  pile-ups. In the case of Figure 3.3, the Z candidate-associated vertex is the hard interaction vertex. In this search, we identify the SUSY primary vertex as the vertex with the highest ∑ p2T in the event, as adopted ATLAS-wide. The efficiency of identifying correctly the hard interaction using this pT -based criteria varies with the physics search. We have verified that this criteria gives a high identification efficiency for our search. In one hard interaction, such as that which produces the Z boson candidate in Figure 3.3, the interaction will be accompanied by an underlying event (UE). While the main partons (QCD constituents in the proton) hard scatter, the remaining partons, including the QCD sea, also interact simultaneously, producing the UE within the same pair of protons. Hence, in this way, the UE differs from pile-ups, where pile-ups occur due to other protons in the bunches interacting. In the 31  Figure 3.4: From Ref. [76]. Cross sections of SM physics for various electroweak and top physics, at the centre-of-mass energy of 7 TeV and 8 TeV.  case of the Z candidate-associated vertex in Figure 3.3, some of the non-leptonic tracks (in grey) associated to this vertex could well be due to the UE.  32  4  Displaced Vertex Selection 4.1  Datasets  This work (except Chapter 8) utilises the collision data collected in 2011, requiring good data-taking condition for the Inner Detector and the Muon Spectrometer. A total of 4.4 fb−1 of integrated luminosity is used. Several Monte Carlo generators have been used to simulate the signal and Standard Model background samples. The samples include a modeling of the multiple pp collisions in an event (pile-up) as observed in the data. Table 4.1 lists the Monte Carlo (MC) samples we have used for the displaced vertex search from a SUSY RPV long-lived neutralino χ10 decay. The signal samples are generated with Pythia [77]. This is a multi-purpose Monte Carlo generator which can handle all the SUSY simulations and the hadronizations in an event. All RPV couplings are set to zero, except the coupling which is of interest to us, i.e. λ211 . The value of the coupling is chosen such that the neutralino decays will produced displaced vertices within the Pixel subdetector (transverse decay length < 180 mm), where there would be a high reconstruction efficiency. The neutralino is produced directly from the squark: q → qχ10 . The squarks can be produced via gg → qq and qq → qq. A production  chain has been shown in Figure 1.7. A diagram of the decay has been shown in Figure 1.6. To aid visualization, we show in Figure 4.1, a reconstructed displaced vertex from the χ10 decay. The η and (zDV , rDV ) distributions of the displaced vertices from the neutralino decays are shown in Figure 4.2, where zDV and rDV are the longitudinal and radial vertex position from the origin (0, 0, 0). We have used various background MC samples, including the QCD , electroweak W → µν, W → τν, Z → µ µ and Z → ττ, and t t¯ samples. The top quark (172.5 GeV mass) MC sample were generated using MC@NLO [78] interfaced to Herwig [79]+Jimmy [80]. The Herwig MC generator is used to simulate the hadronizations in the pp collisions, while the Jimmy generator is used to simulate the underlying event. The MC@NLO generator handles the calculations of 33  Label ML MH HH  ID 106499 114006 118554  mq [GeV] 700 700 1500  mχ 0 [GeV] 1 108 494 494  λ211 1.5 × 10−4 3 × 10−6 1.5 × 10−5  cτ [mm] 101 78 82  < βγ > 3.1 1.0 1.9  σ [fb] 66 66 0.2  Nevents 6 × 104 6 × 104 2.5 × 104  Table 4.1: The signal MC samples used, with the generated q and χ10 masses (denoted as mq and mχ 0 ), 1  the coupling strength λ211 , the lifetime cτ, the average boost factor < β γ >, the cross sections and the number of events generated. The χ10 masses are influenced by the Higgsinogaugino mixing. In the label given to each sample, the first letter stands for either a medium or heavy squark, while the second letter stands for either a light or heavy neutralino. The chosen values of squark and neutralino masses correspond to a wide range in the quantities to which the signal efficiency is most sensitive: neutralino speed and the number of tracks produced in the decay of the neutralino.  Figure 4.1: RPVDispVrt vertex finder has been used to reconstruct the displaced vertex shown in black. 5 tracks (transverse momentum pT > 1 GeV) are associated to the vertex. Also shown are some detector sensors, the beam-pipe and the primary vertex of the event. A legend is given in Appendix B. This simulated event was produced from a Monte Carlo signal dataset with a long-lived 108 GeV χ10 .  the various decay amplitudes of the top quark. The QCD, W and Z samples were generated with Pythia. Since our trigger requires a high pT muon (see Section 4.4), SM processes with decays like W → µν and Z → µ µ will pass the trigger. Events containing top quarks form another background  when t → W b and the W boson decays leptonically. The QCD samples are important to study fake muons in the detector, and when the heavy flavour quarks decay leptonically.  The modeling of the ATLAS detector is done via the Geant4 toolkit [81], which is used to sim-  34  150  0.4  0.3  100  0.2  50 -200  Normalized area  r DV  ×10-3  0  100  0.04 0.03 0.02 0.01  0.1  -100  0.05  0  200  zDV  -2  1.5  100  1  50  Normalized area  r DV 150  100  2  0.08 0.06 0.04 0.02  0.5  0  1  (b) ML: η ×10-3 2  -100  0  η  (a) ML: (zDV , rDV )  -200  -1  0  200  zDV  -2  -1  0  1  2 η  (c) MH: (zDV , rDV )  r DV  ×10-3 1.2  150  1 0.8  100  0.6  Normalized area  (d) MH: η  0.4  50  0.06 0.04 0.02  0.2  -200  -100  0  100  0  200  zDV  -2  -1  0  1  2 η  (e) HH: (zDV , rDV )  (f) HH: η  Figure 4.2: Figure (a), (c) and (e) show the (zDV , rDV ) distributions of the displaced vertices from the neutralino decays in the ML, MH and HH samples respectively. Their corresponding η distributions are shown in Figure (b), (d) and (f). The distributions are normalized to the number of neutralino decays.  35  ulate the interactions of the detector with the incoming particles produced in the pp collisions. The simulation requires a good modeling of the material in the ATLAS detector to ensure accurate estimation of the amount of energy lost by particles when interacting with the material, while traversing through the detector.  4.2  Displaced Vertex Finder  The role of vertexing is to identify the interaction point or the vertex where the production or a decay of a particle took place. The vertex is then used as a reference point for the measurements of the 4-momenta of a track and its tranverse and longitudinal impact parameters d0 and z0 . This is imperative since the track momentum changes along the trajectory while it traverses in the magnetic field of the detector. In the case of Z → e+ e− decay, we can reconstruct the Z mass by combining the 4-momenta of  e+ and e− tracks using the primary vertex (PV) as the reference point at which to measure the mass  bump in a mass distribution. The PV is the correct reference point or vertex since the Z decays promptly, implying the PV is the point of origin for the Z decay products. The tau lepton can decay with a displaced vertex at a distance from the PV. As the decay position is still close to the PV, it can still be used as the reference point to a good approximation. The change in the momentum of its charged daughters are negligible over a short distance from the PV. However, for long-lived particles like the neutralino and K-short (Ks ), the PV is not a good reference point. Their decay position can be far from the production point and the magnetic field will influence the momentum vector of the trajectories of the particles produced from the decay. Figure 4.3 shows the reconstruction of Ks → π + π − where the pions 4-momenta are computed with  respect to the PV and the Ks decay vertex respectively. In this Figure, one observes the absence of the Ks mass peak when the PV is taken as the reference point instead of the displaced vertex location, showing the importance of identifying the correct reference point. Since the PV has already been reconstructed prior to reconstructing a Z mass peak or τ, vertexing is usually omitted. For a χ10 decay, we use the RPVDispVrt vertex finder to search for its decay position or displaced vertex.  4.2.1  RPVDispVrt Vertex Finder  The RPVDispVrt is a displaced vertex finder which has been developed based on the ATLAS VKalVrt framework [82]. In this work, the RPVDispVrt finder is used to search for displaced vetices from the neutralino decay. The RPVDispVrt finder takes as inputs a selected number of tracks, which satisfy pT > 1 GeV and |d0 | > 2 mm. The latter is imposed to reject tracks originating directly from the pp interactions. Tracks from heavy flavour decays, including b hadrons are also  suppressed (see Figure 4.4). On average, only 2% of the tracks in an event survive these criteria. 36  Events / ( 6.2 )  Events / ( 6.9 )  3000 2500 χ2/DOF = 5.724  2000 1500  Double Gaussian + Linear fit Background fit  500 0  400  450  500  10 Data 2011  8  χ2/DOF = 17.251  Double Gaussian + Linear fit Background fit  6 4  Data 2011  1000  ×103  2 550  0  600  400  450  500  550  Mass [MeV]  600 Mass [MeV]  (a) with respect to the primary vertex  (b) with respect to the displaced vertex  Figure 4.3: Invariant mass distribution constructed from 2 tracks, with each track px , py , pz with respect to the primary vertex (left) and with respect to the displaced vertex (right) around Ks meson mass window.  The candidate tracks are then passed into the vertex finding component of the RPVDispVrt package  4.4 fb-1  60 50 40 30 20 10 0  2  4  6 8 10 Secondary track |d0| [mm]  ×103 20 18 16 14 12 10 8 6 4 2 0  4.4 fb-1  105  Entries  r b decay [mm]  to reconstruct displaced vertices:  All b-vertex  104  Remaining b-vertex (no mass cuts)  103 102 10 1 10-1  2  4  6  8 N-tracks b-vertex  (a)  (b)  Figure 4.4: Left : Transverse location of b-decay from beam line rb decay vs d0 of tracks from b-decays. Right : Remaining b-decay truth vertices after cut.  • Stage 1 — 2-track vertex: 2-track vertices are formed using every pair of tracks meeting the above criteria and regardless of their charges. The coordinates of the vertex and its position errors are calculated using the Billoir vertex fitting method with the minimisation of a χ 2 functional [83], defined as  37  χ2 =  ∑  tracks  qpred,i (V, pi ) − qmeas,i  T  Wi qpred,i (V, pi ) − qmeas,i ,  (4.1)  where qmeas,i are the measured 5 parameters of the ith track (see Section 3.1.1), and qpred,i are the predicted track parameters of the ith track, assuming the track with some momenta pi , had originated from a vertex at a location V . Wi is the inverse of the 5 × 5 covariance matrix  corresponding to the 5 parameters of the track. Each accepted reconstructed 2-track vertex fit is required to satisfy χ 2 per degree of freedom < 5. The number of degrees of freedom of a vertex Ndof is related to its number of tracks Ntrk by Ndof = 2Ntrk − 3 [84]. Moreover, there  should be no track hits between the PV and the vertex position. This is imposed to reject fake vertices reconstructed from random track combinations. All successful candidates are passed to the next stage. • Stage 2 — N-track vertex: This stage uses a graph theory technique via incompatibility graphs [85], which has also been used in data mining and in track reconstruction (when candidate tracks are sharing hits usually in a busy event or in a narrow angular region [86][87]). Here, it is used to create N-track “seed”-vertices, which may have come from a common decaying particle, based on the track-vertex relationships which survived Stage 1. For example, suppose one obtains five 2-track displaced vertices in Stage 1. After Stage 2, one might obtain a 4-track displaced vertex (DV) and a 3-track DV from combining multiple 2-track vertices. • Stage 3 — track-vertex uniqueness relationship: In Stage 2, there is no guarantee that each track is associated to one and only one vertex. Stage 3 addresses this issue, by performing an iterative procedure that will ensure at most one vertex for any one track, and that the track has the best χ 2 per degree of freedom relative to that vertex, among all other vertices associated to it after Stage 2. First, the maximallyshared track (track with the most number of associated vertices) is identified along with its worst track-to-vertex χ 2 per degree of freedom. If the χ 2 per degree of freedom > 6, the track is removed from the vertex. Otherwise, we search for two vertices with the smallest spatial distance significance, which contain this track, and merge them. The significance s is defined as s=  (V1 − V2 )T (C1 + C2 )−1 (V1 − V2 ),  (4.2)  with C1 and C2 as the vertex covariance matrices, and V1 and V2 as the positions of the two vertices. This search and merge continues until there are no two vertices with distance 38  significance < 3. The iteration starts again with searching for the next maximally-shared track from the new list of vertices. The iteration stops when each track is assigned to at most one vertex. Finally, if any two or more vertices are located within 1 mm of each other, they are merged and refitted. This is to solve the issue in situations where, there are vertices which contain tracks from the neutralino, which are not associated with any other vertex candidates associated to the same neutralino in an event, thus preventing the DV to be merged with other DVs during the iteration process described previously. We have also checked that at this stage of the vertexing, no two background vertices are likely to be less than 1 mm apart in distance. The χ 2 per degree of freedom distribution is shown in Figure 4.5. To ensure a good quality vertex fit, each DV must satisfy χ 2 per degree of freedom < 5. All successful DV candidates  Vertices  are then stored for further studies. ×103 18 16 14 12 10 8 6 4 2 0 0  1  2  3  4  5  6 χ2/DOF  Figure 4.5: The χ 2 per degree of freedom after Stage 3.  A vertex resolution of several microns can be achieved through this procedure. This is shown in Figure 4.6 in terms of the residuals. For some quantity q, the residual is defined as Residual (q) = qreco − qtrue .  (4.3)  In our case, qreco and qtrue are the reconstructed and true vertex position respectively. The pull distributions are also shown in the same Figure. The pull is defined as Pull (q) =  qreco − qtrue , σqreco  (4.4)  where it is expected to be Gaussian N(0, 1) distributed, with mean = 0 and standard deviation = 1, if the estimation of the vertex position and the error σqreco were unbiased. In Figure 4.7, we show the beam pipe structure built from the distribution of reconstructed ≥ 4−track material vertices. These vertices are produced when particles produced from the pp collisions interact with the material in  the beam pipe. The transverse distance from the detector origin (0, 0, 0), rDV is computed relative 39  ×103 MC  10 8  Gaussian fit  σ = 8.03 ± 0.06 µm  Vertices  Vertices  12  6 4 2 0 -0.1 -0.08-0.06-0.04-0.02 0  0.02 0.04 0.06 0.08 0.1 xreco - xMC [mm]  ×103 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -3  MC Gaussian fit  µ = -0.002 ± 0.004 σ = 1.068 ± 0.003 -2  -1  ×103 9 8 7 σ = 29.37 ± 0.17 µm 6 5 4 3 2 1 0 -0.3 -0.2 -0.1 0  1  2 3 (xreco-xMC)/σreco  (b) Pull x  MC Gaussian fit  Vertices  Vertices  (a) Residual x  0  0.1 0.2 0.3 zreco - zMC [mm]  (c) Residual z  ×103 2.2 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -3  MC Gaussian fit  µ = -0.007 ± 0.004 σ = 1.065 ± 0.003 -2  -1  0  1  2 3 (zreco-zMC)/σreco  (d) Pull z  Figure 4.6: The vertex residual after Stage 3 (left) in x and z, shown with a Gaussian fit to the core. The vertex resolution is the width of Gaussian fit. The pull distributions (right) in x and z are shown with a Gaussian fit. As the detector is symmetric in the transverse direction and have the same detector efficiency in x and y, the resolution in y is the same to that in x.  to the shifted beam-pipe origin (−0.2, −1.9) mm. The vertex resolution is sufficiently small, hence the ability to discern the beryllium and the aerogel components of the beam pipe.  40  Vertices / 0.1 mm  Normalized area 0.06  s = 7 TeV Data 2011  0.05 Beam pipe structure  0.04 0.03 0.02 0.01 0  26  28  30  32  34  36  38  40  r DV relative to (-0.2,-1.9) mm Figure 4.7: Beam pipe structure built from displaced vertices produced through particles interacting with the detector material. ≥ 4-track vertices were used. Table 4.2 gives details of the beam-pipe structure.  Layer Getter coating Beryllium Kapton sheet Inconel (excluded at |z| < 50 mm) Kapton tape Aerogel Kapton tape Aluminium  rmin [mm] 28.998 29 29.875 29.900 30.000 30.120 34.120 34.240  rmax [mm] 29 29.8 29.9 29.910 30.120 34.120 34.240 34.290 Total Total (central |z| < 50 mm)  X0 (%) 0.009 0.227 0.009 0.064 0.043 0.267 0.043 0.056 0.719 0.655  λ (%) 0.001 0.203 0.005 0.006 0.022 0.077 0.022 0.013 0.348 0.342  Table 4.2: Designed properties of the layers constituting the beam pipe ([88] and private correspondence with Grant Gorfine). rmin and rmax are measured relative to the ATLAS global origin. X0 is the radiation length and λ is the nuclear interaction length. A sketch of the beam pipe can be found in [89] and a CERN technical drawing can be found in [90]. Note, apart from the beryllium layer, the positions of other layers are not known to a high precision along the beam pipe. The above figures given are the average values.  41  4.3  Mass  To extract the signal, while suppressing the backgrounds, the mass of the displaced vertex is a useful signal-background discriminator. We shall discuss 3 mass variables in Section 4.3.1, 4.3.2 and 4.3.3 using Figure 4.8. The ML and MH samples with their different neutralino masses, will be used as  Normalized area  examples. 0.07 0.06  0 108 GeV ∼ χ  Invariant mass mDV p -corrected mass T mµ jet  0.05 0.04 0.03 0.02 0.01 0 0  20  40  60  80  100  120  140  160  180  200  Mass [GeV]  Normalized area  (a) 108 GeV χ˜ 10 0.035 0.03  0 494 GeV ∼ χ  Invariant mass mDV p -corrected mass T mµ jet  0.025 0.02 0.015 0.01 0.005 0 0  100  200  300  400  500  600  700  800  900  1000  [GeV]  (b) 494 GeV χ˜ 10  Figure 4.8: The simulated spectra of the invariant mass mDV , pT -corrected mass and mµjet for the (a) 108 GeV χ˜ 10 and (b) 494 GeV χ˜ 10 samples.  4.3.1  Invariant Mass 2  The invariant mass,  m2DV  =  ∑  tracks  Ei  2  −  ∑  pi  , where the sum is over all tracks from the  tracks  decay vertex. The invariant mass is labeled as “Invariant mass mDV ” in Figure 4.8. A sharp peak at the mass of the χ10 is not observed. Instead, a “spread-out” of the invariant mass mDV distribution is observed since some daughter tracks from χ10 are possibly not found and some may be neutral.  42  4.3.2  pT -corrected Mass  To partially recover the missing 4-momenta due to lost of tracks or neutral daughter particles in the decay, we establish the use of a local frame missing momentum. Since the vertex resolution is of O(10 µm), we can therefore assume the true neutralino momentum direction (the flight direction vector) as equivalent to the detector level DV position vector from PV (DV − PV). Taking that as  the new "z-axis", along with DV as the origin of the local coordinate system, we obtain a boost  invariant x − y plane in the local reference frame (see Figure 4.9). For a given signal, we can  calculate the missing momentum MET necessary to satisfy conservation of momentum in the boost invariant plane of the signal as MET = −  ∑  tracks  pT vis i = DV − PV ×  ∑  tracks  pi × DV − PV ,  (4.5)  with pT vis i as the momentum projection in the boost invariant plane for track i and the summation is on all the tracks in the DV. Figure 4.9 illustrates this. In our case, we treat lost tracks, which were supposed to exist or be vertexed, as collectively equivalent to an invisible particle, and hence MET is due to this loss. Let index 1 denote all tracks in the DV collectively and index 2 to denote MET.  Figure 4.9: The boost invariant plane and the missing momentum. pT vis i is the momentum projection in the boost invariant plane for track i. The position of the DV is shown as a circle in in the centre of the boost invariant plane.  Further, let the 4-momentum invariant mass be m1 and m2 , the rapidity be y1 1 and y2 , the transverse momentum be pT 1 and pT 2 , and the transverse energy be E1 and E2 , where E =  m2 + pT 2 , then a  4-momenta invariant mass in general, can be re-written in the following form [91] : 1y = 1 2  E+pz E−pz  , where E and p are the energy and momentum of the particle.  43  m2mother = m21 + m22 + 2E1 E2 cosh (y1 − y2 ) − 2pT1 · pT2 .  (4.6)  For the case of displaced vertex, we make 2 assumptions and utilize 1 constraint : Unknown mass of MET, m2 = 0,  (4.7)  cosh (y1 − y2 ) = 1,  (4.8)  pT1 ·pT2 = −pT 1 pT 2 ,  (4.9)  which will reduce Equation 4.6 to the pT -corrected mass (see Figure 4.8) : mpTcorr =  2  m2DV + MET + MET.  (4.10)  The following relationship also holds : mDV ≤ mpTcorr ≤ true mass. We put a short derivation of  Equation 4.6 leading to mpTcorr in Appendix A. mpTcorr gives the best lower bound on the mass of the signal. To our best knowledge, it was initially introduced by the SLD experiment to study b-decays  0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 0  Normalized area  Normalized area  [92]. Simulated MET of the neutralinos are shown in Figure 4.10.  108 GeV ∼ χ  0  ~ ET  0.04  494 GeV ∼ χ  0  0.035 0.03  ~ ET  0.025 0.02 0.015 0.01 0.005  20  40  60  80  0 0  100 ~ MET [GeV]  (a) 108 GeV χ10  100  200  300  400  500 ~ MET [GeV]  (b) 494 GeV χ10  Figure 4.10: The simulated MET spectra for the (a) 108 GeV χ10 and (b) 494 GeV χ10 samples.  4.3.3  Muon+Jets Invariant Mass  In the usual ATLAS Inner Detector (ID) NEWTracking setup (see Section 3.1.2), we have mentioned that tracks beyond some d0 threshold are reconstructed with low efficiency. Therefore, any muon which is anticipated to be travelling towards the Muon Spectrometer (MS) with a large d0 may not necessarily be a combined ID+MS muon track. However, it has a better chance of being reconstructed as an MS-only track due to the looser d0 requirement of the muon reconstruction algorithm. Thus, we perform an extrapolation. For DV with no ID+MS muon track, all muon candidates in an event are extrapolated to the DV position. If the distance significance of the extrapolated 44  track to the DV < 3, the muon is said to be associated to the DV. The distance significance is the distance between the muon and the DV, weighted by the inverse of their covariance matrices. For all reconstructed jets found in the event, the association to DV is done as follows: • Track-to-jet matching: We match each track in the DV to all available jets. The closest jet to  the track in terms of the ∆R (see Section 2.2) is considered to be a match if the ∆R < 0.4, and  is attached to the DV. • Remaining jets: If there is any missing momentum in the boost invariant plane  MET = −pT muon − pT jet , we search from the remaining unmatched jets which can satisfy  the following and associate it to the DV :  |pT extra jet + MET|  < 0.2.  (4.11)  pT extra jet + MET  The mass mµjet in Figure 4.8 is the 4-momenta mass of the muon and jets combined.  4.4  Selection Criteria  For 2011, we have imposed various criteria which will reduce the backgrounds to this search. They include the selection of the collision events, the triggered muons and the displaced vertices in the events.  4.4.1  Event Selection  Events are required to pass either the EF_mu40_MSonly_barrel or EF_mu40_MSonly_barrel_medium triggers. These triggers select events that contain a muon with pT > 40 GeV at the Event Filter level of the trigger chain (see Section 2.7) in the | η |< 1.07 region. A cosmic veto is also applied, where  the event is rejected if it contains two back-to-back muons satisfying  (π − (φ1 − φ2 ))2 + (η1 + η2 )2 < 0.1,  (4.12)  where φ1 , φ2 , η1 and η2 are the azimuthal angles and pseudorapidities of the two reconstructed muons. This criteria is imposed because muons produced from cosmic rays pass through the detector giving an appearance of two reconstructed muons, with each of them originating from the beam line. To ensure that the primary vertex (PV) is a possible hard interaction vertex, the z-coordinate of the PV in the event must satisfy | zPV |< 200 mm, with at least 5 tracks associated to it.  45  4.4.2  Muon Selection  We have used the MuId combined muon loose selection qualities set out by the Muon Combined Performance Group [93]: • If | η |< 1.90, require n > 5 and noutlier < 0.9n; • If | η |≥ 1.9 and n > 5, require noutlier < 0.9n; • At least 6 SCT hits, where n = nhit +noutlier , nhit is the total number of TRT hits and noutlier is the number of TRT outliers, which is defined as the number of TRT hits associated to a track but its reconstructed trajectory did not cross the corresponding TRT sensors [73]. We do not impose any requirements on the number of Pixel hits. This is to ensure that potential muon candidates from the displaced vertices located within the Pixel subdetector are not rejected. The transverse momentum of the muon should satisfy pT > 50 GeV, i.e. in the region where the trigger efficiency is approximately independent of the muon pT (see Figure 5.7). Moreover, the pT cut ensures that the event recording rate for the retracking program (see Section 3.1.2) is within its capacity. The impact parameter d0 with respect to the primary vertex is required to satisfy |d0 | > 1.5 mm, to also help ensure an acceptable event  recording rate for the re-tracking program by reducing the acceptance of background events, which include Z → µ µ and W → µν decays, where the muons have low |d0 | because they are produced  close to the pp interaction point.  To ensure that the muon candidate is associated with the triggered muon, we require: (∆φ )2 + (∆η)2 < 0.15,  (4.13)  where ∆φ and ∆η is the difference between the azimuthal angles and pseudorapidities of the reconstructed muon and triggered muon.  4.4.3  Vertex Selection  The displaced vertex (DV) is required to satisfy |zDV | < 300 mm and |rDV | < 180 mm. These requirements cover a search for χ10 decaying in the Pixel subdetector region. To minimise back-  grounds originating from the PVs, the transverse distance between the DV and any of the PVs should satisfy (xDV − xPV )2 + (yDV − yPV )2 > 4 mm, where x and y are the x- and y-coordinates of a given vertex.  46  (4.14)  To maximize the significance Z, defined to be [94] Z=  2 (S + B) ln 1 +  S −S , B  (4.15)  where S and B are the number of signal and background vertices passing a cut, the DV candidate is required to satisfy Ntrk ≥ 5 and mDV > 10 GeV, where Ntrk is the number of tracks associated with the DV, and mDV is the invariant mass of the DV (see Section 4.3.1). Figure 4.11 shows the Ntrk  and mDV distributions. Hereafter, the invariant mass mDV will be referred to as the vertex mass of  4.4 fb-1  106 105  0 ∼ χ1 (100 GeV)  4  10  Vertices  Vertices  the DV. These criteria are used to define the signal region (SR) and the control region (CR) of this  104  QCD  10  tt  QCD W,Z tt  102  102  10  10  1  1 10-1  0 ∼ χ1 (100 GeV)  103  W,Z  3  4.4 fb-1  105  0  2 4  6  10-1 0  8 10 12 14 16 18  2  4  6  8 10 12 14 16 18 20 Mass [GeV]  Number of tracks (a) Ntrk  (b) mDV  Figure 4.11: Simulated (a) Ntrk (number of tracks per vertex) and (b) mDV (invariant mass of vertex) distributions for the signal and background. For the mDV distribution, the requirement of Ntrk ≥ 5 has been imposed.  experiment. The SR contains vertices passing all selection criteria described so far, but CR contains vertices that do not. The regions are used for the background estimation for the region before the beam pipe (rDV < 28 mm), which is done in a data-driven manner, i.e. no reliance on the Monte Carlo (see Section 6.1 of Chapter 6). This study is done in a blinded way [95], where the SR is hidden from the experimentalists until the background studies have been completed. The CRs and SRs are specific to the type of backgrounds and detector regions in study. More details are given in Chapter 6). For regions after the beam pipe (rDV > 28 mm), the background estimation is also done in a data-driven manner (see Section 6.2 of Chapter 6). Here, the SR contains vertices that pass all the selection criteria, including a material veto: if a DV is located within the dense material region as defined with a material map of (|zDV |, rDV ) (see Figure 4.12), the DV is rejected. This is to reduce 47  the background arising from the interactions of particles, produced from the pp collisions, with the detector material. The material map was built from displaced vertices found in the control region of the data collected in 2010. To ensure that the muon candidate is associated with the reconstructed  (a)  (b)  (c) Material veto map  Figure 4.12: Our material map is built first from vertices in the 2010 data, reconstructed using the VrtSecInclusive [96] vertexing algorithm, shown as Map (a). The VrtSecInclusive is used by the Tracking Performance Group to examine material interactions in the Inner Detector [97]. A majority of particle-material interactions produce low pT tracks. Hence, the current RPVDispVrt tracks and vertex selection criteria have low efficiency in illuminating the Inner Detector material region, compared to the VrtSecInclusive selection criteria. An (rDV , zDV ) reweighting is then done to the bin contents of Map (a) to yield Map (b). Thereafter, a cut is applied to obtain Map (c) in addition to some manual cleanup for the vacuum inside the beampipe (rDV 30 mm). The material veto is done using Map (c) in a bit-wise manner, i.e. bit 1 to mean rejecting the DV and bit 0 to mean accepting the DV.  DV, the distance between the muon candidate and the DV, d [ triggered muon, DV ] < 0.5 mm. The distribution for the signal is shown in Figure 4.13. The pT -corrected mass and the mass, calculated from the muon and the calorimeter jets, are not used in 2011 as the cuts described so far are sufficient to suppress the backgrounds. They are intended for future use when the backgrounds become large with increasing event pile-up. 48  Probability  1 10-1  All muons  10-2  Matched-to-DV muons  -3  10  10-4 10-5 -3  10  10-2  10-1  102 1 10 distance(muon,DV) [mm]  Figure 4.13: Simulation of the distance of the muons to the reconstructed χ10 DV. Highlighted in green are the muons matched to the MC truth muons of the corresponding χ10 .  4.5  Data vs. MC  In each Figure of this section, the MC entries are normalized to the number of entries in the data. The composition of the samples in the MC (QCD, W, Z and t t¯) follows their respective cross sections. We show in Figure 4.14, φ vs. η of the muons in the events.  49  103  2 102  1  10  -1  0  -1  -0.5  0  0.5  1  1.5 η  -3  1  10  -1  MC  103  2  3  102  1  10  -1  0  -1.5  -1  -0.5  0  0.5  1  1.5 η  -2  MC 104 103 102  -1  -0.5  0  0.5  (d) MC  1  1.5 η  1  -3  -1.5  -1  -0.5  0  (c) Data : (b) 3  0.5  1  1.5 η  10 -1.5  -1  -0.5  (e) MC : (d)  0  0.5  1  1.5 η  (|d0 | > 1.5 mm)  1  MC  104  2  103  1 0  102 10  -2 -3  1  (cosmics veto)  -1  -2 -1.5  -3  1  (|d0 | > 1.5 mm)  0  -1  10  -2  2  1  102  0  (b) Data : (a) φ  φ  (a) Data  -3  1  -2 -1.5  Data 2011  2  φ  -2  3  102  0  -1  3  Data 2011  2  1  -3  3  φ  Data 2011  φ  φ  3  -1.5  -1  -0.5  (f) MC : (e)  0  0.5  1  1.5 η  1  (cosmics veto)  Figure 4.14: Triggered muon φ vs. η for the data in Figure (a), (b) and (c) and for the MC in Figure (d), (e) and (f). Figure (b) and (e) are produced from Figure (a) and (d) after imposing the |d0 | criteria. Figure (c) and (f) are produced from Figure (b) and (e) after imposing the cosmics veto.  50  In Figure 4.14, the data shows an excess of high d0 muons which is not described in the MC. The possibility of the muons originating from cosmic events is rejected, as can be observed in Figure 4.15. This Figure shows the distributions of ∆φ vs. ∑ η (difference in the φ vs. the sum of the η of the muons) for events with at least two muons. The two muons used are the two muons having the largest pT in the event. One observes that these muons are not consistent with a back-to-back muon in the detector, where the two legs of the cosmic muon are expected to have η1 + η2 ≈ 0. The  disagreement between the data and MC extends into the distributions for the displaced vertices as  4  10  2.5  1.5  0 -1 -0.8 -0.6 -0.4 -0.2 0  0.2 0.4 0.6 0.8  1  ∑η  0 -1 -0.8 -0.6 -0.4 -0.2 0  1  3  (b) Data : (a)  MC  ∆φ  ∆φ  (a) Data  2.5  3  0.2 0.4 0.6 0.8  1  2.5 102  2 1.5  103  2 1.5  10  1 0.5  102  1  10  0.5  0 -1 -0.8 -0.6 -0.4 -0.2 0  0.2 0.4 0.6 0.8  (d) MC  1  ∑η  1  0 -1 -0.8 -0.6 -0.4 -0.2 0  (e) MC : (d)  0.2 0.4 0.6 0.8  1  ∑η (|d0 | > 1.5 mm)  1  102 10  0.5 0 -1 -0.8 -0.6 -0.4 -0.2 0  1  104  103  1  ∑η (|d0 | > 1.5 mm)  MC  104  1.5  10  0.5  Data 2011  2  102  1  3 2.5  103  1.5  10  0.5  104  2  102  1  Data 2011  2.5  103  2  3  ∆φ  Data 2011  (c) Data : (b) ∆φ  3  ∆φ  ∆φ  shown by the mass mDV spectra and radial distance rDV distributions in Figure 4.16.  3  0.2 0.4 0.6 0.8  1  ∑η (cosmics veto)  1  MC  2.5  103  2 102  1.5 1  10  0.5 0 -1 -0.8 -0.6 -0.4 -0.2 0  (f) MC : (e)  0.2 0.4 0.6 0.8  1  ∑η (cosmics veto)  1  Figure 4.15: ∆φ vs. ∑ η for events with at least 2 muons, comparing the data in Figure (a), (b) and (c) to those of the MC in Figure (d), (e) and (f). The distributions show that they are not consistent with the possibility of the event being contaminated by cosmic muons, where the two legs of a cosmic muon would have been back-to-back, with ∑ η = η1 + η2 ≈ 0. Figure (b) and (e) are produced from Figure(a) and (d) after imposing the | d0 |> 1.5 mm. Figure (c) and (f) are produced from Figure (b) and (e) after imposing the cosmics veto.  The discrepancy between the data and MC in Figure 4.14 and 4.15 can be due to fake muons, which are defined as tracks that are not associated to any true muons in an event. They may originate from random detector hit coincidences or hadronic leakage from inefficient containment of the calorimeter jets. If the discrepancy is indeed due to some fake muons, then the event composition should be QCD-dominated, since they have a much higher production rate compared to that of W , Z and t t¯ in a pp collision. We have examined that this is indeed the case, based on the better agreement of the data with the QCD MC (see Figure 4.17) compared to the non-QCD MC (see Figure 4.18), 51  albeit with limited MC statistics availability. The QCD sample describes reasonably well the 2-track mass distribution near the Ks → ππ mass window (∼ 0.5 GeV), suggesting a reasonable description  of its production rate. In view of the data/MC discrepancies and the limited MC statistics, we have  105  2-tracks  Data 2011  4.4 fb-1  QCD W,Z  104  Vertices  Vertices  estimated our backgrounds in a data-driven manner instead of using the MC.  104  10 10  W,Z tt  10  10  1  1 5  10  15  10-10  20  5  Mass [GeV] 0 -2 -4  0 -2 -4  Data 2011 QCD  QCD W,Z  3  tt  10 1  1  10-1  20 40 60 80 100 120 140 160 180 r DV [mm]  Significance  Significance  Data 2011  10  10  4  4.4 fb-1  2  102  10-1  3,4-tracks  10  tt  10  104  Vertices  Vertices  (b) 3- and 4-track DV : mDV  W,Z  3  20  2  (a) 2-track DV : mDV  4.4 fb-1  15  4  Significance  Significance  2  2-tracks  10  Mass [GeV]  4  104  QCD  102  2  105  Data 2011  4.4 fb-1  103  tt  3  10-10  3,4-tracks  2 0 -2 -4  (c) 2-track DV : rDV  4  20 40 60 80 100 120 140 160 180 r DV [mm]  2 0 -2 -4  (d) 3- and 4-track DV : rDV  Figure 4.16: The spectra of the invariant mass mDV is shown in (a) for DV with 2 tracks and in (c) for DV with 3 or 4 tracks. The spectra of the radial distance rDV is shown in (c) for DV with 2 tracks and in (d) for DV with 3 or 4 tracks. Spikes are certain locations in rDV correspond to detector material locations.  52  10  2-tracks  -1  4.4 fb  Data 2011 QCD  104  W,Z  104  105  Vertices  Vertices  5  10  1  1 2  4  6  10-10  8 10 12 14 16 18 20  tt  2  4  6  Mass [GeV]  2 0 -2 -4  2 0 -2 -4  (a) 2-track DV : mDV  4.4 fb-1  (b) 3- and 4-track DV : mDV  Data 2011 QCD W,Z  104  102  10  10  1  1 10-10  20 40 60 80 100 120 140 160 180 r DV [mm]  Significance  Significance  4.4 fb-1  2 0 -2 -4  (c) 2-track DV : rDV  4  Data 2011 QCD W,Z tt  10  102  4  3,4-tracks  3  tt  103  105  Vertices  Vertices  2-tracks  8 10 12 14 16 18 20  4  Significance  Significance  Mass [GeV] 4  10-1  QCD  102  10  104  Data 2011  W,Z  10  102  105  4.4 fb-1  3  tt  103  10-10  3,4-tracks  20 40 60 80 100 120 140 160 180 r DV [mm]  2 0 -2 -4  (d) 3- and 4-track DV : rDV  Figure 4.17: data vs. QCD distributions. The distributions of the invariant mass mDV is shown in (a) for DV with 2 tracks and (b) for DV with 3 or 4 tracks. The distributions of the rDV is shown in (c) for DV with 2 tracks and (d) for DV with 3 or 4 tracks. No muon criteria are imposed in the QCD Monte Carlo sample.  53  10  2-tracks  4.4 fb-1  Data 2011 QCD W,Z  104  Vertices  Vertices  5  104  W,Z tt  10 1  1 2  4  6  10-10  8 10 12 14 16 18 20  2  4  6  2 0 -2 -4  4 2 0 -2 -4  (a) 2-track DV : mDV  4.4 fb-1  (b) 3- and 4-track DV : mDV  Data 2011 QCD W,Z  103  tt  4.4 fb-1  Data 2011 QCD W,Z  3  tt  102 10  10  1  1  10-1  20 40 60 80 100 120 140 160 180 r DV [mm]  Significance  Significance  3,4-tracks  10  102  4  104  Vertices  Vertices  2-tracks  8 10 12 14 16 18 20 Mass [GeV]  4  Significance  Significance  Mass [GeV]  10-1  QCD  10  10  104  Data 2011  2  102  105  4.4 fb-1  103  tt  103  10-10  3,4-tracks  2 0 -2 -4  (c) 2-track DV : rDV  4  20 40 60 80 100 120 140 160 180 r DV [mm]  2 0 -2 -4  (d) 3- and 4-track DV : rDV  Figure 4.18: data vs. non-QCD distributions. The distributions of the invariant mass mDV is shown in (a) for DV with 2 tracks and (b) for DV with 3 or 4 tracks. The distributions of the rDV is shown in (c) for DV with 2 tracks and (d) for DV with 3 or 4 tracks. No muon criteria are imposed in the QCD Monte Carlo sample.  54  5  Total Signal Efficiency This Chapter deals with the signal efficiency which is needed for setting limits on the neutralino production cross section in Chapter 7. In the language of probability, we define the total signal vertex efficiency εDV as εDV = Probability reconstructed DV passing all selections | there exists a DV from a χ10 → muon + jets . (5.1)  The evaluation of εDV is done via MC, where it is estimated by computing the probability of the neutralino decay vertex to be reconstructed, given its existence. The efficiency εDV is sometimes broken into three components — acceptance ADV , reconstruction efficiency εDV,reco and trigger efficiency εDV,trigger , such that εDV = ADV · εDV,reco · εDV,trigger : ADV = Probability (reconstructable DV at the truth level | DV at the truth level) ,  (5.2)  εDV,reco = Probability (DV is reconstructed in the data | reconstructable DV at the truth level) ,  (5.3)  εDV,trigger = Probability (DV passes the trigger | DV is reconstructed in the data) .  (5.4)  The acceptance is usually further broken into two components — geometrical aceptance, which in our case, is due to zDV , rDV , η and material veto requirements, and kinematics acceptance, which in our case, is due to the vertex mass and number of tracks requirements. These notions are ambiguous as the mass and number of tracks for a vertex depends on the decay position (zDV , rDV ), hence the acceptance is not factorizable. In practice, we work with the efficiency εDV . Let σ be the cross section for the squark pair production, BR be the branching ratio of a squark to decay, via a long-lived neutralino, to µ + jets, and L be the integrated luminosity, then the fraction of signal events with only one neutralino to decay to µ + jets is 2BR (1 − BR), and the number of 55  such events that pass our selection cuts is (1)  Nsignal = σ L · 2BR (1 − BR) · εDV .  (5.5)  For the case with both squarks to produce a final product of µ + jets via a cascade decay, we have 2 2 and thus, the total number of candidate DV, so the probability of finding at least one is 2εDV − εDV  such signal events expected is  (2)  2 Nsignal = σ L · BR2 · 2εDV − εDV .  (5.6)  Adding Equation 5.5 and 5.6, the total number of events expected in the data is 2 Nsignal = σ L 2BRεDV − 2BR2 εDV + 2BR2 εDV − BR2 εDV εDV BR = σ L · BR · 2εDV 1 − . 2  (5.7) (5.8)  Since 0 ≤ εDV ≤ 1 and 0 ≤ BR ≤ 1, we have the following: 1 1−  εDV ·BR 2  ≤  1 , 1 − εDV 2  (5.9)  which together with Equation 5.8 implies σ · BR = ≤ =  Nsignal 2 · εDV · 1 − εDV2·BR · L Nsignal 2 · εDV · 1 − εDV 2 ·L Nsignal . εevt · L  (5.10) (5.11) (5.12)  For the purpose of setting limits in Chapter 7, Equation 5.11 is used as an approximation to Equation 5.10, which removes the unknown BR from the right-side of the Equation. Moreover, the efficiency 2 , which is equivalent to the event-level efficiency of finding parameter is simply εevt = 2εDV − εDV  at least one DV in an event with two χ10 → muon + jets DV.  As we shall see in Figure 5.3(a) of Section 5.2, the vertex finding efficiency is small: εDV ≤ 0.2  for the 494 GeV χ10 , and εDV ≤ 0.05 for the 108 GeV χ10 samples. Together with the fact that 0 ≤ BR ≤ 1, the term in the bracket in Equation 5.10 may have the following approximation: 1 1−  εDV ·BR 2  ≈ 1+  56  εDV · BR , 2  (5.13)  which implies σ · BR ≈ and therefore  Nsignal εDV · BR · 1+ , 2 · εDV · L 2  Nsignal Nsignal εDV · (1) ≤ σ · BR ≤ · 1+ , 2 · εDV · L 2 · εDV · L 2  (5.14)  (5.15)  where the lower and upper bounds occur when BR = 0 and 1 respectively. This means that the approximation in Equation 5.11 (which is equivalent to the upper bound of σ · BR) will always be  larger than the σ · BR should have been (see Equation 5.10), with a difference of at most 10% and  2.5% for the 494 GeV and 108 GeV χ10 samples respectively. In using Equation 5.11, we are thus setting limits which will be conservative, by at most 10%.  5.1  Efficiency Maps  Figure 5.1 shows the signal vertex efficiency after all selection criteria except the material veto in a (|zDV |, rDV ) decay location map.  57  0.4  60 40 20 0 0  0.3 0.1 100  150  200  250 300 |z | [mm]  0.6 0.5 0.4 0.3  60 40 20 0 0  0.2  50  0.7  180 160 140 120 100 80  Efficiency  0.5  r DV [mm]  0.6 Efficiency  r DV [mm]  0.7  180 160 140 120 100 80  0  0.2 0.1 50  100  150  DV  0  (b) 700 GeV q, ˜ 494 GeV χ10 0.7  180 160 140 120 100 80  0.6 0.5  Efficiency  r DV [mm]  250 300 |z | [mm] DV  (a) 700 GeV q, ˜ 108 GeV χ10  60 40 20 0 0  200  0.4 0.3 0.2 0.1 50  100  150  200  250 300 |z | [mm]  0  DV  (c) 1.5 TeV q, ˜ 494 GeV χ10  Figure 5.1: Signal vertex efficiency rDV vs. |zDV | after all selection criteria except material veto, for (a) ML (medium squark, light neutralino) is the 700 GeV q, ˜ 108 GeV χ10 sample; (b) MH (medium squark, heavy neutralino) is the 700 GeV q, ˜ 494 GeV χ10 sample; (c) HH (heavy squark, heavy neutralino ) is the 1.5 TeV q, ˜ 494 GeV χ10 sample.  5.2  Efficiency vs. cτ  Hypothesis 5.1 Given a signal vertex, its reconstruction efficiency at a particular location in the detector does not depend on its lifetime cτ. Using Hypothesis 5.1, we can obtain the average signal efficiency εDV (cτ) and not rely solely on the specific cτ generated for the MC samples. To illustrate, we use Figure 5.2 as an example to introduce the following steps to obtain the efficiency for a desired cτ: 1. For each toy event, randomly sample an (η, β γ) value from the probability density function d − β γcτ  PDF (see Figure 5.2 top left) and a decay distance from an exponential PDF e  , for the  chosen cτ. The aim is to produce a decay position PDF as in Figure 5.2 (top middle). 58  2. Sample a value of zPV from a Gaussian PDF of the PV z-position in data (top right of Figure 5.2). Shift the DV position by an amount equivalent to zPV to mimic the spread of PV (origin of neutralino production) in the data. 3. Associate each point with the effficiency from the 2D εDV map. 4. After generating enough toys, one can obtain εDV (cτ) =  ∑bins Ni εi , ∑bins Ni  (5.16)  with Ni as the number of toys that fall within the 2-dimensional εDV map bin (bottom of Figure 5.2).  (a) β γ vs. η  (b) ε in (|zDV |, rDV ) relative to the toy PV(0, 0, 0)  (c) PV z-position in the data  (d) ε in (|zDV |, rDV ) relative to the PV in data  Figure 5.2: 700 GeV q, ˜ 494 GeV χ10 . Top plots (left to right) : Distributions of β γ vs. η, decay position (|zDV |, rDV ) with respect to the toy PV (toy MC), z-position of the PV in the data. Bottom plot : decay position with respect to the PV in data, based on the random choice of values from each of the top plots, according to their PDFs.  The resulting vertex efficiency can then be converted to an event-level efficiency via 2 . These are shown in Figure 5.3. We vary the efficiency in each bin in the εevt = 2εDV − εDV  (|zDV |, rDV ) efficiency maps and re-perform the steps above multiple times. The uncertainty of 59  (a)  (b)  Figure 5.3: The left plot shows the vertex selection efficiency as a function of proper decay length cτ. The right plot shows the event-level efficiency (solid curves), with the values obtained directly from the signal MC samples superimposed along with the values of cτ used in the generation of the samples (dashed lines).  the efficiency is taken as the range that encloses a central 68% of the observed efficiency band. These are shown in Figure 5.4 for εevt . The uncertainty was observed to be small. We have tested  (a)  (b)  Figure 5.4: (a) : Event efficiency εevt vs. cτ, plotted multiple times after varying the efficiency in each bin of the 2D efficiency map randomly within its uncertainty. (b) : εevt (solid lines) and the resulting uncertainty (dashed lines), from taking the central 68% of the curves on the left plot. We observe that the uncertainties are small. Also indicated are the original MC samples cτ and its corresponding εevt .  Hypothesis 5.1 using the MC samples MH and HH, where they differ only by their Lorentz boost β γ vs. η distributions (see Figure 5.5). We reweigh the HH sample vertex-by-vertex such that its  60  (a) MH  (b) HH  (c) Lifetime  Figure 5.5: Relativistic boost β γ versus η in the MC truth for (a) MH and (b) HH samples. Figure (c) shows the exponential lifetimes for the two samples MH and HH.  β γ vs. η and lifetime cτ distributions match those in the MH sample, and have verified that the efficiency spectra for the MH and the reweighted HH samples agree. These are shown in Figure 5.6.  (a) Efficiency vs. rDV  (b) Efficiency vs. zDV  Figure 5.6: Vertex finding efficiency after all cuts (except material veto) vs. (a) rDV (a) and (b) zDV for the MH and reweighted HH sample. Note, the efficiency dip-and-rise in (a) is attributed to DV tracks sharing Pixel hits and hence failing selections.  61  5.3  Systematics  In this section, the systematics on the total efficiency will be described. • Trigger We correct the MC trigger efficiency for a single muon using a scale factor SF, defined to be SF =  εdata , εMC  (5.17)  where εdata and εMC is the total efficiency in the data and MC respectively. Note that, the scale factor is applied to εDV . The efficiency in the data and MC are measured using a Z → µ µ  tag-and-probe method [98]. This method identifies two oppositely charged muons in each event that would originate from Z decay via a requirement that |mµ µ − mZ | < 10 GeV and  ∆φµ µ > 2. The 2 muons in one event are placed under 2 categories — tag and probe. Tag muons must satisfy 1. pT > 20 GeV 2. |z0 | wrt PV < 10 mm, | σdd0 | < 10 0  3.  ∑ pT tracks (∆Rµ,tracks <0.2) pT µ  < 0.1  4. Trigger matched. The probe muons should satisfy at least criteria (1)-(3). The efficiency for the EF_mu40_MSonly_barrel(_medium) trigger is extracted via a parameteric fitting to the turnon curves from the data and MC separately, i.e. the curve of the efficiency vs. the pT of the muon, with the following function: f (pT ) =  pT − µ √ 2σ  ε · 1 + erf 2  ,  (5.18)  where µ, σ , and ε are the 3 fit parameters and erf is the Gaussian error function [99]: 2 erf (z) = √ π  z  2  e−t dt.  (5.19)  0  The trigger efficiency on the plateau of the turn-on curve is ε (see Figure 5.7). The efficiency for pT > 50 GeV for the EF_mu40_MSonly_barrel in the MC and in the data,  62  as well as the scale factor are εMC = 0.70 ± 0.001, εdata = 0.69 ± 0.001, εdata = 0.98 ± 0.002. εMC  (5.20)  For the EF_mu40_MSonly_barrel_medium trigger, they are εMC = 0.66 ± 0.001, εdata = 0.60 ± 0.001, εdata = 0.91 ± 0.002. εMC  (5.21)  A systematics of 3.3% is attached to each of the scale factor: 0.1% from the trigger turn-on curve fitting and 3.2% from the efficiency difference in the signal sample and Z → µ µ sample using MC. We have examined the trigger efficiency vs. d0 and z0 . No strong dependence is observed with these two quantities (see Figure 5.8).  (a)  (b)  Figure 5.7: Trigger efficiency vs. probe muon pT for the (a) EF_mu40_MSonly_barrel and (b) EF_mu40_MSonly_barrel_medium trigger. Note, the trigger efficiency in principle cannot achieve 100% due to the incomplete coverage of the muon trigger system by the RPC (see Section 2.6).  • Track reconstruction We randomly remove 4.3% (3.5%) of the DV tracks in the barrel (endcap) from the signal events before vertexing procedure and compare that to the nominal efficiency. The fraction of tracks to be removed for a neutralino decaying in some location L was decided by com63  (a) d0  (b) z0  Figure 5.8: Trigger efficiency vs. muon (a) d0 and (b) z0 in the signal MC sample.  puting the ratio  Number of Ks →ππ decays at L Number of Ks →ππ decays at the beam-pipe  in the JetTauEtmiss stream data and QCD  MC samples, as recommended by the Tracking Performance Group [100]. A data/MC ratio is formed and the largest deviation from 1 is converted into the fraction of tracks needed to be removed prior to vertexing. The difference between track-killed efficiency vs. nominal efficiency (see Figure 5.12) is taken as the systematics from the tracking reconstruction.  Figure 5.9: Nominal signal εevt (solid lines) and tracks-killed εevt (dashed lines).  • Vertex reconstruction The vertex quality cut, which is nominally at χ 2 per degree of freedom > 5 is varied between 4 and 6. The resulting change in the signal efficiency is found to be less than 1%. As a  64  cross-check, the vertex quality cut is varied in the data and the background MC samples, and the shape of their distributions in rDV are compared [101]. Their relative difference is found to be less than 1% for χ 2 per degree of freedom > 2.5. Based on these studies, a relative systematic uncertainty of 1% is applied to the signal efficiency. • Muon reconstruction Scale factors from the ATLAS Muon Combined Performance group (MCP) have been applied to correct the MC to the data [93]. We find that its has < 1% effect on our event efficiency. We have also examined  εdata εMC  vs. d0 which is not considered in the MCP scale factors. The  corresponding d0 data/MC ratio and its contribution to εevent is given in Figure 5.11. The data/MC ratio is found by comparing the data (cosmics muon sample) and MC (signal sample), normalizing it to unity at 2 < |d0 | < 4 mm, after reweighting the samples such that their η distributions match [100], as shown in Figure 5.10.  (a) before reweighting  (b) after reweighting  Figure 5.10: The η distributions of the cosmics and signal sample (a) before and (b) after the reweighting. The data points are from cosmics, and the histograms are from the signals.  • Signal MC composition  The production of neutralinos from the squarks can occur through qq and qq¯ channels. These two production channels produce a non-negligible difference in the β γ distributions for their daughter neutralinos. As recommended by the ATLAS SUSY group, we have compared the signal efficiency maps produced using Pythia and Prospino [102] MC generators, with the latter performing a next-to-leading-order calculation. The difference between the qq and qq¯ 65  Data/MC ratio  3.5 3  ATLAS  1.5  s = 7 TeV  1  2.5  0.5  2  0 -40  1.5  -20  0  20  40  1 0.5 0 -300  -200  -100  0  100  200  300  Muon d0 [mm]  (a) muon d0 data/MC ratio  (b) systematics from muon d0  Figure 5.11: (a) : muon d0 data/MC ratio. (b) : Contribution to efficiency uncertainty from muon d0 (dashed lines), with nominal shown in solid lines.  compositions was found to have negligible contribution to the signal efficiency. • Pile-up To match the distributions of the pile-up µ (the average number of pp interactions per event) in the MC and data, we have used the PileupReweightingTool package [103]. The change on the signal efficiency was found to be negligible before and after the pile-up reweighting. Adding all systematics and statistical uncertainties in quadrature yields the efficiency curve in Figure 5.12.  66  Event selection efficiency  0.6  MH  0.5  ATLAS  ML  0.4  simulation  HH  s = 7 TeV  0.3 0.2 0.1 0  1  102  10  103 cτ [mm]  Figure 5.12: The event selection efficiency as a function of cτ for the three signal samples. The total uncertainties on the efficiency are shown as bands.  67  6  Background Estimation The estimation of backgrounds is done in a data-driven way. To facilitate the background estimations to the signal search, the search regions are labeled as in Figure 6.1. For Region 0, we expect a background of 0+0.06 events. Details are given in Section 6.1 and −0  6.1.1.  For Regions 1-8, we expect a background of (4 ± 4) × 10−3 events. Details are given in Section  6.2 and 6.2.1.  Figure 6.1: Labels for different regions of the detector in terms of (|zDV |, rDV ), used for background estimation.  68  6.1  Region 0 Background Estimation  Tracks in an event can randomly combine to make a fake displaced vertex. This forms a background in the region near the primary vertices which is defined as Region 0 (Figure 6.1). The estimation of the background is problematic using the MC owing to the finite statistics of the MC samples and possibility of imperfect simulation. We use a data-driven background estimation instead. The background is estimated via Nbkg = F (d [ triggered muon, DV ] < 0.5 mm) · NDV , where NDV is the  number of DV satisfying all selection cuts and F is the fraction of DV which statisfies the criteria where the distance between the triggered muon and the DV, d [ triggered muon , DV ] < 0.5 mm. NDV is found via an ABCD method, which has also been used in other studies [104][105][106]. In an ABCD method, we first find two variables X and Y which are uncorrelated in terms of the background we are interested in, so as to define the x- and y-axis of a two-dimensional space. Then, the signal region is defined by the conditions on X and Y separately. The line of equations of these constraints divide the two-dimensional space into four quadrants or regions: A,B,C and D, of which one of them is the signal region. Because the two variables are uncorrelated, one can write µC =  µA µB  · µD ,  where quadrant C is the signal region and µA,B,C,D are the number of expected backgrounds in quad-  rants A,B,C and D. We show an example of the four ABCD quadrants we have used for this work in Figure 6.2. In the ABCD method shown in the Figure, the y-axis is the DV yield found in either the JetTauEtmiss stream events of the EF_mu40_MSonly_barrel(_medium) events, while the x-axis is the vertex mass mDV (see Figure 6.2). The mDV control region is 4 < mDV < 10 GeV, to avoid contamination from SM hadron decays. Treatment of events in the JetTauEtmiss stream, including reweighting, is described in Section 6.1.1. To obtain a larger statistical sample containing fake DVs, the vertexing process is run with a loosened requirement |d0 | > 1 mm in the JetTauEtmiss stream.  We have chosen the JetTauEtmiss stream events since they have a large number of tracks per event, thus a larger statistics of the background DV, compared to the EF_mu40_MSonly_barrel(_medium)triggered events. Assuming background only, we follow the prescription from the Statistics Forum [107] and parameterize the expected number of fake DV in different quadrants as :    NC = µCK + µC     N = µ K + µ D  D  D    NA = µAK + µC τD     N = µ K + µ τ B D D B  (6.1)  where µC is the expected fake DV (random track combinations) in the signal box C of EF_mu40_MSonly_barrel(_medium) in which we are interested and µD is the expected background  69  Figure 6.2: The ABCD box notation. The x-axis is the vertex mass and the y-axis is the JetTauEtmiss- or EF_mu40_MSonly_barrel(_medium)-triggered events. In this method, the data is divided into four quadrants: A,B,C and D. The number of expected background in the signal region, which is shown as quadrant C, is related to the other three quadrants by µC µA µD = µB , where the number of expected backgrounds in quadrants A,B,C and D are denoted as µA ,µB ,µC and µD .  yield in control region D for the JetTauEtmiss stream. The quantity τD is introduced as a scaling factor to relate {µA , µC } to {µB , µD } via  µC µD  =  µA µB  =  µ C τD µD τD  for the random combination DV in the  ABCD box. NA,B,C,D are the observed data in each quadrant. K µA,B,C,D denote the number of other background DV (non-random track combinations) contam-  inating the A,B,C and D quadrants. As real hadron decays are negligible in the quadrants, we drop K µA,B,C,D from Equation 6.1. With the equation simplified, the expected background in signal box C  and its uncertainty can be found by solving simultaneously the 3 equations governing µD , µA and µB in a likelihood estimation: L(NA , NB , ND | µC , µD , τD ) =  70  e−µi µini ∏ ni ! , i=A,B,D  (6.2)  where NA,B,D in are the observed data and the floating parameters are µC with nuisance parameters µD and τD . The expected background yield from random track combinations is NDV is 0+0.06 (see −0  Figure 6.3).  An 8% systematics (see Section 6.1.1) is assigned to account for the differences in mDV distribution in the JetTauEtmiss sample and signal sample. Varying the control region mDV range yields a systematic uncertainty of 2%. With the limited statistics available in MC and data, we quote con(from the ABCD servatively for the estimated background (region before beam pipe) to be 0+0.06 −0  result), assuming the fraction of NDV satisfying d [ triggered muon, DV ] < 0.5 mm is 1. Given the  low number of background vertices, we take the conservative estimate of 0+0.06 background events. −0 The low background is expected as most fake but high track multiplicity vertices can only originate from random combination of tracks in the same jet, in which the relative angle between tracks are small, rendering a low invariant mass vertex. 4.4 fb-1  Signal Region (signal sample) Observed EF_mu40_MSonly 0 N trk ≥ 5 Observed 0 barrel(_medium) Expected 0+0.06 -0  JetTauEtmiss  5 4 3  Observed 2  Observed 17  6  2 1  5  10  15  20  25  30  Number of vertices  s = 7 TeV  0  Mass [GeV]  Figure 6.3: ABCD box result for the expected number of background vertices NDV in Region 0 of the EF_mu40_MSonly_barrel(_medium) data defined by Ntrk ≥ 5 and mDV > 10 GeV.  6.1.1  Justification of the ABCD Method  The aim here is to estimate the number of DV in the EF_mu_40_MSonly_barrel(_medium) triggered events, NDV . Our first attempt to reproduce the distributions of DV originating from random track combinations in the data was to randomly combined any 2,3,4 or N tracks in an event to form a 2-,3-,4- or N-track DV. The results in Figure 6.4 comparing the vertex mass obtained from this method and the data show that they do not agree. In the same Figure, the mass from our random combinations have a stronger or flatter spectra compared to the data in the high mass region. This indicates to us that there are some correlations in the data, which are not accounted for, in our attempt to pick any set of tracks to construct a vertex.  71  Figure 6.4: From Ref. [108]. The left plot shows the vertex mass distributions from the events in the JetTauEtmiss stream. The right plot shows the vertex mass distributions constructed from randomly combining the tracks in an event in the left plot.  Although tracks can randomly combine to produce a fake DV, particles emission are correlated in some way, as they come from some larger entities, including jets (through the hadronization of quarks and gluons) and underlying events. Defining a neighbourhood as the space around a particle trajectory, we state the following ansatz: • Particles with common properties “see” the same neighbourhood. Tracks in a vertex are within the same neighbourhood.  To perform the background estimation, we parameterize the random tracks fake vertices by 2 properties: the leading pT track, pTlead and the number of tracks, Ntrk in the vertex, since a vertex mass distribution is related to Ntrk . The leading pT track act as a surrogate, providing information on the neighbourhood around the DV. The current statistics does not allow us to further parameterize the data, for example, by η (for tracking efficiency and resolution). We have chosen the parameters to be pTlead and Ntrk as their correlation with the vertex mass is expected to be stronger. The number of DV with a given vertex mass mDV in the mDV > 10 GeV signal region (SR) for the signal sample is EF_mu40 EF_mu40 NDV (mDV , SR) = ∑ NDV (s) · PDFEF_mu40 (mDV , SR | s) ,  (6.3)  s  where we have shortened the full trigger name to EF_mu40. The PDF (mDV , SR | s) is part of the  entire probability density function governing mDV in the SR given a set of selections or parameterization conditions {s}. In our case, we have chosen {s} = {pT lead , Ntrk }. 72  Let the JetTau data be any data not triggered by EF_mu40_MSonly_barrel(_medium) and denoting CR as the control region, the ansatz can be written : PDFEF_mu40 (mDV | s) = PDFJetTau (mDV | s) ,  PDF EF_mu40 (mDV , SR | s) = PDFJetTau (mDV , SR | s) , =⇒ PDF (m , CR | s) = PDF (m , CR | s) , EF_mu40  =⇒  DV  JetTau  CR  (6.5)  DV  EF_mu40 EF_mu40 NDV (s) · PDFEF_mu40 (CR | s) NDV (s) · PDFEF_mu40 (mDV , SR | s) = , JetTau JetTau NDV (s) · PDFJetTau (CR | s) NDV (s) · PDFJetTau (mDV , SR | s)  where PDF (CR | s) =  (6.4)  (6.6)  dmDV PDF (mDV , CR | s). Using Equation 6.6 in 6.3, one obtains  EF_mu40 NDV (mDV , SR) = ∑ s  EF_mu40 NDV (CR | s) JetTau · NDV (mDV , SR | s) JetTau NDV (CR | s)  (6.7)  where N (CR | s) = ∑ N (s) · P (CR | s). s  The right side of Equation 6.7 can be interpreted as a sum of multiple ABCD methods, with each ABCD box parameterized by some {s} = {pTlead , Ntrk }, as illustrated pictorially in Figure 6.5.  We reweight the JetTauEtmiss DV {pTlead , Ntrk } to those in the signal sample, using only the CR.  The weight factors from the CR (the ratio in the right side of Equation 6.7) from all the ABCD boxes, which are parameterized by {pTlead , Ntrk }, are used to reweight the JetTauEtmiss sample in the SR. Using this reweighting, the shape of mDV distributions for N EF_mu40 and N JetTau , when  projecting out by pTlead or Ntrk are predicted to agree for all {pTlead , Ntrk }. Since we are working with the entire EF_mu40_MSonly_barrel(_medium) data of 2011, the JetTauEtmiss events are taken  from the whole 2011 as well for this reweighting approach to minimize any systematics from pileup effects. Note, the JetTauEtmiss data can be substituted with any other set of data.  73  Entries  Before reweighting  104 10  3  EF_mu40_MSonly_barrel_medium  102  JetTauEtmiss  10 1 10-1 10-2  20  40  60  80  100  120  140 m DV [GeV]  DV (Muons) DV (Jets)  2 1.5 1 0.5  Entries  0  After reweighting  102  EF_mu40_MSonly_barrel_medium  10  JetTauEtmiss  1 10  -1  10-2  20  40  60  80  100  120  140  DV (Muons) DV (Jets)  m DV [GeV] 2 1.5 1 0.5 0  Figure 6.5: Illustration interpreting the reweighting framework. The dataset which passing the EF_mu40_MSonly_barrel(_medium) trigger and the JetTauEtmiss stream dataset are splitted into different categories according to the leading pT and number of tracks associated to the displaced vertex. For each category, we compute the ratio between the yield in the control region of the dataset which have passed the EF_mu40_MSonly_barrel(_medium) trigger and the JetTauEtmiss stream. This ratio is a scaling factor, which is then applied to the signal region of the JetTauEtmiss stream data to scale the mDV spectra. After all {pTlead , Ntrk } categories have been scaled, we combine all the JetTauEtmiss stream spectra from each category to produce a new spectra, which is expected to describe sufficiently well the mDV spectra in the signal region of the EF_mu40_MSonly_barrel(_medium) data.  74  We have tested the reweighting framework with events from the JetTauEtmiss stream with a control or an inverted sample taken from EF_mu40_MSonly_barrel(_medium) events containing the triggered muon which fails |d0 | > 1.5 mm, as well as with the MC only. Figure 6.6 shows  the mDV distributions for the before-and-after reweighting for the control sample and JetTauEtmiss stream. The Control Region (CR) is chosen to be 4 < mDV < 10 GeV, to avoid contamination from real hadron decays. Figure 6.7 gives the tracks pT and η in the DV and the MET spectra before and  105  4.4 fb-1  Before reweighting  104  inverted EF_mu40_MSonly_barrel(_medium)  2-tracks DV  103  Vertices  Vertices  after reweighting of Figure 6.6.  105  102  10  10  1  1  10-1  10-1  40  60  80  100  120  After reweighting inverted EF_mu40_MSonly_barrel(_medium)  2-tracks DV  103  JetTauEtmiss  102  20  4.4 fb-1  104  20  40  JetTauEtmiss  60  80  4 2 0 -2 -4  2 0 -2 -4  Before reweighting inverted EF_mu40_MSonly_barrel(_medium)  3-tracks DV  10  (b) 2-track DV : After  Vertices  Vertices  4.4 fb-1  JetTauEtmiss  4.4 fb-1  102  After reweighting inverted EF_mu40_MSonly_barrel(_medium)  3-tracks DV  10  JetTauEtmiss  1  1 10-1  20  40  60  80  100  10-1  120  20  40  60  80  Mass [GeV]  100  120  Mass [GeV]  4  Significance  Significance  120  4  (a) 2-track DV : Before  102  100  Mass [GeV] Significance  Significance  Mass [GeV]  2 0 -2 -4  (c) 3-track DV : Before  4 2 0 -2 -4  (d) 3-track DV : After  Figure 6.6: The invariant mass mDV distribution for the EF_mu40_MSonly_barrel(_medium) control (inverted) sample and JetTauEtmiss, before and after the reweighting. Figure (a) and (b) show the distributions before and after reweighing for 2-track DVs, while Figure (c) and (d) show the distributions before and after reweighting for 3-track DVs. The JetTauEtmiss sample in the “Before reweighting” is normalized to the EF_mu40_MSonly_barrel(_medium) entries in the CR (4 < mDV < 10 GeV).  Figure 6.8 shows the framework tested with the MC only, which is equivalent to 0.4 fb−1 worth of statistics. With the MC statistics, limited by the number of events available in the QCD MC  75  Vertices  Vertices  105  Before reweighting  104  inverted EF_mu40_MSonly_barrel(_medium)  ≤ 3-tracks DV  103  105  102  10  10  1  1  10-10  10-10  40  60  80  100  140 160 180 200 pT of tracks in DV [GeV]  2 0 -2 -4  20  40  60  80  Vertices  Vertices  120  140 160 180 200 pT of tracks in DV [GeV]  2 0 -4  (b) pT  Before reweighting  3  10  102  After reweighting  104 3  10  102 inverted EF_mu40_MSonly_barrel(_medium)  10 ≤ 3-tracks DV  1 10-1-3  100  -2  (a) pT  104  JetTauEtmiss  4  Significance  Significance  4  120  inverted EF_mu40_MSonly_barrel(_medium)  ≤ 3-tracks DV  103  JetTauEtmiss  102  20  After reweighting  104  -2  -1  JetTauEtmiss  0  inverted EF_mu40_MSonly_barrel(_medium)  10 ≤ 3-tracks DV  1  1  2  10-1-3  3  -2  -1  JetTauEtmiss  0  1  η of tracks in DV 2 0 -2 -4  2 0 -2 -4  Before reweighting inverted EF_mu40_MSonly_barrel(_medium)  10  10  40  JetTauEtmiss  10  ≤ 3-tracks DV  1 60  4  80  10-10  100 120 ~ MET of DV [GeV]  Significance  Significance  20  inverted EF_mu40_MSonly_barrel(_medium)  3  102  ≤ 3-tracks DV  1  After reweighting  104 10  JetTauEtmiss  102  10-10  (d) η Vertices  Vertices  (c) η  3  3  4  Significance  Significance  4  104  2  η of tracks in DV  2 0 -2 -4  (e) MET  20  40  60  4  80  100 120 ~ MET of DV [GeV]  2 0 -2 -4  (f) MET  Figure 6.7: Tracks pT (Figure (a) and (b)) and η (Figure (c) and (d)) associated to the DV and MET of DV (Figures (e) and (f)) after reweighting in Figure 6.6 for mDV > 10 GeV and Ntrk ≤ 3. The JetTauEtmiss samples in the “Before reweighting” in Figure (a),(c) and (e) are normalized to the total EF_mu40_MSonly_barrel(_medium) entries.  76  sample, the reweighting result shows a consistency within the 8% difference from the before-and-  103  Before reweighting  102  Monte Carlo EF_mu40_MSonly_barrel(_medium) Monte Carlo (passing JetTauEtmiss triggers)  2-tracks DV  10  Vertices  Vertices  after reweighting of Figure 6.6.  103  1  -1  10-1  10  20  40  60  80  100  120  10-2  140  Monte Carlo EF_mu40_MSonly_barrel(_medium) Monte Carlo (passing JetTauEtmiss triggers)  2-tracks DV  10  1  10-2  After reweighting  102  20  40  60  80  100  120  140  Mass [GeV]  4  Significance  Significance  Mass [GeV] 2 0 -2 -4  4 2 0 -2 -4  (a) 2-track DV : Before  (b) 2-track DV : After  Figure 6.8: The invariant mass mDV distribution (a) before and (b) after reweighting in the MC for 2-track DV. The MC sample is divided into those that passed and those that failed EF_mu40_MSonly_barrel(_medium) trigger. For events which failed, they should pass the triggers in the JetTauEtmiss stream.  To enlarge the statistics in the JetTauEtmiss sample, we have loosened the track d0 cut for the vertexing process to |d0 | > 1 mm. Results of the loosened cut at |d0 | > 0.5, 0.75, 1.0, 1.5 and 2.0  20  ×103 2-tracks DV  19  Observed Estimated (After reweighting) Estimated (Before reweighting)  18  Vertices  Vertices  mm are presented in Figure 6.9 with their corresponding mDV distributions in Figure 6.10.  130  Observed Estimated (After reweighting) Estimated (Before reweighting)  110 100  17  90  16  80  15 14 0  3-tracks DV  120  70 0.2 0.4 0.6 0.8  1  60 0  1.2 1.4 1.6 1.8 2 Loosened |d0| [mm]  (a) 2-track DV  0.2 0.4 0.6 0.8  1  1.2 1.4 1.6 1.8 2 Loosened |d0| [mm]  (b) 3-track DV  Figure 6.9: The expected yield of the JetTauEtmiss sample before and after reweighting compared to the magenta line which indicates the number of observed DV. The d0 of the tracks are loosened to |d0 | > 0.5, 0.75, 1.0 and 1.5 mm. The yields for 2-track DV and 3-track DV are shown in Figure (a) and (b) respectively.  77  4.4 fb-1  4  10  3  10  After reweighting inverted EF_mu40_MSonly_barrel(_medium)  ≤ 4-tracks DV  1 10-1  105  10  10 1  0  40  60  80  After reweighting inverted EF_mu40_MSonly_barrel(_medium)  ≤ 4-tracks DV  JetTauEtmiss  102  track |d | > 1.5 mm 20  4.4 fb-1  104 3  JetTauEtmiss  102 10  Vertices  Vertices  105  100  10-1  120  track |d | > 1.0 mm 0  20  40  60  80  Mass [GeV] 4  Significance  Significance  2 0 -2 -4  2 0 -2 -4  104 103  After reweighting inverted EF_mu40_MSonly_barrel(_medium)  ≤ 4-tracks DV  1 -1  10  105  10 1  0  40  60  80  After reweighting inverted EF_mu40_MSonly_barrel(_medium)  ≤ 4-tracks DV  JetTauEtmiss  102  track |d | > 0.8 mm 20  4.4 fb-1  104 103  JetTauEtmiss  102 10  (b) |d0 | > 1.0 mm Vertices  Vertices  (a) |d0 | > 1.5 mm 4.4 fb-1  100  -1  10  120  track |d | > 0.5 mm 0  20  40  60  80  Mass [GeV]  100  120  Mass [GeV]  4  Significance  Significance  120  Mass [GeV]  4  105  100  2 0 -2 -4  (c) |d0 | > 0.75 mm  4 2 0 -2 -4  (d) |d0 | > 0.5 mm  Figure 6.10: The mDV distributions for Ntrk ≤ 4 DV after the reweighting for events in the JetTauEtmiss stream with loosened d0 criteria: Figure (a) for |d0 | > 1.5 mm, Figure (b) for |d0 | > 1.0 mm, Figure (c) for |d0 | > 0.75 mm and Figure (d) for |d0 | > 0.5 mm.  Given the low statistics that we will meet for high Ntrk , it is sufficient to have one ABCD box. No {pTlead , Ntrk } reweighting is done. The expected background yield from ABCD can be  computed via a maximization of the likelihood in the Equation 6.2, with loosened |d0 | > 1 mm for the vertexing in the JetTauEtmiss. Utilising a single ABCD box, we have also tested our predictions  from the reweighting procedure in the signal sample with in a Figure 6.11 gives the result for the signal sample (Ntrk ≤ 4, mDV > 10 GeV) and the result for the Ntrk ≥ 5, mDV > 10 GeV non-retracked  signal sample (see Section 3.1.2 for details on the re-tracking program). For the latter case, we took the Poisson mean for region D to be 0+1.1 −0 , where the positive upper limit is such that, 0 events (as observed) occur with probability 32% (1 σ deviation).  The final results for the signal sample with re-tracking have been shown in Figure 6.3. An 8% systematic uncertainty due to differences in the mDV distribution in the JetTauEtmiss sample and  78  (signal sample) Observed With re-tracking EF_mu40_MSonly 5 N trk ≤ 4 Observed 0 barrel(_medium) Expected 2 ± 0.9  JetTauEtmiss  Observed 106266  Observed 268731  5  10  15  20  25  30  ×103 20 18 16 14 12 10 8 6 4 2 0  s = 7 TeV  4.4 fb-1  (signal sample) Observed No re-tracking EF_mu40_MSonly 0 N trk ≥ 5 Observed 0 barrel(_medium)  5 4  +0.04 -0  Expected 0  JetTauEtmiss  3  Observed 0 Assumed 0 +1.1 -0  Observed 13  6  2 1  5  10  15  Mass [GeV]  20  25  30  Number of vertices  4.4 fb-1  Number of vertices  s = 7 TeV  0  Mass [GeV]  (a)  (b)  Figure 6.11: Results from the ABCD method on (a) the control sample (Ntrk ≤ 4 and mDV < 10 GeV) and (b) the signal sample (Ntrk ≥ 5andmDV > 10 GeV but without re-tracking). Here, we took the Poisson mean for region D to be 0+1.1 −0 , where the positive upper limit is such that, 0 events (as observed) occur with probability 32% (1 σ deviation).  signal sample is assigned, based on the background yield differences before-and-after reweighting in low the Ntrk region. Varying the control region mDV range yields a systematic uncertainty of 2%.  6.2  Regions 1-8 Background Estimation  Regions 1-8 (see Figure 6.1) are dominated by interactions of particles produced from pp collisions with material, including sensors, gas and cables in the detector. These interactions are observed as displaced vertices since the material interactions are located away from the beamline. Furthermore, as the vertexing process can mis-associate a random/stray track to a material interaction DV, some of these vertices containing a stray track can potentially be observed as a high mass DV. The fraction of DV that will contain a random or stray track can be obtained via a method that we have called as the Ks + 1-track approach. In this approach, we search for Ks → ππ decay 2-track vertices and 3-track vertices that contain 2 of the tracks satisfying Ks → ππ criteria. These 3-track  vertices are considered as Ks decay vertices + a stray track mis-associated to it. Figure 6.12 shows the Gaussian with polynomial fits to the 2-track combination spectra in the non-material search regions. The Gaussian mean and width for the pure Ks combination and Ks + 1 combination are fixed to be the same. The fraction of Ks associated with a stray track from the fit is equivalent to the fraction of material interaction DV with a stray track associated to it (see Figure 6.13). As can be seen in the results, the fractions are low as expected, since the vertex position resolution is small. Attempts to obtain the probability density functions (PDF) for 5-track and ≥ 6-track DVs are  hampered by low statistics in the MC for the high mass region. We thus construct a data-driven PDF, 79  0.4  0.45  0.5  0.55  0.6  0.65  60  Region 4  Vertices  3  20 18 16 14 12 10 8 6 4 2 0 0.35  Vertices  × 10  18 Region 2 16 14 12 10 8 6 4 2 0 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 Vertices  Vertices  by adding two distributions: a pure material interaction N-track DV spectrum with an (N − 1)-track 50  × 10  3  40 30 20  50  10 0 0.35  0.7  0.4  0.45  10 0 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 mass [GeV]  25 20 15  5 0.4  0.45  0.5  0.55  0.6  0.65  0.7 mass  60  400 350 300 250  Region 8  Vertices  3  30  0 0.35  0.7  (b) Region 4  10  80  0.65  20  Vertices  Region 6  Vertices  Vertices  100  0.6  30  (a) Region 2 × 10  0.55  mass  mass [GeV]  35  0.5  40  mass  × 10 45 40 35 30 25 20 15 10 5 0 0.35  3  0.4  0.45  0.5  0.55  0.6  0.65  0.7 mass  200  40  150 100  20  50  0 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7  0 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7  mass [GeV]  mass [GeV]  (c) Region 6  (d) Region 8  Figure 6.12: Gaussian + polynomial fits to the 2-track invariant mass (for Ks ) distribution of 2-track DV (insets) and 2 track combinations within 3-track DV, using JetTauEtmiss stream data, for Region (a) 2, (b) 4, (c) 6 and (d) 8.  DV spectrum with an extra random track from the event attached to it. The former is taken from DVs that satisfy an average angle between tracks to be < 1 radian, while the latter is constructed from the combinations of all possible tracks in the event with the DV. The fraction or contribution from each distribution in constructing a PDF for N-track DV can be obtained from the result of the Ks + 1 approach. Figure 6.14 looks at the distributions of 3- and 4-track DV with this approach. Let Nin be the number of DV with i-track in the non-material Region n and Nim be the number of DV with i tracks in material Region m, we estimate the number of DV in ≥ 5-track DV for signal 80  region (Regions 2,4,6 and 8) via a simultaneous fit of all 8 regions for 3,4,5 and ≥ 6-track DV  81  Figure 6.13: Probability of DV containing random track in various data streams.  (a) 3-track DV  (b) 4-track DV  Figure 6.14: A method for modelling the invariant mass distribution, by summing two histograms. The solid black line shows the invariant mass distribution for 3-track (middle) and 4track (right) vertices. The blue lines show vertices where no single track has an average angle wrt all the other tracks in the vertex greater than 1 radian, The red histogram is the invariant mass distribution obtained by adding the 4-momentum of a random track to an (N − 1)-track vertex, to simulate random crossings.  expressed in a likelihood: L (N3m , N4m , N5m , N6m , N3n , N4n |µkm , µkn ) =  ∏  i=3,4,5,≥6  Poisson (Nin |µin )·Poisson (Nim |µim )·constraints (6.8)  The constraints in Equation 6.8 are taken from an exponential fit to NDV vs. Ntrk for each Region (32 Gaussian constraints for the Poisson mean taken from the fit) and another 16 constraints from 82  the ratio between µin and the Possion mean for the Region m before it, µim , using events in the JetTauEtmiss and Egamma streams. The constraints to the likelihood and the PDFs are elaborated in the next Section. To obtain the expected background for mDV > 10 GeV, we integrate PDFs for 5-track and ≥ 6-track vertices and multiplying with the yield obtained from maximizing the likelihood in Equation 6.8.  6.2.1  The Constraints in the Likelihood  The constraints in the likelihood in Equation 6.8 are motivated by two ansätze : • Material interaction is independent of the physics stream, be it the JetTauEtmiss, Egamma or the Muons stream.  • Material interaction depends on the density of nuclei in each Region and the energy of the incoming particle interacting with the nuclei.  Denoting τN to be the probability of a nuclei undergoing material interaction to produce an N-track vertex, then, the Poisson distribution of the number of N-track DV produced in Region i given Ni number of nuclei is Poisson (µiN ) = Poisson (Ni · τN ). The ratio of the Poisson mean of Region n (non-material layer) to the Poisson mean Region m (material layer) is  µnN µmN  =  Nn ·τN Nm ·τN  =  Nn Nm ,  implying  that the ratio depends only on the number of nuclei in these two Regions in line with Ansatz 2. Figure 6.15 gives these ratios for various two Regions and we expect that these ratios are the same, regardless of JetTauEtmiss, Egamma or Muons stream (Ansatz 1). These ratios are used to give 16 constraints to the Poisson means in Equation 6.8. The energy of the incoming particle correlates positively with the number of tracks emitted from a material interaction, suggesting a possibility of the existence of some function that relates the expected number of DV, NDV vs. Ntrk in each Region. Figure 6.16 looks at these distributions and an exponential fit to the JetTauEtmiss data. The function is observed to fit well in all Regions and the results of these fits are used to constrain the Poisson means in Equation 6.8. A test on this using other data streams is listed in Table 6.1 with the corresponding distributions in Figure 6.17. The JetTauEtmiss result in the Table from the fit is compared with the actual data yield, providing a consistency check for the method. For events passing the EF_mu40_MSonly_barrel(_medium) triggers, we expect a background of (4 ± 4) × 10−3 vertices. Given the low number of background  vertices, we take the conservative estimate of (4 ± 4) × 10−3 background events. This is not a  surprising result as we do not expect nuclear interactions to have a high invariant mass.  83  Ratio of NDV  Ratio of NDV  0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0  Region 2 : Region 1  0.03  Region 4 : Region 3  0.025 0.02  0.015 0.01 JetTauEtmiss  3  JetTauEtmiss  0.005  Egamma  4  5  0  6  Egamma  3  4  5  Ntrk in DV  (b) NDV ratio of Region 4 : Region 3  Ratio of NDV  Ratio of NDV  (a) NDV ratio of Region 2 : Region 1  0.12  Region 6 : Region 5  0.1  JetTauEtmiss  0.08  Egamma  0.06  0.5  Region 8 : Region 7  0.4  JetTauEtmiss Egamma  0.3 0.2  0.04  0.1  0.02 0  6 Ntrk in DV  3  4  5  0  6 Ntrk in DV  3  4  5  6 Ntrk in DV  (c) NDV ratio of Region 6 : Region 5  (d) NDV ratio of Region 8 : Region 7  Figure 6.15: Ratio of the number of DV, NDV in Region N to those in Region (N − 1) vs. Ntrk in DV for: (a) Region 1 and 2, (b) Region 3 and 4, (c) Region 5 and 6, and (d) Region 7 and 8.  Figure 6.16: The number of displaced vertices, NDV vs. the number of tracks in each displaced vertex, Ntrk with an exponential fit in each Region.  84  Stream JetTauEtmiss Egamma Muons (events failing trigger)  Expected background 859 ± 88 45 ± 7 30 ± 3  Observed 891 52 28  9 8 7  Vertices  Vertices  Table 6.1: Comparing the expected background yield using the method described in this Section and the observed number of DV (Ntrk ≥ 5) in various data streams.  5-tracks DV Muons stream (failed EF_mu40_MSonly)  6  Ntrk PDF  5 4 3  (N-1)  trk  3.5  ≥ 6-tracks DV  3  Muons stream (failed EF_mu40_MSonly)  2.5  Ntrk PDF  2  PDF  (N-1)  1.5  trk  PDF  1  2 1  0.5  0  2  4  6  8  10  12  14  16  18  20  0  2  4  6  8  10  12  14  mass [GeV]  Vertices  Vertices  5-tracks DV  12  Egamma stream  10  Ntrk PDF (N-1)  8  trk  PDF  5  Egamma stream Ntrk PDF (N-1)  trk  PDF  2  4  1  2 2  4  6  8  10  12  14  16  18  20  0  2  4  6  8  10  12  14  mass [GeV]  Vertices  Vertices  JetTauEtmiss stream Ntrk PDF  10  (N-1)  trk  18  20  (d) ≥ 6-track DV (Egamma stream)  5-tracks DV  102  16  mass [GeV]  (c) 5-track DV (Egamma stream)  ≥ 6-tracks DV JetTauEtmiss stream Ntrk PDF  10  PDF  (N-1)  trk  PDF  1  1  10-1 0  20  ≥ 6-tracks DV  4 3  6  0  18  (b) ≥ 6-track DV (Muons stream)  (a) 5-track DV (Muons stream) 14  16  mass [GeV]  2  4  6  8  10  12  14  16  18  10-1 0  20  mass [GeV]  2  4  6  8  10  12  14  16  18  20  mass [GeV]  (f) ≥ 6-track DV (JetTauEtmiss stream)  (e) 5-track DV (JetTauEtmiss stream)  Figure 6.17: Distributions of 5,≥ 6-track DV compared with PDFs using different data streams.  85  7  Search Results No vertices were found in the signal region after it was unblinded, consistent with the expected background of < 0.06. The unblinding is done once the non-signal regions have been understood and consistency checks on the kinematics distributions of the displaced vertices between our dataof-interest and other datasets used in the data-driven background estimation, have been performed. If there was any excess in the data vs. our expectation, there are several variables that can be used to understand the events in the data, including the angles subtended by every two tracks in the vertex, its vertex coordinates and any calorimeter energy deposition that matches to the decay products in that vertex. The subtended angles are useful, since signal vertices have large angles between the two jets and the muon, while the backgrounds do not. The calorimeter energy is useful to check the consistency of the tracks and their momentum sum to that of the corresponding calorimeter energy. Figure 7.1 shows the data and a simulated signal sample overlaid. To aid readers to visualize how a DV looks like in the data, we show two events in the data which have failed some selection criteria but containing a reconstructed displaced vertex with a large mass and a large number of tracks (see Figure 7.2 and Figure 7.3).  86  Vertex mass [GeV]  1.4 2  10  1.2 ATLAS  10  1  Signal region  ∫Ldt = 4.4 fb  0.8 Data 2011  -1  1  Signal MC  s = 7 TeV  3 4 5 6 7 8 10 20 30 40 Number of tracks in vertex  0.6 0.4 0.2 0  Figure 7.1: Vertex mass (mDV ) vs. vertex track multiplicity (Ntrk ) for displaced vertices in events with no muon requirements other than the trigger, and all other selection criteria except the mDV and Ntrk requirements. Shaded bins show the distribution for the Monte Carlo simulated signal HH sample (see Table 4.1), and the data are shown as filled ellipses, with the area of the ellipse proportional to the number of vertices in the corresponding bin.  87  Muon pT = 39 GeV d0 = −0.4 mm DV mass = 11 GeV 8 tracks (rDV , zDV ) = (56, 131) mm Tracks pT [GeV] pz [GeV] 17.5 40.3 25.1 11.0 5.6 13.6 4.1 1.8 1.7 3.7 1.6 3.2 1.3 2.5 0.4 1.2  Figure 7.2: Run 189822, Event 71110743 (passed EF_mu40_MSonly_barrel_medium). The DV fails the material veto cut. A legend is given in Appendix B.  88  DV mass = 14 GeV 8 tracks (rDV , zDV ) = (85, 279) mm Tracks pT [GeV] pz [GeV] 11.6 38.7 8.0 26.8 4.1 12.3 4.0 15.1 3.7 11.8 1.3 0.1 1.2 4.1 1.2 3.0  Figure 7.3: Run 189875, Event 19332017 (failed EF_mu40_MSonly_barrel(_medium)). A legend is given in Appendix B.  89  7.1  Limits on New Particle Production  Given that no excess was found in the signal region, we proceed to set limits on the models considered. Figure 7.4 shows the squark pair production cross section × BR limits, set for various  neutralino mass vs. cτ at the 95% confidence level using the CLs method [109], where BR is the branching ratio for a squark to decay, via a long-lived neutralino, to charged hadrons and a muon. The cross sections are calculated with the Prospino Monte Carlo simulator [102], with the uncertainties computed using two different sets of parton distribution functions (CTEQ6.6 and MSTW2008NLO [110]), and by varying the factorisation and renormalisation scales each up and down by a factor of two [111]. A 1.8 % luminosity uncertainty is also assigned [112]. We are unable to produce a model independent limit as the displaced vertex reconstruction efficiency is dependent on the lifetime and the Lorentz boost of the long-lived particle of a specific model. Nevertheless, we have chosen MC signal samples containing long-lived neutralinos with different Lorentz boosts to cover different scenario possibilities (see Table 4.1). Based on Refs. [113][114], the CLs method can be described as follows: 1. Given the observed data in the Signal Region, the maximum likelihood L is defined as L (data | σ , θ ) = Poisson data | Nsig (σ , θ ) + Nbkg (θ ) · PDF(θ | θ ),  (7.1)  where Nsig and Nbkg are the signal and background yields respectively, which depends on a set of theoretical and experimental nuisance parameters θ . Nsig also depends on the free parameter σ which is the cross section we wish to place an upper limit. The probability density function, PDF for θ are taken to be Gaussian distributions. 2. The CLs method uses the profile likelihood ratio, qσ as the test statistics : qσ = − ln  Lmax σ (data|σ , θˆσ ) Lmax σ ,θ (data|σˆ , θˆ )  for 0 ≤ σˆ ≤ σ , else 0,  (7.2)  where the likelihood in the denominator is to be maximised with respect to σ and the set of nuisance parameters, θ including the expected background, such that at this maxima, σ = σˆ , θ = θˆ . The likelihood in the numerator is to be maximised with respect to θ for a given σ , such that at this maxima, θ = θˆσ . 3. The data in definition 7.2 can be the observed data or pseudo-data generated to obtain the test statistics distributions necessary to compute the CLs value: CLs (σ ) =  Probability(qσ ≥ qobs σ ) , Probability(q0 ≥ qobs 0 ) 90  (7.3)  where qobs is the value when the data is the observed experimental data. To generate the pseudo-data, the best-fit values for θˆ obs and θˆσobs according to the background only and sig0  nal+background hypotheses are used. Any signal with a lifetime cτ giving CLs < 0.05 is excluded at the 95% confidence level.  Figure 7.4: Upper limits at 95% confidence level using the CLs method, on the squark pair production cross section σ times the branching ratio BR for a squark to decay, via a long-lived neutralino, to a muon and quarks, vs. the neutralino lifetime for the three Monte Carlo simulated signal samples (see Table 4.1) with three different combinations of squark and neutralino masses, based on the observation of zero events satisfying all criteria in the 4.4 fb−1 2011 data sample. The expected background for this search is < 0.06. The shaded areas around the three curves (red, green and blue) represent the ±1σ uncertainty bands on the expected limits. The blue and green horizontal lines, with shaded areas around them, show the squark pair production cross sections calculated from the Prospino Monte Carlo simulator. The shaded areas represent the uncertainties on these cross sections. The computation procedures of these uncertainties can be found in Ref. [111]. A 1.8 % uncertainty is assigned to the total 4.4 fb−1 integrated luminosity used in this search [112]. As noted in Table 1.3, this search has never been attempted in other previous experiments. However, we have also previously published one with the 2010 data [115].  91  8  Going Forward We close this work with our outlook going forward for the displaced vertex community in ATLAS. In Section 8.1, we present some of the future challenges for the long-lived neutralino search, and in Section 8.2, we introduced a work in progress of a new idea for an alternate search strategy for long-lived particles with a different decay mode.  8.1  Improvements  Relying on a Muon Spectrometer only muon trigger is not sustainable as the number of pile-up interactions increases with luminosity. A 2012 event is displayed in Figure 8.1, showing the astounding number of pile-ups and one hard interaction PV. With an increase in pile-ups, new but tighter trigger requirements will be introduced. However, these new triggers reduce signal efficiencies. A dedicated displaced vertex trigger will be the way forward and is under progress. The trigger can be initialized at Level 1 where the Inner Detector information is available. A DV dedicated trigger is expected be less susceptible to fakes compared to Muon Spectrometer only triggers.  92  Figure 8.1: An event with a Z → µ µ candidate amongst 25 reconstructed PV in the data collected in 2012.  8.2  pp → V0 +V0 + ISR + X  We have also examined some distributions using the 2012 data, pertaining to possible new signals with a production Lagrangian term gV0V0 qq (see Figure 8.2) with a new Beyond Standard Model (BSM) long-lived V0 → SS (g V0 SS), where g and g are the couplings and S is some charged par-  ticle. Note, we are assuming V0 to be charged under a new BSM sector, hence pair production, or alternatively, Y → V0V0 , i.e. both V0 originate from a new particle Y decay.  In what follows, the long-lived γd from lepton-jets models [116] (see Figure 8.3) and long-lived  πv in Hidden Valley models [117] (see Figure 8.3) will be used as a guide to find some signalbackground discriminators for some generic V0 , i.e. • Lepton-jets : 400 MeV γd , cτ = 60 mm; 93  S q  V0  S  X q¯ V0  ISR  S  S  Figure 8.2: qq → V0 +V0 + ISR + X. All physics objects from the black region are collectively refered to as X. ISR is the initial state radiation from a photon or a gluon.  • Hidden Valley : 40 GeV πv , cτ = 50 mm. The discriminators should ideally be independent of the mass of V0 and contain a “left-right” skew property. We shall first assume nothing about the nature of X.  (a) Lepton-jets : Long-lived γd  (b) Hidden Valley : Long-lived πv  Figure 8.3: Lepton-jets and Hidden Valley models. Figure (a) adapted from [118]. Note, in lepton-jets, the notation l ± refers to e, µ, π. In the Hidden Valley model, πv → fermion + antifermion.  A corollary from Figure 4.9 is that the tracks from V0 are back-to-back in the plane perpendicular to the direction of flight of the V0 , which implies two conditions — same pvis T for both tracks and ∆φ = π. Both these conditions are combined into one variable :  normalized MET,  MET =  94  vis pT vis 1 + pT 2  2  vis pT vis 1 + pT 2  2  (8.1)  While the MET predicts the accumulation of signals near 0, this quantity separates out the background (fakes), so that they are more likely to accumulate near MET = 1. This is due to fake DVs arising mostly from jets, i.e. regions where tracks are travelling within the same angular region.  1  1  Vertices  Vertices  Figure 8.4 displays the spectra of MET for the DVs in the signal and background.  0.4 GeV signal QCD -1  40 GeV signal QCD -1  10  10  10-2  10-2  10-3 0  0.2  0.4  0.6  0.8  10-3 0  1  ~ normalized MET  0.2  (a) 0.4 GeV γd  0.4  0.6  0.8  1 ~ normalized MET  (b) 40 GeV πv  Figure 8.4: The normalized MET computed for each DV for the QCD sample vs (a) γd and (b) πv . Note, the yields in the y-axis are arbitrary. We are more interested in the shape of their spectra. Material veto is used.  Notice however, there are signals accumulating near MET = 1 due to identifying the wrong PV, i.e. the leading PV in the event is not the signal PV. To counter this, we choose the minima of MET for the DV given the whole set of PVs in the event (see Figure 8.5). / as Variable 8.2 (see Figure 8.6). To complement the MET, we introduce METZ  /, normalized METZ  /= METZ  vis pT vis 1 + pT 2  2  vis pT vis 1 + pT 2  2  | detector x-y plane; no z information  (8.2)  / serves 2 purposes. Firstly, the METZ / can help to reduce any ambiguity from a ratio The METZ / is a of two large numbers in MET resulting in a small MET value. Secondly, since the METZ 2-dimensional quantity in momentum and space (no z-component knowledge), it is immune to the misidentification of the hard interaction PV, hence assisting the MET, which is prone to it. Further, we have also examined the spectra of the widely used | cos θ ∗ |, defined to be the  absolute value of the cosine of the angle between the momentum vector of the DV track (in the DV rest frame) and (DV − PV), which are shown in Figure 8.7 and the spectra of also another 95  1  Vertices  Vertices  1 0.4 GeV signal QCD -1  40 GeV signal QCD -1  10  10  10-2  10-2  10-3 0  0.2  0.4  0.6  0.8  10-3 0  1  ~ normalized MET  0.2  (a) 0.4 GeV γd  0.4  0.6  0.8  1 ~ normalized MET  (b) 40 GeV πv  1  0.4 GeV signal  0.8  QCD  0.6  ~ normalized METZ  ~ normalized METZ  Figure 8.5: Minima of normalized MET given the whole set of PVs in an event for the QCD sample vs (a) γd and (b) πv . Note, the yields in the y-axis are arbitrary. We are more interested in the shape of their spectra. Material veto is used.  1  0.8  QCD  0.6  0.4  0.4  0.2  0.2  0 0  40 GeV signal  0.2  0.4  0.6  0.8  0 0  1  ~ normalized MET  0.2  (a) 0.4 GeV γd  0.4  0.6  0.8  1 ~ normalized MET  (b) 40 GeV πv  / vs MET distribution for the QCD sample vs signal (a) γd and (b) πv . Figure 8.6: METZ  commonly used cos α, defined to be the cosine of the angle between the momentum vector of the DV (lab frame) and (DV − PV), which are shown in Figure 8.8.  96  Vertices  Vertices  1 0.4 GeV signal QCD -1  1 40 GeV signal QCD -1  10  10  10-2  10-2  10-3 0  0.2  0.4  0.6  0.8  10-3 0  1  0.2  0.4  0.6  |cos θ*|  0.8  1 |cos θ*|  (a) 0.4 GeV γd  (b) 40 GeV πv  1  Vertices  Vertices  Figure 8.7: | cos θ ∗ | of the QCD sample vs (a) γd and (b) πv .  0.4 GeV signal QCD  1  10-1  10-1  10-2  10-2  10-30.9  0.92  0.94  0.96  0.98  10-30.9  1  40 GeV signal QCD  0.92  0.94  0.96  cos α  0.98  1 cos α  (a) 0.4 GeV γd  (b) 40 GeV πv  Figure 8.8: cos α of the QCD sample vs (a) γd and (b) πv .  8.2.1  Data vs MC  In what follows, we show a first look into some figures for the data and MC pertaining to a displaced vertex V0 search, satisfying the following minimal set of selection criteria : E VENT S ELECTION • the event has a PV. D ISPLACED V ERTEX S ELECTION 97  • 2-tracks opposite-signed; • both tracks should satisfy pT > 2 GeV; • |zDV | < 300 mm and |rDV | < 180 mm; • |rDV − rPV | > 4 mm,  for all PVs in the event;  • material veto; • we run over all PVs in the event, to determine its minima of MET and the corresponding PV is assumed to be the hard interaction PV;  • | cos θ ∗ |< 0.6 for mDV < 1 GeV; • cos α > 0.9; / < 0.2; • METZ • MET > 0.2 (signal-depleted region). Note, the significance has not been optimized. In all Figures hereafter, the MC is normalized to the number of entries in the data in the signal-depleted region. We aim at searching for events with at least one DV in association with some triggered physics objects produced from sector X as in Figure 8.2. Using this selection criteria, the data passing any trigger can be examined for potential new physics. As a demonstration, we have examined the signal-depleted regions in the data passing 3 selected triggers: EF_e18_medium1_g25_loose (requires a pT > 18 GeV electron passing medium1 cuts [119] and a pT > 25 GeV photon passing loose cuts [120]), EF_xe80T_tclcw_loose (requires missing energy > 80 GeV passing a certain trigger chain marked by “T”. Nomenclatures can be found in [121][122]) and EF_j360_a10tcem (requires a jet with tranverse energy ET > 360 GeV. The jet reconstruction process is encoded in the label “a10tcem” [121][122]). Figures related to them are shown in Figure 8.9, 8.10, 8.11, 8.12, 8.13 and 8.14. Note, at this moment, we have insufficient MC compared with the statistics in the data. Our exploration on V0 shall end here. The search on a new V0 displaced vertex is a “work in progress”. So far, we have showed the capabilities of some new quantities in reducing the background and applied them to the 2012 data. Much of course needs to be done to bring into a better agreeement between the MC and the data in the signal-depleted control region. We invite interested readers to continue our exploration in V0 .  98  2  10  s = 8 TeV  tt  EF_e18_medium1_g25_loose  W Z  mass > 10 GeV rDV < 28 mm  -1  14.3 fb  Data  Vertices  Vertices  Data  103  QCD  s = 8 TeV  W Z  mass > 10 GeV rDV > 28 mm  -1  14.3 fb  102  10  tt  EF_e18_medium1_g25_loose  QCD  10 1 10-10  1 0.2  0.4  0.8  10-10  1  ~ Normalized MET  2 0 -2 -4  0.2  tt  EF_e18_medium1_g25_loose  W Z  mass > 10 GeV rDV < 28 mm  -1  14.3 fb  0 -4  105 104 3  QCD  10  10  s = 8 TeV  tt  EF_e18_medium1_g25_loose  W Z  mass > 10 GeV rDV > 28 mm  -1  14.3 fb  QCD  10 1 0.2  0.4  0.6  0.8  10-10  1  Mass [GeV]  0.2  0.4  0.6  0.8  1  Mass [GeV]  4  Significance  Significance  Data  102  1 10-10  1 ~ Normalized MET  2  Vertices  Vertices  10  0.8  (b) rDV > 28 mm  Data  s = 8 TeV  0.6  -2  (a) rDV < 28 mm  2  0.4  4  Significance  Significance  4  0.6  2 0 -2 -4  (c) rDV < 28 mm  4 2 0 -2 -4  (d) rDV > 28 mm  Figure 8.9: Figure (a) and (b) : The spectra of MET for EF_e18_medium1_g25_loose triggered data for rDV < 28 mm and rDV > 28 mm respectively. Mass < 1 GeV. Ks mass window (430 < mDV < 580 MeV) and Λ0 mass window (1100 < mDV < 1130 MeV is vetoed.). Figure (c) and (d) : The mDV distributions for MET > 0.2 data and MC for rDV < 28 mm and rDV > 28 mm respectively. Note, the tracks used to reconstruct the vertices shown in the plots are considered massless.  99  102  tt  EF_e18_medium1_g25_loose  s = 8 TeV  W Z  mass > 10 GeV rDV < 28 mm  -1  14.3 fb  10  103  Vertices  Vertices  Data  0  0.2  0.4  0.6  1 ~ Normalized MET  Significance  Significance  10-1  0.8  2 0 -2 -4  14.3 fb  0  0.2  W Z  mass > 10 GeV rDV < 28 mm  14.3 fb  Data  102  QCD  1 25  30  1 ~ Normalized MET  -4  1 20  0.8  0  10  15  0.6  2  10  35  10-110  40  Mass [GeV]  s = 8 TeV  W Z  mass > 10 GeV rDV > 28 mm  -1  14.3 fb  15  tt  EF_e18_medium1_g25_loose  20  25  30  35  QCD  40  Mass [GeV]  4  Significance  Significance  QCD  -2  Vertices  Vertices  tt  EF_e18_medium1_g25_loose  -1  10-110  Z  (b) rDV > 28 mm  Data  s = 8 TeV  0.4  4  (a) rDV < 28 mm  10  W  mass > 10 GeV rDV > 28 mm  -1  1  4  2  tt  EF_e18_medium1_g25_loose  10  1 10-1  s = 8 TeV  102  QCD  Data  2 0 -2 -4  (c) rDV < 28 mm  4 2 0 -2 -4  (d) rDV > 28 mm  Figure 8.10: Figure (a) and (b) : The spectra of MET for EF_e18_medium1_g25_loose triggered data for rDV < 28 mm and rDV > 28 mm respectively. Mass > 10 GeV. Figure (c) and (d) : The mDV distributions for MET > 0.2 data and MC for rDV < 28 mm and rDV > 28 mm respectively.  100  10  102  tt  EF_xe80T_tclcw_loose  s = 8 TeV  W Z  mass < 1 GeV rDV < 28 mm  14.3 fb-1  3  10  QCD  s = 8 TeV  0.2  0.4  0.6  0.8  10-10  1  -2 -4  0.2  W  1 ~ Normalized MET  0 -2 -4  Z  mass < 1 GeV rDV < 28 mm  5  10  4  10  QCD  s = 8 TeV  tt  EF_xe80T_tclcw_loose  W Z  mass < 1 GeV rDV > 28 mm  14.3 fb-1  103  QCD  102  10  10  1  1 0.2  0.4  0.6  0.8  10-10  1  Mass [GeV]  0.2  0.4  0.6  0.8  1  Mass [GeV]  4  Significance  Significance  0.8  Data  Vertices  Vertices  tt  EF_xe80T_tclcw_loose  14.3 fb-1  0.6  (b) rDV > 28 mm  Data  10-10  QCD  2  (a) rDV < 28 mm  s = 8 TeV  0.4  4  Significance  ~ Normalized MET  0  102  Z  1  2  10  W  mass < 1 GeV rDV > 28 mm  14.3 fb-1  10  4  3  tt  EF_xe80T_tclcw_loose  102  1  Significance  4  10  10  10-10  Data  Vertices  Vertices  Data  3  2 0 -2 -4  (c) rDV < 28 mm  4 2 0 -2 -4  (d) rDV > 28 mm  Figure 8.11: Figure (a) and (b) : The spectra of MET for EF_xe80T_tclcw_loose triggered data for rDV < 28 mm and rDV > 28 mm respectively. Mass < 1 GeV. Ks mass window (430 < mDV < 580 MeV) and Λ0 mass window (1100 < mDV < 1130 MeV is vetoed.). Figure (c) and (d) : The mDV distributions for MET > 0.2 data and MC for rDV < 28 mm and rDV > 28 mm respectively.  101  Vertices  EF_xe80T_tclcw_loose  s = 8 TeV 2  10  tt W Z  mass > 10 GeV rDV < 28 mm  -1  14.3 fb  103  QCD  2  10  10  0  0.2  0.4  0.6  10-1  1 ~ Normalized MET  0 -2 -4  14.3 fb  0  0.2  W Z  mass > 10 GeV rDV < 28 mm  14.3 fb  103  QCD  2  10  1 30  35  10-110  40  Mass [GeV]  s = 8 TeV  W Z  mass > 10 GeV rDV > 28 mm  -1  14.3 fb  15  tt  EF_xe80T_tclcw_loose  20  25  30  35  QCD  40  Mass [GeV]  4  Significance  Significance  1 ~ Normalized MET  Data  1 25  0.8  -4  10  20  0.6  0  10  15  0.4  2  Vertices  Vertices  tt  EF_xe80T_tclcw_loose  s = 8 TeV -1  10-110  QCD  (b) rDV > 28 mm  Data  10  Z  -2  (a) rDV < 28 mm  2  W  mass > 10 GeV rDV > 28 mm  -1  4  Significance  0.8  2  103  tt  EF_xe80T_tclcw_loose  1  4  Significance  s = 8 TeV  10  1 10-1  Data  Vertices  Data  103  2 0 -2 -4  (c) rDV < 28 mm  4 2 0 -2 -4  (d) rDV > 28 mm  Figure 8.12: Figure (a) and (b) : The spectra of MET for EF_xe80T_tclcw_loose triggered data for rDV < 28 mm and rDV > 28 mm respectively. Mass > 10 GeV. Figure (c) and (d) : The mDV distributions for MET > 0.2 data and MC for rDV < 28 mm and rDV > 28 mm respectively.  102  Data  EF_j360_a10tcem  s = 8 TeV  102  tt W Z  mass < 1 GeV rDV < 28 mm  14.3 fb-1  Vertices  Vertices  103  104 103  QCD  Data  s = 8 TeV  W Z  mass < 1 GeV rDV > 28 mm  14.3 fb-1  2  10  10  tt  EF_j360_a10tcem  QCD  10 1 10-10  1 0.2  0.4  0.8  10-10  1  ~ Normalized MET  2 0 -2 -4  0.2  tt  EF_j360_a10tcem  W Z  mass < 1 GeV rDV < 28 mm  14.3 fb-1  0 -4  105 104  QCD  3  10  10  s = 8 TeV  tt  EF_j360_a10tcem  W Z  mass < 1 GeV rDV > 28 mm  14.3 fb-1  QCD  10 1 0.2  0.4  0.6  0.8  10-10  1  Mass [GeV]  0.2  0.4  0.6  0.8  1  Mass [GeV]  4  Significance  Significance  Data  102  1 10-10  1 ~ Normalized MET  -2  Vertices  Vertices  10  0.8  (b) rDV > 28 mm  Data  s = 8 TeV  0.6  2  (a) rDV < 28 mm  2  0.4  4  Significance  Significance  4  0.6  2 0 -2 -4  (c) rDV < 28 mm  4 2 0 -2 -4  (d) rDV > 28 mm  Figure 8.13: Figure (a) and (b) : The spectra of MET for EF_j360_a10tcem triggered data for rDV < 28 mm and rDV > 28 mm respectively. Mass < 1 GeV. Ks mass window (430 < mDV < 580 MeV) and Λ0 mass window (1100 < mDV < 1130 MeV is vetoed.). Figure (c) and (d): The mDV distributions for MET > 0.2 data and MC for rDV < 28 mm and rDV > 28 mm respectively.  103  102  tt  EF_j360_a10tcem  s = 8 TeV  W Z  mass > 10 GeV rDV < 28 mm  14.3 fb-1  10  102  QCD  0  0.2  0.4  0.6  10-1  1 ~ Normalized MET  Significance  0.8  2 0 -2 -4  0  0.2  Vertices  tt  EF_j360_a10tcem  W Z  mass > 10 GeV rDV < 28 mm  14.3 fb-1  30  1 ~ Normalized MET  0  Data  102  QCD  1 25  0.8  -4  1 20  0.6  -2  10  35  10-110  40  Mass [GeV]  s = 8 TeV  W Z  mass > 10 GeV rDV > 28 mm  14.3 fb-1  15  tt  EF_j360_a10tcem  20  25  30  35  QCD  40  Mass [GeV]  4  Significance  Significance  QCD  2  10  15  0.4  4  Vertices  Data  s = 8 TeV  10-110  Z  (b) rDV > 28 mm  103 10  W  mass > 10 GeV rDV > 28 mm  14.3 fb-1  (a) rDV < 28 mm  2  tt  EF_j360_a10tcem  1  4  Significance  s = 8 TeV  10  1 10-1  Data  Vertices  Vertices  Data  2 0 -2 -4  (c) rDV < 28 mm  4 2 0 -2 -4  (d) rDV > 28 mm  Figure 8.14: Figure (a) and (b) : The spectra of MET for EF_j360_a10tcem triggered data for rDV < 28 mm and rDV > 28 mm respectively. Mass > 10 GeV. Figure (c) and (d) : The mDV distributions for MET > 0.2 data and MC for rDV < 28 mm and rDV > 28 mm respectively.  104  9  Conclusion A search for long-lived, heavy particles in final states with a muon and multi-track displaced vertex √ has been performed with 4.4 fb−1 of data recorded in 2011 at s = 7 TeV with the ATLAS detector at the Large Hadron Collider. We have focused our search on particles decaying in the ATLAS Inner Detector region, which can be at a distance up to 180 mm from its production point, in the transverse direction. No excess of events above the expected background is observed. The results are interpreted in the context of R-parity violating supersymmetric scenarios in which the neutralino is the lightest supersymmetric particle. We set an upper bound on the squark pair production cross-section × the  branching ratio for a squark to decay, via a long-lived neutralino, to charged hadrons and a muon, as a function of its lifetime. For example, the limit for the cross section of the neutralino with a proper lifetime of 1 mm decaying in a µqq channel via an R-parity violating λ coupling is 3 × 10−2 pb.  Although the results are interpreted in terms of specific SUSY scenario, the displaced vertex search is more general and powerful, and can be used to set limits on many other models of new physics. In this work, we have also given an introduction to a potential search in the future by using 2-track displaced vertices. We have introduced several new signal-background discriminators and a list of minimal selection criteria for this kind of search.  105  Bibliography [1] F. Halzen and A. D. Martin, Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons, 1984. → Cited on page 1, 3, 4 [2] P. Langacker, “Introduction to the Standard Model and Electroweak Physics,” arXiv:0901.0241v1. → Cited on page 1, 4 [3] G. Sterman et al., “Handbook of perturbative QCD,” Rev. Mod. Phys., vol. 67, pp. 157–248, 1995. → Cited on page 1 [4] J.  C. Romão. http://porthos.ist.utl.pt/~romao/homepage/publications/mssm-model/ mssm-model.pdf. 24-Jun-2011. → Cited on page 1, 5  [5] → Cited on page 1, 5 [6] http://en.wikipedia.org/wiki/File:Standard_Model_of_Elementary_Particles.svg. 4-Dec-2012. → Cited on page 2  Accessed  [7] F. Boehm and P. Vogel, Physics of Massive Neutrinos. Cambridge, 1992. → Cited on page 1 [8] W. Greiner and J. Reinhardt, Quantum Electrodynamics. Springer-Verlag, 1994. → Cited on page 3 [9] S. L. Glashow, “Partial-symmetries of weak interactions,” Nucl. Phys., vol. 22, no. 4, pp. 579 – 588, 1961. → Cited on page 3 [10] A. Salam, “Renormalizability of Gauge Theories,” Phys. Rev., vol. 127, pp. 331–334, Jul 1962. → Cited on page 3 [11] S. Weinberg, “A Model of Leptons,” Phys. Rev. Lett., vol. 19, pp. 1264–1266, 1967. → Cited on page 3 [12] W. Greiner, S. Schramm, and E. Stein, Quantum Chromodynamics. Springer, 2002. → Cited on page 3 [13] The Super-Kamiokande Collaboration, “Search for Proton Decay via p → e+ π 0 and p → µ + π 0 in a Large Water Cherenkov Detector,” Phys. Rev. Lett., vol. 102, p. 141801, 2009. → Cited on page 4, 9  106  [14] The Particle Data Group, “The Review of Particle Physics,” Phys. Rev. D, vol. 86, p. 010001, 2012. → Cited on page 4 [15] “Latest update in the search for the Higgs boson.” https://cdsweb.cern.ch/record/1459565. → Cited on page 4 [16] The ATLAS Collaboration, “Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC,” Phys. Lett. B, vol. 716, no. 1, pp. 1 – 29, 2012. → Cited on page 4 [17] The CMS Collaboration, “Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC,” Phys. Lett. B, vol. 716, no. 1, pp. 30 – 61, 2012. → Cited on page 4 [18] S. Dittmaier et al., “Handbook of LHC Higgs Cross Sections,” CERN-2011-002. → Cited on page 4 [19] S. Dawson, “Introduction to the physics of Higgs bosons,” BNL-61012. → Cited on page 4 [20] Y. Nir, “ABCD method in searches.” http://www.weizmann.ac.il/particle/nir/uploads/file/ chapter1.pdf, 3-Jan-2013. → Cited on page 5 [21] S. P. Martin, A Supersymmetry Primer in Perspectives on Supersymmetry. World Scientific, 1998. → Cited on page 5, 7, 8 [22] G. Bertone, D. Hooper, and J. Silk, “Particle dark matter: evidence, candidates and constraints,” Phys. Rept., vol. 405, no. 5–6, pp. 279 – 390, 2005. → Cited on page 6, 7 [23] A. Chamseddine, R. Arnowitt, and P. Nath, “Locally Supersymmetric Grand Unification,” Phys. Rev. Lett., vol. 49, pp. 970–974, 1982. → Cited on page 6 [24] K. Intriligator, N. Seiberg, and D. Shih, “Dynamical SUSY breaking in meta-stable vacua,” JHEP, vol. 2006, no. 04, p. 021, 2006. → Cited on page 6 [25] H. Baer and X. Tata, Weak Scale Supersymmetry: From Superfields to Scattering Events. Cambridge, 2006. → Cited on page 7 [26] G. R. Farrar and P. Fayet, “Phenomenology of the production, decay, and detection of new hadronic states associated with supersymmetry,” Phys. Lett. B, vol. 76, no. 5, pp. 575 – 579, 1978. → Cited on page 7 [27] S. Profumo, “Quest for supersymmetry: Early LHC results versus direct and indirect neutralino dark matter searches,” Phys. Rev. D, vol. 84, p. 015008, 2011. → Cited on page 7 [28] C. Laura, K. Jihn, and L. Roszkowski, “Axions as Cold Dark Matter,” Phys. Rev. Lett., vol. 82, pp. 4180–4183, 1999. → Cited on page 8 [29] S. Förste et al., “Proton hexality in local grand unification,” Phys. Lett. B, vol. 693, no. 3, pp. 386 – 392, 2010. → Cited on page 8 107  [30] K. Hagiwara et al., “Review of Particle Properties,” Phys. Rev. D, vol. 66, p. 010001, 2002. → Cited on page 9 [31] H. Dreiner, G. Polesello, and M. Thormeier, “Bounds on broken R-parity from leptonic meson decays,” Phys. Rev. D, vol. 65, p. 115006, 2002. → Cited on page 9 [32] R. Barbier et al., “R-Parity-violating supersymmetry,” Phys. Rept., vol. 420, no. 1–6, pp. 1 – 195, 2005. → Cited on page 9 [33] S. Dawson, “R-parity breaking in supersymmetric theories,” Nucl. Phys. B, vol. 261, no. 0, pp. 297 – 318, 1985. → Cited on page 9 [34] CDF Collaboration, “Search for heavy metastable particles decaying to jet pairs in pp colli√ sions at s = 1.96 TeV,” Phys. Rev. D, vol. 85, p. 012007, 2012. → Cited on page 10 [35] CDF Collaboration, “Search for heavy, long-lived neutralinos that decay to photons at CDF II using photon timing,” Phys. Rev. D, vol. 78, p. 032015, 2008. → Cited on page 10 [36] The D0 Collaboration, “Search for Resonant Pair Production of Neutral Long-Lived Particles √ Decaying to bb in pp Collisions at s = 1.96 TeV,” Phys. Rev. Lett., vol. 103, p. 071801, 2009. → Cited on page 10 [37] The D0 Collaboration, “Search for Long-Lived Particles Decaying into Electron or Photon Pairs with the D0 Detector,” Phys. Rev. Lett., vol. 101, p. 111802, Sep 2008. → Cited on page 10 [38] The CMS Collaboration, “Search in leptonic channels for heavy resonances decaying to long-lived neutral particles,” arXiv:1211.2472v1. → Cited on page 10 [39] The CMS Collaboration, “Search for Long-Lived Particles using Displaced Photons in pp Collisions at sqrts = 7 TeV,” CMS-PAS-EXO-11-035. → Cited on page 10 [40] ATLAS Collaboration, “Search for a Light Higgs Boson Decaying to Long-Lived Weakly √ Interacting Particles in Proton-Proton Collisions at s = 7 TeV with the ATLAS Detector,” Phys. Rev. Lett., vol. 108, p. 251801, 2012. → Cited on page 10 [41] The ATLAS Collaboration, “Search for long-lived, heavy particles using a muon and multi√ track displaced vertex, in proton-proton collisions at s = 7 TeV with the ATLAS detector,” accepted by Phys. Lett. B, arXiv:1210.7451. → Cited on page 10 [42] O. S. Brüning et al., LHC Design Report. Geneva: CERN, 2004. → Cited on page 12, 13 [43] The ATLAS Collaboration, “The ATLAS Experiment at the CERN Large Hadron Collider,” JINST, vol. 3, no. 08, p. S08003, 2008. → Cited on page 12, 17, 21, 22, 23 [44] The ALICE Collaboration, “The ALICE experiment at the CERN LHC,” JINST, vol. 3, no. 08, p. S08002, 2008. → Cited on page 12 [45] The CMS Collaboration, “The CMS experiment at the CERN LHC,” JINST, vol. 3, no. 08, p. S08004, 2008. → Cited on page 12 108  [46] The LHCb Collaboration, “The LHCb Detector at the LHC,” JINST, vol. 3, no. 08, p. S08005, 2008. → Cited on page 12 [47] http://www.weltmaschine.de/cern_und_lhc/lhc. Accessed 14-Aug-2012. → Cited on page 14 [48] http://lhc.web.cern.ch/lhc/LHCUnder.pdf. Accessed 14-Aug-2012. → Cited on page 14 [49] J. Wenninger et al., “Operation of the LHC at High Luminosity and High Stored Energy,” CERN-ATS-2012-101. → Cited on page 13 [50] “ATLAS inner detector: Technical design report. Vol. 2,” CERN-LHCC-97-17. → Cited on page 18 [51] S. Haywood, “The ATLAS Inner Detector,” Nucl. Instr. Meth. Phys. Res. Sect. A, vol. 408, no. 1, pp. 242 – 250, 1998. → Cited on page 19 [52] ATLAS Collaboration, “ATLAS calorimeter performance Technical Design Report,” no. CERN-LHCC-96-40. → Cited on page 21 [53] ATLAS Collaboration, ATLAS muon spectrometer: Technical Design Report. CERN. CERN-LHCC-97-22. → Cited on page 22  Geneva:  [54] The ATLAS Collaboration, “ATLAS level-1 trigger: Technical Design Report,” Tech. Rep. ATLAS-TDR-012, CERN, Geneva. → Cited on page 23 [55] The ATLAS Collaboration, “Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics,” arXiv:0901.0512v4. → Cited on page 24 [56] A. Nisati, “A muon trigger algorithm for Level-2 feature extraction,” Tech. Rep. ATL-DAQ2000-036, CERN, Geneva. → Cited on page 24 [57] P. Jenni et al., ATLAS high-level trigger, data-acquisition and controls: Technical Design Report. ATLAS Technical Design Report, Geneva: CERN, 2003. → Cited on page 24 [58] C. Eck et al., LHC computing Grid: Technical Design Report. Version 1.06 (20 Jun 2005). Technical Design Report LCG, Geneva: CERN, 2005. → Cited on page 24 [59] The ATLAS Collaboration, “Concepts, Design and Implementation of the ATLAS New Tracking (NEWT),” tech. rep., CERN. ATL-SOFT-PUB-2007-007. ATL-COM-SOFT-2007002. → Cited on page 25, 27 √ [60] “Muon Performance in Minimum Bias pp Collision Data at s =7 TeV with ATLAS,” no. ATLAS-CONF-2010-036. → Cited on page 25, 29 [61] The ATLAS Collaboration, “Jet energy measurement with the ATLAS detector in proton√ proton collisions at s = 7 TeV,” CERN-PH-EP-2011-191. → Cited on page 25 [62] E. Bouhova-Thacker et al., “Vertex Reconstruction in the ATLAS Experiment at the LHC,” ATL-INDET-PUB-2009-001. ATL-COM-INDET-2009-011. → Cited on page 25, 30 109  [63] JLC Physics Group, “Introduction to Helical Track Manipulations.” http://www-jlc.kek.jp/jlc/ sites/default/files/groups/soft/kaltest/doc/helixmanip.pdf, 9-Jan-2013. → Cited on page 25 [64] P. F. Åkesson et al., “ATLAS Tracking Event Data Model,” ATLAS Note. ATL-SOFT-PUB2006-004. ATL-COM-SOFT-2006-005. CERN-ATL-COM-SOFT-2006-005. → Cited on page 25 [65] T. G. Cornelissen et al., “Updates of the ATLAS Tracking Event Data Model (Release 13),” ATL-SOFT-PUB-2007-003. ATL-COM-SOFT-2007-008. → Cited on page 25 [66] The CMS Collaboration, “Search for new physics with long-lived particles decaying to photons and missing energy,” arXiv:1207.0627v1. → Cited on page 27 [67] R. Frühwirth, “Application of Kalman filtering to track and vertex fitting,” Nucl. Instrum. Meth. A, vol. 262, no. 2ó3, pp. 444 – 450, 1987. → Cited on page 27 [68] F. Brochu, “Reconstruction of tracks with large impact parameter in the Inner Detector,” ATL-PHYS-INT-2012-010. → Cited on page 27, 28 [69] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/DesdmRpvll. 28-Jun-2011. → Cited on page 28 [70] https://twiki.cern.ch/twiki/bin/view/AtlasProtected/MuidMuonCollection. 16-Mar-2010. → Cited on page 29 [71] https://twiki.cern.ch/twiki/bin/view/AtlasProtected/StacoMuonCollection. 29-Apr-2010. → Cited on page 29 [72] P. V. C. Hough, “Machine Analysis of Bubble Chamber Pictures,” in International Conference on High Energy Accelerators and Instrumentation, (CERN), 1959. → Cited on page 29 [73] The ATLAS Collaboration, “Search for supersymmetry in final states with jets, missing trans√ verse momentum and one isolated lepton in s = 7 TeV pp collisions using 1 fb−1 of ATLAS data,” Phys. Rev. D, vol. 85, p. 012006, 2012. → Cited on page 29, 46 [74] M. Cacciari, G. P. Salam, and G. Soyez, “The anti-kt jet clustering algorithm,” JHEP, vol. 2008, no. 04, p. 063, 2008. → Cited on page 30 [75] The ALICE Collaboration, “Measurement of inelastic, single- and double-diffraction cross sections in proton–proton collisions at the LHC with ALICE,” submitted to Eur. Phys. J. C, arXiv:1208.4958. → Cited on page 30 [76] J. F. Laporte, “Latest Results of LHC: Atlas and CMS,” vol. ATL-GEN-SLIDE-2012-494. → Cited on page 32 [77] T. Sjöstrand, S. Mrenna, and P. Skands, “PYTHIA 6.4 physics and manual,” JHEP, vol. 2006, no. 05, p. 026, 2006. → Cited on page 33 110  [78] P. Torrielli and S. Frixione, “Matching NLO QCD computations with PYTHIA using MC@NLO,” JHEP, vol. 2010, pp. 1–19, 2010. → Cited on page 33 [79] G. Corcella et al., “HERWIG 6: an event generator for hadron emission reactions with interfering gluons (including supersymmetric processes),” JHEP, vol. 2001, no. 01, p. 010, 2001. → Cited on page 33 [80] J. Butterworth, J. Forshaw, and M. Seymour, “Multiparton interactions in photoproduction at HERA,” Zeitschrift für Physik C, vol. 72, pp. 637–646, 1996. → Cited on page 33 [81] S. A. The GEANT4 Collaboration et al., “GEANT4: A simulation toolkit,” Nucl. Instrum. Meth. A, vol. 506, pp. 250–303, 2003. → Cited on page 34 [82] V. Kostyukhin, “VKalVrt - package for vertex reconstruction in ATLAS,” no. ATL-PHYS2003-031. → Cited on page 36 [83] P. Billoir and S. Qian, “Fast vertex fitting with a local parametrization of tracks,” Nucl. Instr. Meth. Phys. Res. Sect. A, vol. 311, no. 1ó2, pp. 139 – 150, 1992. → Cited on page 37 [84] P. Avery, “Applied Fitting Theory VI: Formulas for Kinematic Fitting,” CBX 98-37, 1998. → Cited on page 38 [85] S. R. Das, “On a New Approach for Finding All the Modified Cut-Sets in an Incompatibility Graph,” IEEE Transactions On Computers, vol. C-22 No.2, pp. 187–193, 1973. → Cited on page 38 [86] H. Grote, “Pattern recognition in high-energy physics,” Rep. Prog. Phys., vol. 50, no. 4, p. 473, 1987. → Cited on page 38 [87] F. Fröhlich, H. Grote, C. Onions, and F. Ranjard no. CERN/DD/76/5, 1976. → Cited on page 38 [88] G. Gorfine, “Inner Detector and Beampipe Geometry Status.” https://indico.cern.ch/getFile. py/access?contribId=7&resId=1&materialId=slides&confId=59815. 27-May-2009. → Cited on page 41 [89] P. Bernat, M. Donega, M. Kado, and L. Serin, “Study of the π 0 Dalitz decays and Photons Conversions in the Beam Pipe using 900 GeV and 7 TeV Minimum Bias Data,” vol. ATLCOM-PHYS-2010-330. → Cited on page 41 [90] J. Humbert, ATLAS VI Vacuum Chamber - Installation Assembly. Number: LHCVC1I_0036 v.0 and EDMS Id: 522329 v.0. → Cited on page 41 [91] A. Barr, C. Lester, and P. Stephens, “A variable for measuring masses at hadron colliders when missing energy is expected; mT2 : the truth behind the glamour,” J. Phys. G, vol. 29, no. 10, p. 2343, 2003. → Cited on page 43 [92] K. Abe et al., “Measurement of Rb using a vertex mass tag,” Phys. Rev. Lett., vol. 80, pp. 660– 665, Jan 1998. → Cited on page 44 111  [93] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/MCPAnalysisGuidelinesRel17MC11a. 14-Aug-2012. → Cited on page 46, 65 [94] G. Cowan, K. Cranmer, E. Gross, and O. Vitells, “Asymptotic formulae for likelihood-based tests of new physics,” Eur. Phys. J. C, vol. 71, pp. 1–19, 2011. → Cited on page 47 [95] A. Roodman, “Blind Analysis in Particle Physics,” SLAC-PUB-10281. → Cited on page 47 [96] V. Jain and V. Kostyukhin, “A study of hadronic interactions in the ATLAS Inner Detector,” vol. ATL-COM-PHYS-2010-055. → Cited on page 48 [97] The ATLAS collaboration, “A study of the material in the ATLAS inner detector using secondary hadronic interactions,” JINST, vol. 7, no. 01, p. P01013, 2012. → Cited on page 48 [98] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/MCPAnalysisGuidelinesEPS2011. 24-Sep-2011. → Cited on page 62 [99] http://mathworld.wolfram.com/Erf.html. Accessed 9-Dec-2012. → Cited on page 62 [100] N. Barlow et al., “Search for Heavy Medium-Lived Particles at ATLAS,” no. ATL-COMPHYS-2011-161. → Cited on page 64, 65 [101] N. Barlow et al., “Update of search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS,” ATLAS Note. ATL-COM-PHYS-2012-785. → Cited on page 65 [102] R. H. W. Beenakker and M. Spira, “PROSPINO: A Program for the production of supersymmetric particles in next-to-leading order QCD,” arXiv:hep-ph/9611232. → Cited on page 65, 90 [103] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/ExtendedPileupReweighting. 10-Jul2012. → Cited on page 66 [104] The CMS Collaboration, “Search for physics beyond the standard model in opposite-sign √ dilepton events in pp collisions at s = 7 TeV,” JHEP, vol. 2011, pp. 1 – 33, 2011. → Cited on page 69 [105] The ATLAS Collaboration, “Observation of W → τν Decays with the ATLAS Experiment,” Tech. Rep. ATLAS-CONF-2010-097, CERN, Geneva. → Cited on page 69 √ [106] The ATLAS Collaboration, “Search for Neutral MSSM Higgs bosons in s = 7 TeV pp collisions at ATLAS,” tech. rep., CERN, Geneva. ATLAS-CONF-2012-094. → Cited on page 69 [107] ATLAS Statistics Forum, “ABCD method in searches.” https://twiki.cern.ch/twiki/pub/ AtlasProtected/ATLASStatisticsFAQ/ABCD.pdf, 25-Jan-2012. → Cited on page 69 [108] “Update. Backgrounds inside the beampipe.” https://indico.cern.ch/getFile.py/access? contribId=0&resId=0&materialId=slides&confId=179344. → Cited on page 72 112  [109] A. L. Read, “Presentation of search results: the CLs technique,” J. Phys. G, vol. 28, no. 10, p. 2693, 2002. → Cited on page 90 [110] A. D. Martin, W. J. Stirling, R. S. Thorne, and G. Watt, “Parton distributions for the LHC,” Eur. Phys. J. C, vol. 63, pp. 189–285, 2009. → Cited on page 90 [111] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/SUSYSignalUncertainties. 25-Jul2012. → Cited on page 90, 91 √ [112] “Improved Luminosity Determination in pp Collisions at s = 7 TeV using the ATLAS Detector at the LHC,” ATLAS-CONF-2012-080. → Cited on page 90, 91 [113] The ATLAS Collaboration, “Procedure for the LHC Higgs boson search combination in summer 2011,” ATL-PHYS-PUB-2011-011. → Cited on page 90 [114] The CMS Collaboration, “Combination of SM Higgs Searches,” CMS-PAS-HIG-11-032. → Cited on page 90 [115] The ATLAS Collaboration, “Search for displaced vertices arising from decays of new heavy particles in 7 TeV pp collisions at ATLAS,” Phys. Lett. B, vol. 707, no. 5, pp. 478 – 496, 2012. → Cited on page 91 [116] N. Arkani-Hamed and N. Weiner, “LHC signals for a SuperUnified theory of Dark Matter,” JHEP, vol. 2008, no. 12, p. 104. → Cited on page 93 [117] M. J. Strassler and K. M. Zurek, “Echoes of a hidden valley at hadron colliders,” Phys. Lett. B, vol. 651, no. 5-6, pp. 374 – 379, 2007. → Cited on page 93 [118] A. Policicchio, “Search for displaced lepton jets: plans for 2012 data analysis.” https: //indico.cern.ch/contributionDisplay.py?contribId=2&confId=205063. 31-Aug-2012. → Cited on page 94 [119] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/ElectronIdentification. Accessed 13Nov-2012. → Cited on page 98 [120] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/PhotonIdentification. Nov-2012. → Cited on page 98  Accessed 13-  [121] L. Ancu et al., “The Design and Performance of the ATLAS Jet Trigger for the Event Filter,” tech. rep., CERN, Geneva. ATL-DAQ-INT-2011-003. → Cited on page 98 [122] https://twiki.cern.ch/twiki/bin/viewauth/AtlasProtected/FinalSusyTrigger2012. Accessed 13Nov-2012. → Cited on page 98  113  Appendix A  pT-corrected Mass Consider, a particle L decaying to particle 1 and 2. Note, even if the particle decays to > 2 daughters, one can always sum their 4-momenta, such that, we are left with only 2 daughters. Then, the mass of L is  m2L = (E1 + E2 )2 − (p1 + p2 )2 ,  m2L = m21 + m22 + 2E1 E2 − 2pz1 pz2 − 2pT1 · pT2 , E1 E2 pz1 pz2 − − 2pT1 · pT2 , m2L = m21 + m22 + 2E1 E2 E1 E2 E1 E2 with E = Notice that,  m2 + p2T = E E  2  −  pz E  Hence, ∃ y such that  (A.1)  m2 + p2x + p2y and bolded letters are vectors. 2 Ei Ei  = 1,  E1 E2 E1 E2  ≥ 1,  = cosh yi and  pz1 ·pz2  pzi Ei  E1 E2  is unbounded and  E1 E2 E1 E2  2  −  = sinh yi . It turns out that y = 12 ln  pz1 ·pz2  E1 E2 E+pz E−pz  2  ≥ 1.  . Thus, (A.1)  can be re-written as  m2L = m21 + m22 + 2E1 E2 cosh (y1 − y2 ) − 2pT1 · pT2 .  (A.2)  Suppose particle 2 is invisible to the detector, then, our most conservative estimate for its mass, m2 = 0 and cosh (y2 − y1 ) = 1. Then, m2L ≥ m21 + 2E1 E2 − 2pT1 · pT2 .  (A.3)  Since pT1 = −pT2 in the local frame (Figure 4.9), this finally reduces to the pT -corrected mass, mpTcorr = E1 + pT1 =  m21 + pT1 2 + pT1 ≤ mL . 114  (A.4)  Appendix B  Event Display Legend  115  

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