Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2013 The Higgs Boson: The Search for the Standard Model Higgs Boson and Investigation of Its Properties Joseph P. Bochenek Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES THE HIGGS BOSON: THE SEARCH FOR THE STANDARD MODEL HIGGS BOSON AND INVESTIGATION OF ITS PROPERTIES By JOSEPH P. BOCHENEK A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Summer Semester, 2013 Joseph P. Bochenek defended this dissertation on May 23, 2013. The members of the supervisory committee were: Harrison B. Prosper Professor Directing Dissertation Michael Ruse University Representative Andrew Askew Committee Member Takemichi Okui Committee Member Nicholas Bonesteel Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with the university requirements. ii ACKNOWLEDGMENTS I want to thank all of the people at the FSU High Energy Physics group who helped me along the way. To my advisor Harrison Prosper, whose love for ideas and enthusiasm for science always served as a reminder for why we do physics in the first place. Thanks to Nicola De Filippis and Kurtis Johnson for many interesting discussions, late nights at work, and for sharing many delicious pizzas with me in Florida, Italy and Switzerland. I am grateful to Pushpalatha Bhat for her ideas and support while I was at CERN. Thanks also to my mother, who instilled a fascination with nature and science from an early age, and my father for giving me a healthy sense of skepticism, which is indispensable in conducting good research. Also, thanks to my friends on the fifth floor for making things fun and interesting over coffee in the day and beers at night: Nobuo, Karoline, Thomas, Brendan, and everyone else. Thanks especially to Dianna without whose support, encouragement, and love I would never have made it this far. iii TABLE OF CONTENTS List of Tables ........................................ vii List of Figures ....................................... viii List of Symbols ....................................... xiii Abstract ........................................... xiv 1 Introduction 1 1.1 Theory ....................................... 2 1.1.1 Introduction to the Standard Model .................. 2 1.1.2 Anatomy of the Standard Model .................... 4 1.2 Symmetries .................................... 6 1.3 Gauge Invariance ................................. 8 1.3.1 Example: Scalar Electrodynamics ................... 8 1.4 The Standard Model Symmetry Group ..................... 11 1.5 The Higgs Field .................................. 14 1.5.1 The Higgs Mechanism .......................... 14 1.5.2 Spontaneous Symmetry Breaking .................... 17 1.5.3 Standard Model Higgs Field ....................... 19 1.5.4 Hierarchy Problem and Other Issues . 22 1.6 Higgs Properties ................................. 23 1.6.1 Decay Width ............................... 23 1.6.2 Higgs Boson Self Coupling ........................ 24 1.6.3 Couplings ................................. 24 1.6.4 Spin and Parity .............................. 28 2 Experimental Apparatus 32 2.1 The Large Hadron Collider ........................... 32 2.2 The Compact Muon Solenoid .......................... 33 2.2.1 Tracking System ............................. 38 2.2.2 Electromagnetic Calorimeter ...................... 39 2.2.3 Hadronic Calorimeter .......................... 40 2.2.4 Muon System ............................... 41 2.2.5 Trigger .................................. 43 iv 3 Objects 46 3.1 Tracks ....................................... 46 3.2 Particle Flow ................................... 48 3.3 Vertices ...................................... 49 3.4 Electrons ..................................... 50 3.4.1 Electron Reconstruction ......................... 50 3.4.2 Electron Energy Measurement ..................... 51 3.4.3 Electron Identification .......................... 55 3.5 Muons ....................................... 57 3.5.1 Muon Reconstruction .......................... 57 3.5.2 Muon Momentum Measurement .................... 57 3.5.3 Muon Identification ........................... 58 3.6 Lepton Isolation ................................. 58 3.6.1 Pileup Correction ............................. 59 3.7 Jets ........................................ 60 3.7.1 Jet Reconstruction ............................ 60 3.7.2 Jet Identification ............................. 61 3.7.3 Jet Energy Correction .......................... 61 3.8 Photons ...................................... 62 3.8.1 Photon Reconstruction, Identification, and Isolation . 62 4 Analysis 63 4.1 Analysis Overview ................................ 63 4.2 Datasets ...................................... 65 4.3 Event Selection .................................. 69 4.3.1 Analysis Triggers ............................. 69 4.3.2 Primary Vertices ............................. 69 4.3.3 Leptons .................................. 69 4.3.4 Event Criteria .............................. 71 4.3.5 FSR Recovery .............................. 73 4.4 Signal and Background Models ......................... 74 4.4.1 Signal Models ............................... 74 4.4.2 Irreducible Background ......................... 75 4.4.3 Reducible Background .......................... 75 4.5 Lepton Efficiency ................................. 82 4.6 Event-by-Event Uncertainty ........................... 85 4.7 Multivariate Discriminant ............................ 89 4.7.1 Introduction ............................... 89 4.7.2 Classifiers ................................. 90 4.7.3 Training Events .............................. 96 4.7.4 BNN Training .............................. 98 4.7.5 Discriminant Performance . 101 4.8 Systematic Uncertainties ............................. 105 4.8.1 Systematic Uncertainty Priors . 105 4.8.2 Summary of Systematic Uncertainties . 107 v 5 Results and Interpretation 113 5.1 Results ....................................... 113 5.2 Statistical Analysis ................................ 113 5.3 Likelihood Function ............................... 117 5.4 Nuisance Parameters ............................... 119 5.5 Discovery, Parameter Estimation, and Hypothesis Testing . 120 5.5.1 Discovery Significance . 121 5.5.2 Parameter Estimation . 122 5.5.3 Spin/Parity Hypothesis Testing . 123 5.6 Measurements ................................... 124 5.6.1 Discovery Significance . 124 5.6.2 Higgs Mass and Couplings . 124 5.6.3 Higgs Spin and Parity . 126 5.7 Conclusion .................................... 126 Appendices 128 A Marginalization of Statistical Uncertainties 128 B Priors 133 References .......................................... 139 Biographical Sketch .................................... 145 vi LIST OF TABLES 1.1 Fields of the standard model and their group symmetries [1] . 13 1.2 Coupling modifiers and signal strength modifiers for decay channels which are observable with 2012 data at the LHC. The µ are measured separately for each channel and can then be used to constrain the global κ parameters. 28 3.1 The five track parameters that define the helical pattern of a charged particle traversing the tracker. To fully define the trajectory we need a position on the path of the particle, the charge to momentum ratio (which detrmines the radius of the helix) of the particle, and the angle of the momentum of the particle with respect to the magnetic field. ................... 47 4.1 Data sets and triggers used in the analysis. ................... 67 4.2 Triggers in 2012 data analysis. .......................... 68 4.3 Monte Carlo simulation data sets used for the signal and background processes. Z stands for Z, Z∗, γ∗; ℓ means e, µ or τ; V stands for W and Z. 68 4.4 Parameters used to define neural network functions and hyperparameters in the BNNs. ..................................... 98 4.5 A summary of the systematic uncertainties affecting the overall scale in 7 TeV data listed in terms of κ value. 110 4.6 Systematic uncertainties affecting the overall scale in 8 TeV data listed in terms of κ value. ..................................... 110 vii LIST OF FIGURES 1.1 Two dimensional example of Higgs potential. The red circle signifies the de- generate space of minimum energy. ....................... 16 1.2 Predicted production cross section (right) and branching ratio (left) for a stan- dard model Higgs boson produced in proton-proton collisions at the LHC [2]. 24 1.3 Higgs production mechanisms at the LHC: gluon-gluon fusion (right), vector boson fusion (left). ................................. 26 1.4 Angles that characterize the decay of a resonance to two Z bosons [3]. 30 2.1 Cross section of the LHC beam pipe (left) and a map of the magnetic field produced by the superconducting dipole magnets (right). 33 2.2 Aerial view of the land above the LHC with an illustration of the accelerator ring and the location of each detector. ( c CERN) . 34 2.3 Outline of the LHC accelerator complex, which consists of a chain of accel- erators yielding protons with progressively higher energies. The acceleration chain starts with the LINAC, where protons are first accelerated to an energy of 50 GeV. The Proton Synchrotron Booster (PSB) increases the energy to 1.4 GeV,