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Study of the fiducial cross section of the Higgs boson
decaying into four leptons and study of muon isolation
in the ATLAS experiment at the LHC
Arthur Alexis Jules Lesage
To cite this version:
Arthur Alexis Jules Lesage. Study of the fiducial cross section of the Higgs boson decaying into four leptons and study of muon isolation in the ATLAS experiment at the LHC. High Energy Physics -Experiment [hep-ex]. Université Paris-Saclay, 2017. English. �NNT : 2017SACLS208�. �tel-01623878�
Thèse de doctorat de l'Université Paris-Saclay préparée au Commissariat à l'Énergie Atomique et aux Énergies Alternatives (CEA),
au sein du Département de Physique des Particules (DPhP) de l'Institut de Recherche sur les lois Fondamentales de l'Univers (IRFU)
Study of the production cross section of the
Higgs boson decaying into four leptons
and study of muon isolation
in the ATLAS experiment at the LHC
Thèse présentée et soutenue à Saint-Aubin, le 22 septembre 2017
M. Arthur Lesage
NN
T
: 2017SACLS
208
Thèse de
doctorat
École doctorale nº517 Sciences physiques : particules, hadrons, énergie, noyau, instrumentation, imagerie, cosmos et simulation (PHENIICS)
Spécialité de doctorat : physique des particules
Composition du Jury : M. Patrick Puzo
Professeur, Université Paris Sud XI Président
Mme Chiara Mariotti
Professeure, INFN (Torino) Rapporteuse
Mme Chariclia Petridou
Professeure, Université Aristote (Thessaloniki) Rapporteuse Mme Chiara Roda
Professeure assistante, Université des Études de Pise Examinatrice Mme Stefania Spagnolo
Professeure associée, Université del Salento Examinatrice M. Reisaburo Tanaka
Chargé de recherche, Laboratoire de l'Accélérateur Linéaire (LAL) Examinateur Mme Rodanthi Nikolaidou
Acknowledgements
Conducting a PhD in physics was my objective as a student and I want to thank everyone who helped me in this adventure, as well as introducing me to the universe of particle physics.
My warmest thanks go to Rosy. You gave me the opportunity to do my PhD thesis within the ATLAS group of the DPhP at CEA under your valuable supervision. You constantly believed in my capability to perform challenging studies, giving me the chance to collaborate in an extraordinary international environment, which is CERN. On top of having a great visibility in the ATLAS collaboration, you made sure our work would be promoted among the analysis groups. We tackled the problems together with a great efficiency and achieved so much in three years. I thank you for your devolution every day: at the beginning when you assisted me with patience in my discovery of particle physics, and in the end to ensure I would defend our work in a great international conference (LHCP2017) and through the writing of my thesis. You gave me the opportunity to work on a well-structured project which combines performance and analysis works: from the muon isolation to studies in the Higgs-to-four-lepton final state. Although not always on the same boat, I enjoyed the scientifically rich conversations I had with you, which helped me to find the correct answers to my questions. I wish you all the best for your next challenges within the collaboration, but I already know you will face them brilliantly.
I also want to thank you Vanina for your support throughout the thesis. A bit like a second mother with Rosy, you took care my project was coherent and was progressing regularly. Your help in our battles against administration was immensely appreciated (and not only by me!). It is important for every PhD student to have a godmother/father and you played your role with great dedication.
I would also like to thank all the members of the jury of my thesis. Thank you Pr. Chiara Mariotti and Pr. Chara Petridou for being my rapporteuses and making very valuable comments to my manuscript. Thank you also Pr. Patrick Puzo, Dr. Chiara Roda, Dr. Stefania Spagnolo and Dr. Reisaburo Tanaka for your interesting remarks and the discussions we had. Thanks to all of you for helping me to graduate. I thank the DPhP group (especially Claude), for accepting me within your team and funding my work as a PhD student. This adventure (including participation to lectures, seminars and conferences) would not have been possible without your support.
The preparation of the PhD is a demanding but exciting experience. I thank all my friends from CERN, CEA and other locations in the world for their support, help and understanding! Thank you Carlo and Andrea for the amazing time we had together. Thank you Joaquín, Florencia and Roberta for the moments we shared and for welcoming me at your lovely places. Between empanadas and matés, you helped me to improve my Espanish so much! Baptiste, I remember our enjoyable moments at the summer school in Norway and the seminars in France. Laura and Éloi, your company at CEA and CERN counted at lot and I learnt a lot meeting you. Thank you Maria for introducing me to CERN and for our conversations. I hope you will keep nice memories of France and French in general. I also spent nice time with you Denys, Inna, Martha and Martina. I want to thank you Philippe and Samira for your help, although I could not participate to the NSW project as much as I wanted.
My PhD thesis would not have been completed without the essential help of my colleagues at CERN. I want to thank you Bijan, Andrea and Sarah for your help in the analysis. Publishing the first H4` paper at your side was very motivating. Thank you Dongliang and Miha for the dedication you brought to the muon isolation task force. We achieved to set up a robust framework useful to the entire collaboration.
Thank you Simona, Davide, Kostas, José and Luigi for the nice atmosphere in Saint-Genis. Having housemates and landlords like you is a rich experience which I enjoyed everyday.
My last thanks go to my family. Merci Huguette et Jean pour m’avoir accueilli très souvent sur Paris. Vous m’avez toujours soutenu dans mes études et je vous dois beaucoup. Merci à mes parents qui ont
toujours cru en moi et dont le soutien a été déterminant lors de ma thèse. Merci à tous les autres qui me sont proches et qui comptent beaucoup : avoir un premier docteur dans la famille, ça se fête !
Contents
1 Introduction 1
I The ATLAS experiment at the LHC 3
2 The Large Hadron Collider 5
2.1 Luminosity . . . 7
2.2 The experiments at the LHC and the physics reach . . . 8
2.3 Physics runs and upgrades . . . 9
3 The ATLAS experiment 11 3.1 Geometry of the detector . . . 11
3.2 The Inner Detector . . . 12
3.2.1 The Insertable B-Layer (IBL) . . . 14
3.2.2 The Pixel detectors and the Silicon micro-Strip Trackers (SCT) . . . 15
3.2.3 The Transition Radiation Tracker . . . 16
3.2.4 Inner Detector tracking performance . . . 16
3.3 The calorimeters . . . 19
3.3.1 The electromagnetic calorimeter . . . 20
3.3.2 The hadronic calorimeters . . . 20
3.3.3 The forward calorimeter . . . 22
3.3.4 Performance of the calorimeters . . . 23
3.3.5 Electron reconstruction and associated performance . . . 24
3.4 The Muon Spectrometer . . . 25
3.4.1 Momentum measurement . . . 27
3.4.2 The toroid magnets . . . 28
3.4.3 Precision chambers . . . 28
3.4.4 Trigger chambers . . . 30
CONTENTS
3.4.6 Muon reconstruction . . . 32
3.4.7 Muon identification . . . 33
3.4.8 Measurement of the reconstruction and identification efficiencies . . . 34
3.5 The trigger, data acquisition and detector control systems . . . 35
3.6 The software framework . . . 36
3.6.1 Data management and data formats . . . 37
3.6.2 The simulation chain . . . 37
II Muon isolation 39 4 Introduction 41 5 Isolation variable definitions 43 5.1 Track-based isolation . . . 43
5.1.1 Inner Detector tracks . . . 43
5.1.2 Calculation of isolation variables . . . 44
5.1.3 Core energy . . . 45
5.1.4 Variable calculation . . . 45
5.2 Calorimeter-based isolation . . . 45
5.2.1 Topocluster definition . . . 46
5.2.2 Calculation of the calorimeter-based isolation . . . 48
5.2.3 Isolation corrections . . . 51
5.2.4 Final formula for the calorimeter-based isolation . . . 55
6 Muon isolation working points 57 6.1 Working point definition . . . 57
6.1.1 Muon working points . . . 58
6.1.2 Electron working points . . . 59
6.2 Cut values associated to isolation working points . . . 59
6.2.1 Creation of the cut maps for muons . . . 59
6.2.2 Cut map binning for muons . . . 59
6.2.3 Cuts applied to the muon isolation variables . . . 60
CONTENTS
7 Muon isolation performance 63
7.1 The Tag-And-Probe method . . . 63
7.2 Isolation variable distributions . . . 65
7.2.1 Track-based isolation . . . 66
7.2.2 Calorimeter-based isolation . . . 75
7.3 Efficiency calculation . . . 76
7.4 Scale factors . . . 80
7.5 13 TeV results . . . 80
7.5.1 Efficiencies and scale factors . . . 80
7.5.2 Systematic uncertainties . . . 82
7.5.3 Scale factor validation (closure test) . . . 87
7.6 Conclusion and potential improvements . . . 88
8 Correction for close-by objects 93 8.1 Correcting for the contributions of close-by objects . . . 93
8.1.1 Calorimetric isolation . . . 93
8.1.2 Track-based isolation . . . 94
8.2 Software implementation . . . 94
8.3 Case of missing information from the topoclusters . . . 95
8.4 Performance . . . 95
8.4.1 The Loose isolation working point . . . 96
8.4.2 Muon variables . . . 97
8.4.3 Conclusions . . . 97
III Production cross-section of the Higgs boson decaying into four leptons 99 9 Introduction 101 10 The Higgs boson in the Standard Model 103 10.1 The electromagnetic, strong and weak interactions . . . 103
10.1.1 From the Dirac equation to the photon . . . 103
10.1.2 The strong interactions . . . 104
10.1.3 The electroweak sector . . . 105
10.2 The Higgs mechanism . . . 107
10.2.1 The Higgs potential . . . 107
10.2.2 The ground state . . . 107
CONTENTS
10.2.4 Generation of the boson masses . . . 109
10.3 Inclusion of the Higgs mechanism to the Standard Model . . . 109
10.4 The Higgs discovery . . . 111
10.4.1 Constraints on the mass of the Higgs boson . . . 111
10.4.2 The discovery of the Higgs boson . . . 112
10.5 The Higgs boson production and decay channels at the LHC . . . 114
10.5.1 Production mechanisms at the LHC . . . 114
10.5.2 Decay channels of the Higgs boson . . . 116
10.5.3 The total width of the Higgs boson . . . 116
10.6 Beyond the Standard Model . . . 117
11 The Higgs boson decaying into four leptons 119 11.1 The four-lepton final state . . . 119
11.2 Data and Monte Carlo samples . . . 121
11.2.1 Data samples . . . 121
11.2.2 Simulated samples . . . 121
11.3 Lepton reconstruction and trigger . . . 124
11.3.1 Electron reconstruction and identification . . . 124
11.3.2 Muon reconstruction and identification . . . 126
11.3.3 Jet reconstruction and identification . . . 126
11.3.4 b tagging . . . 126
11.3.5 Triggers . . . 127
11.4 Event selection . . . 128
11.4.1 Selection of events for the analysis . . . 128
11.4.2 Vertexing of the four leptons in the final state . . . 130
11.4.3 Final state radiation recovery and mass constraints . . . 132
11.4.4 Possible improvements of the general selection . . . 136
11.5 Background estimation and shape modelling . . . 136
11.5.1 Z+ µµ background channel . . . 137
11.5.2 Z+ ee background channel . . . 144
11.5.3 Results of the Z+ µµ and Z + ee background yields per category . . . 148
11.5.4 Background shape modelling . . . 148
11.6 Systematic uncertainties . . . 149
11.6.1 Background theoretical systematic uncertainties . . . 150
11.6.2 Experimental systematic uncertainties . . . 150
CONTENTS
12 Measurements of the inclusive and differential cross sections 159
12.1 Fiducial phase space definition . . . 160
12.1.1 Fiducial event selection . . . 160
12.1.2 Electrons . . . 160
12.1.3 Muons . . . 160
12.1.4 Jets . . . 161
12.1.5 Higgs boson candidates . . . 161
12.1.6 Dressed lepton definition . . . 162
12.2 Acceptance and correction factors . . . 162
12.2.1 Acceptance factor . . . 163
12.2.2 Correction factor . . . 165
12.2.3 Fiducial and total cross sections . . . 166
12.3 Signal extraction . . . 166
12.3.1 Asymptotic approximation . . . 167
12.3.2 Pseudo data generation . . . 167
12.4 Measurement of the inclusive cross sections . . . 168
12.4.1 Inclusive acceptance and correction factors . . . 168
12.4.2 Background checks . . . 169
12.4.3 Uncertainties . . . 170
12.4.4 Checks on pseudo data . . . 173
12.4.5 Results with 36.1 fb−1 . . . 175
12.5 Differential measurements . . . 180
12.5.1 Methodology of the measurements . . . 180
12.5.2 Differential variables . . . 182
12.5.3 Migration studies . . . 186
12.5.4 Purity studies . . . 188
12.5.5 Acceptance and correction factors . . . 195
12.5.6 Uncertainties . . . 206
12.5.7 Background and Asimov checks . . . 206
12.5.8 Results using 36.1 fb−1 . . . 208
12.6 Double-differential measurements . . . 213
12.6.1 Factors and uncertainties . . . 214
12.6.2 Bin definition and methodology checks . . . 216
12.6.3 Results using 36.1 fb−1 . . . 219
12.7 Interpretations of the measurements . . . 219
CONTENTS
Appendices 225
A Additional information on the validation of the isolation scale factors 227
B Models in case of missing topocluster information for isolation close-by correction 241
C Trigger efficiencies in the Higgs-to-four-lepton channel 243
D Influence of alternative selections for the Higgs-to-four-lepton analysis 247
D.1 Influence of keeping all the quadruplets until the end of the selection . . . 247
D.2 Influence of applying the isolation selection at an earlier stage . . . 250
E Résumé de la thèse en français 251 E.1 Étude de l’isolation des muons . . . 252
E.1.1 Définition des variables d’isolation pour le Run 2 . . . 252
E.1.2 Définition des points de fonctionnement . . . 254
E.1.3 Performance de l’isolation au Run 2 . . . 254
E.1.4 Correction de l’isolation pour les objets proches . . . 256
E.2 Mesure de la section efficace de production du boson de Higgs en quatre leptons . . . 256
E.2.1 La chaîne de décomposition du boson de Higgs en quatre leptons . . . 256
E.2.2 Méthodologie des mesures et définition de l’espace de phase fiduciel . . . 257
E.2.3 Mesures des sections efficaces inclusives . . . 259
E.2.4 Mesures des sections efficaces différentielles et interprétations . . . 260
List of Figures
2.1 Experiments and accelerators at CERN . . . 6
2.2 The various octants of the LHC . . . 6
2.3 Pile-up conditions in Run 2 . . . 8
3.1 The ATLAS coordinates . . . 12
3.2 The ATLAS detector . . . 13
3.3 Layout of the Inner Detector . . . 13
3.4 Material in the Inner Detector . . . 14
3.5 Insertable B-layer layout . . . 15
3.6 Expected tracking performance of the Inner Detector using simulation prior to Run 1 . . . 16
3.7 Efficiency to extend a track reconstructed in the pixel detector measured using Run 2 data 17 3.8 Expected resolution of the Inner Detector against∣η∣ for simulated pions prior to Run 1 . . 17
3.9 Measured longitudinal impact parameter resolution as function of pT and η, using Run 1 and Run 2 data . . . 18
3.10 Measured transverse impact parameter resolution as function of pT and η, using Run 1 and Run 2 data . . . 18
3.11 Expected distribution of the material in the calorimeters . . . 19
3.12 The various calorimeters . . . 20
3.13 Geometry of the electromagnetic calorimeters . . . 22
3.14 Geometry of the tile calorimeters . . . 22
3.15 Electron pair invariant mass distribution from Z→ ee decays in data compared to simula-tion after the applicasimula-tion of the full calibrasimula-tion . . . 23
3.16 Comparison of the noise in the LAr calorimeters between data 2015 and simulation . . . 24
3.17 Electron reconstruction procedure . . . 25
3.18 Electron reconstruction and identification efficiencies in Z→ ee events . . . 26
3.19 The Muon Spectrometer in the y — z plane . . . 26
3.20 Sagitta of a muon track . . . 28
3.21 Design of the MDT chambers . . . 29
LIST OF FIGURES
3.23 Design of the RPC chambers . . . 30
3.24 Layout of the TGC chambers . . . 31
3.25 The Muon Spectrometer alignment system . . . 32
3.26 Muon Spectrometer alignment performance in Run 2 . . . 33
3.27 Muon reconstruction efficiencies measured in Z→ µµ and J/ψ → µµ events using Run 2 data 35 3.28 The triggers in ATLAS . . . 36
3.29 The simulation chain of ATLAS . . . 38
5.1 Summary sketch of the calculation of pvarconeT . . . 45
5.2 The clustering algorithm . . . 48
5.3 ∆Rraw optimisation . . . 49
5.4 Topocluster selection . . . 51
5.5 Characteristics of the muon core energy . . . 52
5.6 Average energy loss of muons in the various layers of the calorimeters and in the ID and MS 52 5.7 ∆Rcore optimisation . . . 53
5.8 Evolution against pe T of ETtopocone20 for electrons with and without leakage correction . . . . 53
5.9 Distribution of the pile-up density as a function of ηµ . . . 54
5.10 Evolution of the pile-up correction against the pile-up conditions . . . 55
6.1 Cut values on topoetcone20 for the various muon isolation working points . . . 60
6.2 Cut values on ptvarcone30 for the various muon isolation working points . . . 61
7.1 Data-simulation comparison of shifted µ and nPV before MC reweighting . . . 64
7.2 Data-MC comparison of shifted µ and nPV after MC reweighting . . . 65
7.3 Data / simulation comparison of ptvarcone30 . . . 66
7.4 Evolution of ptvarcone30 with pile-up . . . 66
7.5 Evolution of ptvarcone30 with the muon kinematics . . . 67
7.6 Distributions of pvarcone30 T with various track selection criteria . . . 69
7.7 Distributions of the vertex density before and after reweighting . . . 70
7.8 Distribution of the variables used to calculate ρvtx . . . 71
7.9 Distributions of pvarcone30 T against the vertex density ρvtx . . . 72
7.10 Distributions of pvarcone30 T with various track selection criteria, after ρvtx reweighting . . . . 73
7.11 Distributions of pvarcone30 T against the reweighted vertex density ρvtx . . . 74
7.12 Data-simulation comparison of topoetcone20 . . . 75
7.13 Data-simulation comparison of topocore . . . 75
7.14 Evolution of topoetcone20 with pile-up . . . 76
LIST OF FIGURES
7.16 Fit of the background fractions in the bin 4< pT< 5 GeV for the background correction of
the isolation efficiencies . . . 77
7.17 Validation checks using pseudo data for the background corrections of the isolation effi-ciencies (FixedCutLoose working point) . . . 79
7.18 Results of the isolation efficiency correction for the FixedCutLoose working point . . . 79
7.19 Efficiencies and scale factors of the LooseTrackOnly, Loose, FixedCutLoose, GradientLoose, Tight and Gradient working points . . . 81
7.20 Muon isolation efficiencies and scale factors for the FixedCutTightTrackOnly working point. 82 7.21 Systematic uncertainty contributions for the LooseTrackOnly, Loose, FixedCutLoose, Gra-dientLoose, Tight and Gradient isolation working points . . . 85
7.22 Systematic uncertainty contributions on the muon isolation scale factors for the FixedCut-TightTrackOnly working point . . . 86
7.23 Validation plots of the FixedCutLoose scale factors integrated over η . . . 87
7.24 Validation plots of the FixedCutLoose scale factors in various η regions (η< 0) . . . 89
7.25 Validation plots of the FixedCutLoose scale factors in various η regions (η> 0) . . . 90
7.26 Validation plots of the FixedCutLoose scale factors, in various ∆Rµj regions, where no additional ∆Rµj systematics were added . . . 91
7.27 Validation plots of the FixedCutLoose scale factors, in various ∆Rµj regions, where addi-tional ∆Rµj systematics were added . . . 92
8.1 Efficiencies of the Loose isolation working point for electrons and muons, before and after correction for close-by objects . . . 95
8.2 Muon distribution of pvarcone30 T before and after correction for close-by objects . . . 96
8.3 Complementary information for the correction of the variable ptvarcone30 of muons . . . . 96
8.4 Muon distribution of ETtopocone20 before and after correction for close-by objects . . . 97
8.5 Complementary information for the correction of the variable topoetcone20 of muons . . . . 98
10.1 The Higgs potential . . . 108
10.2 Theoretical limits on mH . . . 112
10.3 Electroweak precision measurements from LEP, SLC and Tevatron experiments . . . 113
10.4 Exclusion limits of mH measured by the LEP and Tevatron experiments. . . 113
10.5 Diagrams of the main Higgs boson production mechanisms at the LHC . . . 114
10.6 Higgs boson production cross sections as a function of the centre-mass energy . . . 115
10.7 Higgs boson branching ratios as a function of mH . . . 116
10.8 Feynman diagrams for the first corrective loops contributing to mH . . . 118
11.1 Feynman diagrams of the main background processes of the Higgs-to-four-lepton decay channel . . . 120
11.2 Four-lepton vertex cut efficiencies . . . 133
LIST OF FIGURES 11.4 Distributions of the leading mass in the various control regions for the Z+ µµ background
estimation, before the fit . . . 138
11.5 Sketch presenting the method used to extrapolate the Z+ µµ background yields to the signal region . . . 140
11.6 Validation plots of the simultaneous fit for the Z+ µµ background estimation . . . 140
11.7 Results of the fit for the data in the three control regions for the Z+µµ background estimation141 11.8 Kinematic distributions in the Z+ µ control sample . . . 143
11.9 Shapes used for the fit and distributions after the fit of ninnerPix in the 3`+ X control region145 11.10Shape of the four-lepton invariant mass for reducible backgrounds . . . 148
11.11Distributions of the 4` invariant mass for the triboson and t¯t+ V backgrounds . . . 149
11.12Selected event yields against data period . . . 154
11.13Inclusive four-lepton invariant mass distribution . . . 154
11.14Four-lepton invariant mass distribution per decay channel . . . 155
11.15Inclusive four-lepton pT distributions . . . 156
11.16Inclusive Higgs boson variable distributions . . . 157
11.17Inclusive jet distributions . . . 158
12.1 Comparison of the four-lepton invariant mass using dressed and born lepton definitions . . 162
12.2 Comparison of theA and C factors at mH = 125 GeV using the dressed and born particle-level lepton definitions . . . 164
12.3 Invariant mass distributions of the lepton pair in the Z+ µµ control sample . . . 170
12.4 Invariant mass distributions of the lepton pair in the Z+ ee control sample . . . 171
12.5 Comparison of the m4` distributions between Asimov data and MC for closure test . . . 174
12.6 Inclusive fiducial cross section fit on Asimov data, per single channel (POI1) . . . 176
12.7 Inclusive fiducial cross section fit on Asimov data, for the various parameters of interest POI2, POI3 and POI4 . . . 177
12.8 Log-likelihood scans for the inclusive fiducial cross section per single channel (POI1) . . . . 178
12.9 Log-likelihood scans for the inclusive fiducial cross, for various parameters of interest POI2, POI3 and POI4 . . . 179
12.10Observed and expected inclusive cross sections . . . 180
12.11Sketch of the Higgs boson kinematic variables . . . 183
12.12Expected signal and background yields for the p4` T differential variable . . . 183
12.13Expected signal and background yields for the∣y4`∣ differential variable . . . 184
12.14Expected signal and background yields for the∣cos (θ∗)∣ differential variable . . . 184
12.15Expected signal and background yields for the m12 differential variable . . . 185
12.16Expected signal and background yields for the m34 differential variable . . . 185
12.17Expected signal and background yields for the njets differential variable . . . 186
LIST OF FIGURES
12.19Expected signal and background yields for the mjj differential variable . . . 187
12.20Expected signal and background yields for the∣∆ηjj∣ differential variable . . . 188
12.21Expected signal and background yields for the ∆φjj differential variable . . . 188
12.22Expected signal and background yields for the nbjets differential variable . . . 189
12.23p4` T and m12 migration matrices . . . 189
12.24m12and ∣y4`∣ migration matrices . . . 190
12.25∣cos (θ∗)∣ and njets migration matrices . . . 190
12.26pleading jetT and mjj migration matrices . . . 191
12.27∣∆ηjj∣ and ∆φjj migration matrices . . . 191
12.28nbjets migration matrix . . . 192
12.29Purity of production modes for the Higgs boson kinematic differential variables . . . 193
12.30Purity of production modes for the jet differential variables . . . 194
12.31Acceptance and correction factors per production mode, in bins of p4` T . . . 197
12.32Acceptance and correction factors per production mode, in bins of∣y4`∣ . . . 198
12.33Acceptance and correction factors per production mode, in bins of m34 . . . 199
12.34Acceptance and correction factors per production mode, in bins of m12 . . . 200
12.35Acceptance and correction factors per production mode, in bins of∣cos (θ∗)∣ . . . 201
12.36Acceptance and correction factors per production mode, in bins of njets . . . 202
12.37Acceptance and correction factors per production mode, in bins of pleading jetT . . . 203
12.38Acceptance and correction factors per production mode, in bins of mjj . . . 204
12.39Acceptance and correction factors per production mode, in bins of∣∆ηjj∣ . . . 204
12.40Acceptance and correction factors per production mode, in bins of ∆φjj . . . 205
12.41Acceptance and correction factors per production mode, in bins of nbjets . . . 205
12.42Comparison of measured and expected differential fiducial cross section in bins of p4` T . . . . 206
12.43Comparison of measured and expected differential fiducial cross section in bins of the Higgs boson variables . . . 207
12.44Comparison of measured and expected differential fiducial cross section in bins of njets and pleading jetT . . . 208
12.45Comparison of measured and expected differential fiducial cross section in bins of the jet variables . . . 209
12.46Binning chosen for the double-differential(m12, m34) variable . . . 213
12.47Expected signal and background yields for the p4`T (njets= 0) differential variable . . . 214
12.48Expected signal and background yields for the p4`T (njets= 1) differential variable . . . 214
12.49Expected signal and background yields for the p4` T (njets≥ 2) differential variable . . . 215
12.50Expected signal and background yields for the(m12, m34) differential variable . . . 215
12.51Acceptance and correction factors per production mode, in bins of p4` T (njets= 0) . . . 216
12.52Acceptance and correction factors per production mode, in bins of p4` T (njets= 1) . . . 217
LIST OF FIGURES 12.53Acceptance and correction factors per production mode, in bins of p4`
T (njets≥ 2) . . . 218
12.54Acceptance and correction factors per production mode, in bins of(m12, m34) . . . 218
12.55Double-differential migration matrices . . . 220
12.56Inclusive(m12, m34) distribution for the various bins . . . 221
12.57Comparison of measured and expected double-differential fiducial cross sections . . . 222
12.58Limits on contact-interaction decay to the left and right-handed leptons, and coupling to the Z bosons for the Higgs-to-four-lepton channel . . . 224
A.1 Validation plots of the LooseTrackOnly scale factors, integrated over η and in various η regions . . . 228
A.2 Validation plots of the Loose scale factors, integrated over η and in various η regions . . . . 229
A.3 Validation plots of the Tight scale factors, integrated over η and in various η regions . . . . 230
A.4 Validation plots of the GradientLoose scale factors, integrated over η and in various η regions231 A.5 Validation plots of the Gradient scale factors, integrated over η and in various η regions . . 232
A.6 Validation plots of the FixedCutTightTrackOnly scale factors, integrated over η and in various η regions . . . 233
A.7 Validation plots of the LooseTrackOnly scale factors, in various ∆Rµj regions . . . 234
A.8 Validation plots of the Loose scale factors, in various ∆Rµj regions . . . 235
A.9 Validation plots of the Tight scale factors, in various ∆Rµj regions . . . 236
A.10 Validation plots of the GradientLoose scale factors, in various ∆Rµj regions . . . 237
A.11 Validation plots of the Gradient scale factors, in various ∆Rµj regions . . . 238
A.12 Validation plots of the FixedCutTightTrackOnly scale factors, in various ∆Rµj regions . . . 239
E.1 Efficacités et facteurs d’échelle du point de fonctionnement FixedCutLoose . . . 255
List of Tables
2.1 The LHC programme . . . 10
2.2 Run 2 expectations . . . 10
3.1 Segmentation of the calorimeters . . . 21
3.2 Number of muon chambers for each η region . . . 27
3.3 Muon reconstruction efficiencies and fake rates . . . 35
6.1 Muon and electron isolation working points . . . 58
6.2 Preliminary assessment of the efficiencies of the isolation working points from Z→ µµ decays 61 6.3 Preliminary assessment of the signal efficiencies and background rejections of the isolation working points from t¯t decays . . . 62
7.1 Selection criteria on tag and probe muons for isolation efficiency measurements . . . 64
7.2 The Loose and TightPrimary track working points . . . 68
7.3 The various systematic contributions for the muon isolation scale factors . . . 84
10.1 Properties of the quarks . . . 105
10.2 Properties of the bosons . . . 110
10.3 Properties of the leptons . . . 110
11.1 SM Higgs boson production cross sections for the various production modes . . . 123
11.2 Electron discriminating variables . . . 125
11.3 HLT triggers used during 2015 data taking . . . 128
11.4 HLT triggers used during 2016 data taking . . . 129
11.5 Summary of the event selection requirements . . . 131
11.6 Example cut flow using gluon-gluon fusion simulated events . . . 132
11.7 Results of the closure test of the simultaneous fit for the Z+ µµ background estimation . . 141
11.8 Results of the simultaneous fit using the data for the Z+ µµ background estimation . . . . 141
11.9 Final estimates in the signal region for the Z+ HF, t¯t, Z + LF and WZ components of the Z+ µµ backgrounds . . . 142
LIST OF TABLES 11.10Efficiencies of isolation and impact parameter selections for background muons selected in
Z+ µ events . . . 142
11.11Isolation and impact-parameter efficiencies for background muons in the light- and heavy-flavour enriched Z+ µ samples. . . 142
11.12Fit result of the yields in the 3`+ X control region with the efficiency used to extrapolate to the signal region . . . 147
11.13Data / MC scale factors for the MC simulated f and γ contributions accompanying recon-structed Z events . . . 147
11.14Contributions of the systematic uncertainties for the cross-section measurements in the H4` channel . . . 152
11.15Number of events expected and observed for a mH = 125 GeV Higgs boson . . . 153
11.16Expected signal rates per final state . . . 153
12.1 Fiducial phase space definition . . . 161
12.2 Relative loss in event yields using born or dressed lepton definitions . . . 163
12.3 Relative loss in event yields using various ∆R`γ cuts in the dressed lepton definition . . . . 163
12.4 Fiducial leakage estimation from the ggF production mode at mH = 125 GeV . . . 165
12.5 Inclusive acceptance factors per production mode and decay channel . . . 169
12.6 Inclusive correction factors per production mode and decay channel . . . 169
12.7 Uncertainties on the inclusive correction and acceptance factors . . . 173
12.8 Expected and fitted inclusive cross section using Asimov dataset and assuming an integrated luminosity of 36.1 fb−1 . . . 175
12.9 Observed and expected inclusive cross section using 36.1 fb−1 of recorded data . . . 181
12.10Binning chosen for the Higgs kinematic differential variables . . . 182
12.11Binning chosen for the jet differential variables . . . 186
12.12Acceptance and correction factors per production mode, in bins of p4`T . . . 196
12.13Acceptance and correction factors per production mode, in bins of∣y4`∣ . . . 197
12.14Acceptance and correction factors per production mode, in bins of m34 . . . 198
12.15Acceptance and correction factors per production mode, in bins of m12 . . . 199
12.16Acceptance and correction factors per production mode, in bins of∣cos (θ∗)∣ . . . 200
12.17Acceptance and correction factors per production mode, in bins of njets . . . 201
12.18Acceptance and correction factors per production mode, in bins of pleading jetT . . . 202
12.19Acceptance and correction factors per production mode, in bins of mjj . . . 203
12.20Acceptance and correction factors per production mode, in bins of∣∆ηjj∣ . . . 203
12.21Acceptance and correction factors per production mode, in bins of ∆φjj . . . 204
12.22Acceptance and correction factors per production mode, in bins of nbjets . . . 205
12.23Comparison of measured and expected differential fiducial cross section in bins of p4` T . . . . 210
LIST OF TABLES
12.25Comparison of measured and expected differential fiducial cross section in bins of m12 . . . 210
12.26Comparison of measured and expected differential fiducial cross section in bins of m34 . . . 211
12.27Comparison of measured and expected differential fiducial cross section in bins of∣cos (θ∗)∣ 211 12.28Comparison of measured and expected differential fiducial cross section in bins of njets . . . 211
12.29Comparison of measured and expected differential fiducial cross section in bins of pleading jetT 212 12.30Comparison of measured and expected differential fiducial cross section in bins of mjj . . . 212
12.31Comparison of measured and expected differential fiducial cross section in bins of∣∆ηjj∣ . . 212
12.32Comparison of measured and expected differential fiducial cross section in bins of ∆φjj . . 212
12.33Comparison of measured and expected differential fiducial cross section in bins of nbjets . . 212
12.34Binning chosen for the double-differential p4` T against njets variables . . . 213
12.35Acceptance and correction factors per production mode, in bins of p4` T (njets= 0) . . . 216
12.36Acceptance and correction factors per production mode, in bins of p4` T (njets= 1) . . . 217
12.37Acceptance and correction factors per production mode, in bins of p4` T (njets≥ 2) . . . 218
12.38Acceptance and correction factors per production mode, in bins of(m12, m34) . . . 219
12.39Comparison of measured and expected differential fiducial cross section in bins of p4` T (njets= 0)220 12.40Comparison of measured and expected differential fiducial cross section in bins of p4` T (njets= 1)221 12.41Comparison of measured and expected differential fiducial cross section in bins of p4` T (njets≥ 2)221 12.42Comparison of measured and expected differential fiducial cross section in bins of(m12, m34)223 C.1 Efficiencies of various triggers configurations used in 2015 . . . 244
C.2 Efficiencies of various triggers configurations used in early 2016 . . . 245
C.3 Efficiencies of various triggers configurations used in late 2016 . . . 246
D.1 MC samples used for the late quadruplet selection and for the early isolation cut studies . . 248
D.2 Results of the standard selection . . . 248
D.3 Results of the late quadruplet selection . . . 249
D.4 Comparison late and standard quadruplet selections . . . 249
D.5 Results of early isolation selection . . . 249
D.6 Comparison early isolation and standard quadruplet selections . . . 250
E.1 Nombre d’événements attendus et observés sous l’hypothèse du boson de Higgs de masse mH = 125 GeV . . . 257
Chapter 1
Introduction
Particle physics aims at studying the smallest constituents of matter in the universe by describing their fundamental properties and interactions. The underlying theory is the so-called Standard Model which was developed in the last century and proved to be really successful in predicting the elementary in-teractions between particles, as well as foreseeing the existence of new particles which were discovered afterwards. In order to perform particle physics research, state-of-the-art facilities were built at CERN (European Organization for Nuclear Research) close to Geneva, the latest being the LHC (Large Hadron Collider) which collides beams of protons at world-record centre-of-mass energies√s. The machine entered
operation in 2009 and thanks to the data collected and analysed by the ATLAS and CMS experiments at √s= 8 TeV, the discovery of the Higgs boson was announced in July 2012. This particle was the missing piece of the Standard Model and its discovery comforted the theory in its predictions, as the boson turned out to satisfy all the requirements from the model. After a long shut-down, the LHC restarted in 2015 and delivers proton-proton collisions at √s = 13 TeV, doubling its previous records. In 2015 and 2016,
36.1 fb−1 of data was recorded by the ATLAS experiment alone, superseding the statistics obtained from the previous periods of data taking. The higher centre-of-mass energy enables to probe a wider phase space to test the validity of the Standard Model and possibly discover new physics beyond the model. The increased statistics available also allow precise measurements of the properties of the particles to confirm or infirm the most recent predictions and theories.
The main topic of this thesis is the study of the recently discovered Higgs boson in its decay to two Z bosons, in turn decaying to four leptons. Thanks to very good detector resolution and lepton reconstruction, the mass of the two decaying Z bosons enables very fine measurement of the mass of the Higgs, as well as suppressing background contamination resulting in very low yields. The overall sensitivity is therefore high, and together with the Higgs boson decaying to two photons, the Higgs boson was discovered in 2012 in this channel. With the new data taking conditions in 2015 and 2016, the sensitivity is further improved by a factor of two with respect to 2012, with the increased √s. Precise
measurements can hence be performed to better understand the properties of the Higgs boson, including the measurement of its mass and its couplings to other bosons, and probe the validity of the Standard Model and the possible existence of new physics. Using 36.1 fb−1 of data, the total, differential and double-differential cross sections in the Higgs-to-four-lepton decay channel are calculated and compared to the most recent Standard-Model predictions.
In addition to the analysis of the Higgs boson decaying to four leptons, dedicated studies on the isolation of muons are performed. These studies consist in assessing whether a particle is produced together with ambient activity surrounding its trajectory in the detectors and in which proportions this activity relates to the energy of the particle. This is a powerful tool in discriminating signal events (composed of
Chapter 1. Introduction well-isolated muons) from background processes. Isolation variables are defined and selection criteria are applied to them in order to reduce background contamination. The work described in this thesis consists in improving the definition of the variables to cope up with the challenging data taking conditions as well as to increase background rejection. Working points are defined as sets of cuts on the variables to fulfil the needs of the various analysis groups. One of these working points is specifically designed for the Higgs-to-four-lepton analyses. The related signal efficiencies are finally calculated using Z boson decays to two muons. The correspondence between data and simulation is estimated by deriving scale factors defined as ratios of efficiencies, and used by the analysis groups to correct their predictions.
The thesis is organised as follows. A brief description of the LHC machine is given in Chap. 2, which explains how the protons are accelerated in beams before colliding at the centres of the experiments. The programme of the physics runs, which correspond to period of data taking, is outlined with an overview of the future prospects of the machine. The physics conditions in Run 2 (2015 - 2016) are specifically compared to those of Run 1 (2011 - 2012). Chapter 3 focuses on the detailed description of the detector. The design and technologies used for each sub-detector to meet the requirements in terms of particle identification and reconstruction are outlined. For each system, a comparison is given between the expected performance, and the results obtained in Run 1 and Run 2. Changes in detector design during the long shut down 1 of the LHC (2013 - 2015) to face the increased radiation rates are detailed. Chapter5gives a definition of the isolation variables grouped into two categories: the track-based isolation using information from the Inner Detector, and the calorimeter-based isolation relying on energy deposits in the calorimeters. The changes with respect to Run 1 are highlighted, especially the use of a clustering algorithm to retrieve the energy of the calorimeter cells, as well as using a variable cone size for the track isolation. Cuts are applied to these variables to define isolation working points, described in Chap. 6. These working points are characterised in terms of expected signal efficiencies and background rejection. The performance studies of muon isolation are summarised in Chap.7, corresponding to 36.1 fb−1 of data recorded by the ATLAS detector. The distributions of the isolation variables are compared between data and simulation and deviations are further analysed. Specific care is brought to ensure the variables are robust against the challenging physics conditions. The signal efficiencies of the isolation working points are then calculated using the Tag-And-Probe method on Z boson decays to two muons. Agreement between data and simulation is translated into scale factors, which are measured along with systematic uncertainties. Chapter 8finally presents the tool enabling the correction of the isolation variables in case of events where several signal objects are close to each other. After a brief summary of the Standard Model and its limitations in Chap. 10, insisting on how the Higgs boson is produced and decays at the LHC, the analysis strategy of the Higgs-to-four-lepton decay channel is described in Chap. 11. The theory predictions used for the studies are detailed together with the criteria applied on the leptons and jets to select the events. The methodology used to estimate the background yields and shapes is described, and results with 36.1 fb−1of data are presented in terms of the number of observed events and the expected signal and background yields for the various possible final states. Finally, Chap.12outlines the measurements of the Higgs-to-four-lepton production cross section. Using the signal and background yields and shapes, an extended Poissonian likelihood is defined and the cross sections are extracted using a fit on the four-lepton invariant mass. The results are given in the phase space corresponding to the analysis (fiducial cross section) and are also extrapolated to the total phase space (total cross section) using factors which are calculated for each production mode and each final state. Measurements are also performed in bins of differential variables (kinematics of the four-lepton final state and variables related to the jets of the event). The inclusive and differential measurements offer the opportunity to probe the validity of the Standard Model: observations are compared to predictions and constraints are set on the anomalous contact-interaction decays of the Higgs boson to left and right-handed leptons, and the anomalous coupling of the Higgs boson to the Z bosons.
Part I
Chapter 2
The Large Hadron Collider
The LHC [1] is the world’s most recent and most powerful accelerator designed to study particle physics. It is the biggest machine of the European Organisation for Nuclear Research (CERN) close to Geneva (Switzerland and France), which can deliver proton-proton collisions with a centre-of-mass energy up to √
s= 14 TeV and can accelerate lead ions (Pb) up to√s= 2.8 TeV per nucleon.
The LHC is a 26.7 km superconducting double-ring collider, which was built using the tunnel hosting the Large Electron-Positron Collider (LEP). This tunnel is divided into eight straight sectors and eight arcs, and is located between 45 m and 170 m below the surface. While the LEP was in operation from 1989 to 2000, with electron-positron collisions from 90 GeV up to 209 GeV, the LHC entered in operation in 2008 after a major upgrade of the machine.
The LHC targets centre-of-mass energies which are about seven times higher than the records set by the particle accelerator Tevatron (now inactive, since 2011) in the United States, at the Fermi National Accelerator Laboratory [2]. For the LHC to reach its designed energies, several steps are needed. Figure
2.1illustrates the various machines involved in accelerating and preparing the two beams of protons for the collisions. First, hydrogen atoms (composed of an electron and a proton) undergo a strong electric field which separates the orbiting electrons. The remaining protons are injected into the LINAC2 accelerator, which increases their energy up to 50 MeV. Afterwards, the Proton Synchrotron Booster (PSB) accelerates these protons from 50 MeV to 1.4 GeV. The beam is then injected into the Proton Synchrotron (PS) where it is accelerated to an energy of 25 GeV before being sent to the Super Proton Synchrotron (SPS) where the beam energy reaches 450 GeV. Finally, the beam enters the LHC (two beams are sent at the same time, one clockwise, the other anticlockwise, the filling time is 4 min 20 s per LHC ring). The two injected beams are accelerated for 20 min to a total√s= 13 TeV (reached so far).
Under optimal conditions, the beams can circulate in the LHC for approximately ten hours, travelling more than 1012m, at a speed close to 0.999999991 times the speed of light. The beams are prepared in bunches in the smaller subsystems, because of the radio frequency (RF) technique used for the acceleration. Protons are accelerated when the electric field has the correct orientation while passing through an accelerating cavity and these conditions are fulfilled at special times of the RF cycle of the field. Under nominal operation, a proton beam is composed of 2808 bunches, each bunch containing about 1011protons. While travelling around the LHC, the bunches get squeezed (they get a length of 16 µm close to the interaction points to maximise the probability of collisions) and expanded (they acquire lengths of a few centimetres far from the collision points).
The LHC consists of eight arcs and eight insertions. 154 bending magnets are installed in each arc, whereas an insertion is composed of a long straight section surrounded with two transition sections, referred to as the dispersion suppressors, which absorb the dispersed particles of the beams, avoiding
Chapter 2. The Large Hadron Collider
CERN
faq
LHC
the guide
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Figure 2.1 – The various experiments and accelerators at CERN. The collisions of the beams in the LHC happen at four points where the major experiments are located: ALICE, ATLAS, CMS and LHCb [3].
What
are sectors and octants in the machine?The LHC is not a perfect circle. It is made of eight arcs and eight ‘insertions’. The arcs contain the dipole ‘bending’ magnets, with 154 in each arc. An insertion consists of a long straight section plus two (one at each end) transition regions — the so-called ‘dispersion suppressors’. The exact layout of the straight section depends on the specific use of the insertion: physics (beam collisions within an experiment), injection, beam dumping, beam cleaning.
A sector is defined as the part of the machine between two inser-tion points. The eight sectors are the working units of the LHC: the magnet installation happens sector by sector, the hardware is com-missioned sector by sector and all the dipoles of a sector are con-nected in series and are in the same continuous cryostat. Powering of each sector is essentially independent.
An octant starts from the middle of an arc and ends in the middle
Octa nt 8 O cta nt 7 Octa nt 6 Octant 5 Oct ant 4 O ct an t 3 O cta nt 2 Octant 1 Beam dump Arrêt des faisceaux
Injection
Injection
Beam cleaning Nettoyage des faisceaux
CMS
LHCb ATLAS
ALICE
Beam cleaning Nettoyage des faisceaux
Figure 2.2 – The LHC is divided into eight octants, which start and end at the middle of an arc. Therefore, an octant includes a complete insertion [4].
reflections along the pipes. The straight sections have different layouts depending on the use of the insertion. Four types of insertions are used: for physics (beam collisions at the interaction points of the experiments), for the injection of the beams, for the dumping of the beams and for the beam cleaning (to increase the focusing and the purity of the beams). As shown in Fig.2.2[4], an octant starts and ends at the middle of an arc, therefore including a complete insertion.
The LHC has various vacuum systems ensuring the beam vacuum, which is essential for the purity and the stability of the collisions, and taking care of the insulation of the cryomagnets used to cool down
2.1 Luminosity
the magnets. Pressures as low as 10−8Pa are achieved. Various types of magnets are used along the accelerator to bend the particles, for a total of about 9600 magnets. The limiting factor of the LHC is not the acceleration of the particles, but the bending power of the dipole magnets.
The LHC programme is composed of Runs, periods of time during which collisions happen (proton-proton or heavy ions) and long shut-downs, during which the equipments of the LHC and the experiments are upgraded to achieve the new targeted luminosity and√s. During the shut-downs, the caverns (where
the experiments are located) and the LHC tunnel are accessible for maintenance and some parts of the detectors can be replaced or improved. On the contrary, during runs, the LHC provides collisions which are recorded by the various experiments, and both the tunnels and the caverns cannot be accessed.
2.1
Luminosity
One of the essential parameters of a collider is the instantaneous luminosityL, which is a measurement of the probability of an interaction per unit of time. For a given process p, the number of events per second generated by the interactions is related to its integration over time:
Np= σp∫ Ldt, (2.1)
where σp is the cross section of the process p. The instantaneous luminosity depends on the parameters of the collider:
L = N4πεb2nbfrγ
nβ∗ F, (2.2)
where Nb is the number of particles per bunch (1011at the LHC), nb is the number of bunches per beam,
fr is the revolution frequency, γ is the relativistic gamma factor, εn is the transverse beam emittance
normalised to the beam size, β∗ is the beta function at the collision point related to the beam focusing and F is the geometric luminosity reduction factor accounting for the angle between the two beams when they collide [5,6,7].
Increasing the number of bunches per beam is one of the ways to reach higher instantaneous lu-minosities. At full luminosity the LHC uses a bunch spacing of 25 ns (about 7 m of spacing), which corresponds to a frequency of 40 MHz. Each beam consists of about 3000 bunches of particles. Taking into account the frequency of the bunch injection, the LHC supports instantaneous luminosities of the order of 1034cm−2s−1. A second parameter which can be optimised to reach higher luminosities is the beta function at the collision points. This quantity is high far from the interaction points, but reduced as much as possible in the vicinity of the experiments.
To account for the total number of events for a specific process, the luminosity integrated over time is the relevant parameter (referred to as integrated luminosity ∫ Ldt). During Run 1 (2012), the total integrated luminosity was of 23.3 fb−1 with an instantaneous luminosity of less than 1034cm−2s−1. After the long shut down, the LHC restarted in mid 2015 for the Run 2. Instantaneous luminosities of 1.5 to 2.0× 1034cm−2s−1were reached in 2016, leading to an integrated luminosity of 36.1 fb−1 for the combined 2015 and 2016 datasets. By the end of 2018, the total integrated luminosity should reach 100 fb−1.
As an example, for the H → ZZ∗ → 4` decay channel, subject of the last part of this thesis, the integrated luminosity of the year 2012 corresponds to 20 expected Higgs candidates at √s = 8 TeV.
Chapter 2. The Large Hadron Collider
Mean Number of Interactions per Crossing 0 5 10 15 20 25 30 35 40 45 50 /0.1] -1 Delivered Luminosity [pb 0 20 40 60 80 100 120 140 160 180 200 =13 TeV s Online, ATLAS
∫
Ldt=33.5 fb-1 > = 13.7 µ 2015: < > = 24.2 µ 2016: < > = 22.9 µ Total: < 7/16 calibrationFigure 2.3 – Pile-up conditions in Run 2, represented using the number of interac-tion per bunch crossing µ for the data 2015, data 2016 and combined datasets [9].
greater) and the increase of cross section at√s= 13 TeV (two times greater). Note that for the data 2015
and 2016 combined, 106 events are expected in this channel.
A drawback from an increased instantaneous luminosity is the increased number of interactions per bunch crossing (referred to as pile-up). For each proton-proton interaction, a vertex is formed from which the decay products interesting to the studies emerge. This is the primary vertex. Additional vertices are also created from decay products or other interactions, referred to as secondary vertices. These vertices are recorded by the detectors at the same time as the primary vertex and mask the useful information coming from the latter. This makes the selection of good events for the analyses harder.
Two kinds of pile-up have to be taken into account. In-time pile-up corresponds to more than one interaction in the same bunch of crossings: the primary vertex is mixed with secondary vertices arising from the same interaction. The second type, referred to as out-of-time pile-up, concerns interactions between several consecutive bunch crossings. Because of the LHC bunch spacing of 25 ns, signal modula-tion from multiple interacmodula-tions in surrounding bunch crossings is possible to which the sub-detectors are sensitive [8].
The notion of pile-up will be further detailed in the chapter 5.2. A general relationship between the instantaneous luminosity and in-time pile-up is given by:
⟨µ⟩ = Lσpp
nbfLHC, (2.3)
where ⟨µ⟩ is the mean number of inelastic pp interactions per bunch crossing, σpp is the total inelastic pp cross section and fLHC is the frequency of injection of the bunches (40 MHz for a bunch spacing of
25 ns). In 2012 (at the end of Run 1), the instantaneous luminosity reached L = 7.7 × 1033cm−2s−1 with ⟨µ⟩ ≈ 22.7. In 2015 (2016), the instantaneous luminosity reached 5.0 × 1034cm−2s−1 (14× 1034cm−2s−1), and ⟨µ⟩ ≈ 14 (⟨µ⟩ ≈ 25) with a maximum value of 40 (50), as shown in Fig. 2.3[9].
2.2
The experiments at the LHC and the physics reach
The current knowledge of the forces governing the physics of the particles and the properties of the universe is summarised by the Standard Model (SM). Whereas this model was experimentally tested and
2.3 Physics runs and upgrades
provided very precise predictions of the physical constants as well as anticipating the existence of particles before their discoveries, some essential questions remain unanswered. The LHC was specifically designed to address these issues. This section briefly summarises the physics scopes of the experiments at LHC. A more detailed description of the SM and the Higgs mechanism is provided in part III.
With these challenging goals, the LHC was approved for construction in December 1994 and could be built within a single stage after the LEP closure in 2000. In the mean time, four experiments – ALICE (A Large Iron Collider Experiment), ATLAS (A Toroidal LHC ApparatuS), CMS (Compact Muon Solenoid) and LHCb – were installed at the four sites where the proton beams collide. The goals of these experiments are briefly described in the following. Later, smaller experiments joined the programme: MoEDAL [10], TOTEM [11] installed close to CMS and LHCf [12] located in the vicinity of ATLAS.
ALICE [13] was designed to analyse heavy ion collisions. It focuses on studying the quark-gluon plasma in conditions which are close to those at the very early stages of the universe, according to models. Although the other collaborations also benefit from the heavy ion collisions, ALICE is specifically devoted to studying them.
ATLAS [14], together with CMS [15], are general-purpose detectors which aim at covering the widest range of physics possible at the LHC. To name but a few, these experiments focus on the Higgs mechanism, precise measurements of the parameters of the SM, and the study of beyond-SM models such as SUSY or extra dimensions. The ATLAS experiment will be further described in Chap. 3.
The CMS detector is built around a huge superconducting solenoid which can generate a very high and homogeneous magnetic field up to 3.8 T. This compact structure enables the reconstruction of leptons and photons with high accuracy and efficiencies to probe the widest phase space.
LHCb [16] specialises in studying the violation of symmetry (CP violation) between matter and an-timatter in interactions of particles containing the b-quark. Understanding this asymmetry would add valuable ground to the matter-antimatter issue. This experiment uses a detector which, instead of sur-rounding the beam line, is composed of a series of various sub-detectors, which aim at detecting the very forward particles.
2.3
Physics runs and upgrades
Since its original design, the LHC underwent several upgrades in order to increase its luminosity and√s.
Increasing the luminosity and √s pushes further the requirements on the various parts of the detectors,
because of higher radiation levels necessitating more resilient equipment. Furthermore, the flow of data is also increased and more sophisticated trigger algorithms have to be developed to cope up with the data taking rates, and the new pile-up conditions.
The successful operation of the LHC in Run 1 allowed the various experiments to record data, which improved the common understanding of the Standard Model with the discovery of the Higgs boson [17,
18, 19] in 2012 [20,21], as well as providing very precise measurements of the parameters of the model (mass of the bosons as well as cross sections and estimation of the fundamental constants). Overall more than 2000 papers were published by the various experiments at CERN (more than 400 for ATLAS alone). For the Run 2, the trigger algorithms of the experiments were improved to abide by the reduced bunch spacing (reduced from 50 ns to 25 ns), which is the major change to reach higher instantaneous luminosities. A more detailed schedule of the Run 2 is given in Tab. 2.2.
Subsequently, the Runs 3 and 4 will allow the accelerator to provide even higher luminosities at the same centre-of-mass energy. Table 2.1 gives an overview of the various expected physics runs at the
Chapter 2. The Large Hadron Collider Table 2.1 – The various physics Runs and upgrades of the LHC programme [22].
Phys. Run Period Max. L [cm−2s−1] √s [TeV] Bunch spacing ∫ Ldt
Run 1 2010 - 2013 (passed) 3 - 7× 1033 7 - 8 50 ns 25 fb−1 achieved
Long shut-down 1 (phase 0 upgrade)
Run 2 2014 - 2018 (current Run) 1× 1034 13 25 ns 100 fb−1expected
Long shut-down 2 (phase 1 upgrade)
Run 3 2019 - 2022 (expected) 2 - 3× 1033 14 25 ns 300 fb−1expected
Long shut-down 3 (phase 2 upgrade)
Run 4 2022 - 2030 (expected) 5× 1034 14 25 ns 3000 fb−1 expected
Table 2.2 – Run 2 expectations [22].
Year Max. L [cm−2s−1] ∫ Ldt [fb−1]
2015 (passed) 5.0× 1033 3.36
2016 (passed) 1.37× 1034 36
2017 and 2018 (expected) 1.7× 1034 ≥ 75
LHC [22]. The targeted instantaneous luminosities are about five times bigger as compared to the original design. Parts of the detectors of the experiments will have to be replaced using technologies which are more resilient to extreme radiation conditions. In particular, ATLAS plans to replace the very forward regions of its detector. The discovery of new physics within these Runs may trigger the construction of an even bigger accelerator, in which the LHC would be a part of the injector [23].
Chapter 3
The ATLAS experiment
The ATLAS (A Toroidal LHC ApparatuS) experiment is one of the four biggest experiments at the LHC, located at point 1. To observe physical processes on a broad range, the detector has to meet the following requirements [14]:
• Full azimuthal coverage and optimised geometrical acceptance.
• Accurate measurement of the coordinates of the particles (tracking) and precise assessment of the momentum over a wide range (from a few MeV to the TeV scale).
3.1
Geometry of the detector
The ATLAS collaboration uses a set of coordinates which are related to the geometry of the detector, as presented in Fig. 3.1. The z axis of the right-handed Cartesian system used by the collaboration is the beam axis. Perpendicular to this axis is the (x, y) plane. The x and y axes point towards the centre of the LHC ring and upwards, respectively [14].
At z = 0, the detector is symmetric across the (x, y) plane (transverse plane), dividing the detector into two sides A (z> 0) and C (z < 0). The related cylindrical coordinates are defined as follows: R is the distance to the z axis, φ and θ are the azimuthal and polar angles, respectively.
The rapidity y is defined as
y= 1
2ln(
E+ pz E− pz) ,
(3.1) where E and pz are the energy and the z component of the momentum of the particle, respectively. The
rapidity transforms additively under boosts in the z direction: differences in rapidity ∆y and the particle density per unit of rapidity dN/dy are Lorentz invariants. In the ultra-relativistic limit, where E is much greater than the mass of the particle M, the pseudo-rapidity defined as
η= − ln (tanθ
2) (3.2)
approximates the rapidity. The pseudo-rapidity is a function of θ and is mass-independent. It is therefore widely used in particle physics [24]. Since particles are expected to be produced uniformly in η, the ATLAS detectors are segmented according to this variable.
Chapter 3. The ATLAS experiment
x
y
z
Beam axis
Centre of
the LHC
y
x
z
R
Transverse
plan
✓
p
✓
p
Figure 3.1 – The system of coordinates used in the ATLAS collaboration.
The azimuthal angle φ is not affected by boosts in the z direction. As a consequence, distances in the azimuthal pseudo-rapidity plane can easily be measured using ∆R=√(∆φ)2+ (∆η)2.
In the ATLAS frame, only components in the(x, y) plane are invariant under boosts in the z direction. Therefore, the transverse momentum of a particle is preferred and defined as pT= p sin θ =
√
p2x+ p2y, where p is the norm of the momentum of the particle. The momentum of the particle can then be calculated
using p=√p2T+ p2z.
In order for the ATLAS detector (shown in Fig. 3.2) to identify various physics processes, a good reconstruction of the final-state particles with their properties (the type of the particle, its charge, mass, energy, momentum and position) is needed. For all kinds of particles to be identified, the detector is divided into several sub-detectors with specific targets. The Inner Detector (ID) surrounds the beam pipe and charged particles produced at the interaction point (IP) are bent by the solenoidal magnetic field to assess their charge and measure their transverse momentum. Then, these particles reach the Calorimeters (Cal) where electrons, photons and hadrons shower, having their transverse energy estimated. Only muons traverse the calorimeters to enter the Muon Spectrometer (MS), where their momentum is precisely measured thanks to the toroid magnets surrounding the MS chambers. Only neutrinos remain transparent to the detectors and need to be identified using the missing energy in the transverse plane.
A brief description of the sub-detectors is given in the following subsections. A more detailed review can be found in Ref. [14].
3.2
The Inner Detector
Precise measurements of the coordinates of the track particles rely on a high bending power of the magnets and a fine granularity of the detectors in assessing the positions of the hits of the charged particles. Combining these two features, the Inner Detector (ID) provides a state-of-the-art pattern recognition, measurements of the momenta and vertices, and allows a good electron identification.
These functionalities are achieved using four sub-systems. Starting from the most inner part to the outer layers, the ID is composed of precision silicon detectors (the insertable B-layer IBL, the pixel
3.2 The Inner Detector
Figure 3.2 – Overview of the ATLAS detector. The interaction point (IP) is located at the centre of the detector, surrounded with the Inner Detector (ID), the Calorimeters (Cal) and the Muon Spectrometer (MS) [25].
(a) General view
Figure 1: Sketch of the ATLAS inner detector showing all its components, including the new insertable B-layer (IBL). The distances to the interaction point are also shown.
(b) Radial view
Figure 3.3 – Layout of the ATLAS Inner Detector (ID), with (a) the general and (b) the radial views [26].
![Figure 3.9 – Measured longitudinal impact parameter resolution in data as a function of (a) p T and (b) η , compared between Run 1 and Run 2 [33].](https://thumb-eu.123doks.com/thumbv2/123doknet/12858442.368405/39.918.162.754.124.363/figure-measured-longitudinal-impact-parameter-resolution-function-compared.webp)
![Figure 3.16 – Comparison of the noise in the LAr calorimeters between data 2015 and simulation [41].](https://thumb-eu.123doks.com/thumbv2/123doknet/12858442.368405/45.918.99.817.121.404/figure-comparison-noise-lar-calorimeters-data-simulation.webp)
![Figure 3.18 – Electron reconstruction and identification efficiencies in Z → ee events using 2015 data [43].](https://thumb-eu.123doks.com/thumbv2/123doknet/12858442.368405/47.918.164.753.120.440/figure-electron-reconstruction-identification-efficiencies-events-using-data.webp)
![Figure 6.1 – Cut values on topoetcone20 as a function of p µ T and η µ [46], for the (a) Gradient , (b) GradientLoose , (c) Loose and (d) Tight working points, respectively.](https://thumb-eu.123doks.com/thumbv2/123doknet/12858442.368405/81.918.88.835.118.676/figure-values-topoetcone-function-gradient-gradientloose-working-respectively.webp)
