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Higgs Phenomenology in the Standard Model and Beyond

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Higgs Phenomenology in the Standard Model and Beyond Higgs Phenomenology in the Standard Model and Beyond A Dissertation Presented by Bryan Jonathan Field to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Physics Stony Brook University May 2005 Copyright °c by Bryan Jonathan Field 2005 Stony Brook University The Graduate School Bryan Jonathan Field We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. John Smith C.N. Yang Institute for Theoretical Physics, Stony Brook University Dissertation Director George Sterman C.N. Yang Institute for Theoretical Physics, Stony Brook University Chairman of Dissertation Christopher Jacobsen Department of Physics, Stony Brook University Sally Dawson High Energy Theory Group Department of Physics, Brookhaven National Laboratory This dissertation is accepted by the Graduate School. Dean of the Graduate School ii Abstract of the Dissertation Higgs Phenomenology in the Standard Model and Beyond by Bryan Jonathan Field Doctor of Philosophy in Physics Stony Brook University 2005 The way in which the electroweak symmetry is broken in nature is currently unknown. The electroweak symmetry is theoretically broken in the Standard Model by the Higgs mechanism which gen- erates masses for the particle content and introduces a single scalar to the particle spectrum, the Higgs boson. This particle has not yet been observed and the value of it mass is a free parameter in the Standard Model. The observation of one (or more) Higgs bosons would confirm our understanding of the Standard Model. In this thesis, we study the phenomenology of the Standard Model Higgs boson and compare its production observables to those of the Pseudoscalar Higgs boson and the lightest scalar Higgs boson of the Minimally Supersymmetric Standard Model. We study the production at both the Fermilab Tevatron and the future CERN Large Hadron Collider (LHC). In the first part of the thesis, we present the results of our calculations in the framework of pertur- bative QCD. In the second part, we present our resummed calcu- lations. iii For my parents, Margaret and Christopher, who never got to see this... ... and for my Angeliki, who understood. Contents List of Figures xiii List of Tables xiv Preface xv Acknowledgements xx Cirriculum Vitæ xxi 1 Introduction 1 1.1 Standard Model . 2 1.2 SM as a Field Theory . 5 1.2.1 Symmetries . 5 1.2.2 Gauge Invariance . 6 1.2.3 Goldstone bosons . 9 1.3 Electroweak Symmetry Breaking . 9 1.3.1 Higgs mechanism . 10 1.3.2 Bounds on Higgs mass . 13 1.4 SM Lagrangian . 19 1.4.1 Feynman rules . 20 1.4.2 Polarizations, gauges, and ghosts . 22 1.5 Quantum Chromodynamics (QCD) . 24 1.5.1 Quark Model . 24 1.5.2 Regularization and renormalization . 25 1.5.3 Running of αs and pQCD . 28 1.6 Partons, Hadrons, and Observables . 30 1.6.1 Lowest order cross-section . 32 1.6.2 Higher order cross-sections . 34 1.7 Resummation . 40 1.8 Why supersymmetry? . 41 v 1.8.1 MSSM . 44 1.9 HQET . 47 1.10 SM predictions . 49 1.11 Roadmap ahead . 51 I Higgs Phenomenology in pQCD 52 2 Distinguishing scalar from pseudoscalar Higgs production at the LHC 53 2.1 Introduction . 53 2.2 Effective Lagrangian . 54 2.3 Observables and Moments . 55 2.4 Conclusions . 61 3 NLO corrections to differential cross sections for pseudoscalar Higgs boson production 64 3.1 Introduction . 64 3.2 Effective Lagrangian . 65 3.3 Kinematics . 67 3.4 Corrections . 68 3.5 Conclusions . 74 4 Scalar and Pseudoscalar Higgs Boson Plus One Jet Production at the LHC and Tevatron 78 4.1 Introduction . 78 4.2 Partonic Processes - Heavy Quark Effective Theory . 80 4.3 Partonic Processes - Full Theory . 83 4.3.1 Gluon fusion (gg → gΦ) . 83 4.3.2 Quark-antiquark annihilation (qq¯ → gΦ) . 85 4.3.3 HQET Matrix Elements . 85 4.3.4 Small Quark Mass Limit . 86 4.4 Observables . 87 4.5 Numerical Results . 88 4.5.1 Standard Model . 88 4.5.2 Minimal Supersymmetric Standard Model . 88 4.6 Conclusions . 92 vi II Resummation and the Higgs Boson 100 5 Next-to-leading Log Resummation of Scalar and Pseudoscalar Higgs Boson Differential Cross-Sections at the LHC and Tev- atron 101 5.1 Introduction . 101 5.2 Heavy Quark Effective Theory . 102 5.2.1 Scalar Higgs Matrix Elements . 104 5.2.2 Pseudoscalar Higgs Matrix Elements . 109 5.3 Resummation . 111 5.3.1 Formalism . 112 5.3.2 Matching . 114 5.3.3 Higgs Resummation . 115 5.4 Results and Conclusions . 120 6 Higgs Boson Resummation via Bottom-Quark Fusion 132 6.1 Introduction . 132 6.2 Setup . 134 6.3 Resummation . 135 6.4 Results and Conclusions . 138 Bibliography 153 A Cross-sections and widths 154 A.1 Cross-section . 154 A.2 Width . 155 B The Clifford Algebra 156 B.1 Algebra and Group Theory . 157 C Group Theory 160 C.1 SU(2) ............................... 160 C.2 SU(3) ............................... 160 D Loop Integrals 162 D.1 Feynman parametrization . 162 D.2 Tensor Reduction . 163 E Mathematical Reference 164 E.1 Euler Gamma . 164 E.2 Beta function . 164 E.3 Dilogarithms . 165 vii E.4 Expansions . 165 viii List of Figures 1.1 Spontaneous symmetry breaking. 11 1.2 Sample Higgs-Higgs scattering diagrams. 15 1.3 Theoretical Higgs mass limits. 16 1.4 WW scattering (sample diagrams). 18 1.5 Electroweak fit for the SM Higgs mass (February 2005). 19 1.6 Parton Model. 32 1.7 Drell-Yan W ± production (sample diagrams). 33 1.8 Phase space singularities. 38 1.9 Self energy mass corrections. 42 1.10 Effective gluon-gluon-Higgs vertex. 48 2 1.11 Function |F1/2| approaches the HQET limit. 49 1.12 Tevatron Run II and LHC total cross-sections. 50 2.1 Total cross-sections for scalar and pseudoscalar Higgs plus two jets. These curves are for the LHC with the cuts described in the text. 56 2.2 Normalized transverse momentum spectrum of the scalar or pseudoscalar Higgs production channels plus two jets. The Higgs mass for both the scalar and pseudoscalar is 120 GeV. Note that the pseudoscalar Higgs has been displaced down by 10% to allow the two curved to be distinguished. These curves are for the LHC with the cuts described in the text. 57 2.3 Normalized opening angle in the center-of-momentum frame be- tween the Higgs and the highest pt jet for the scalar and pseudo- scalar Higgs production channels plus two jets. The Higgs mass for both the scalar and pseudoscalar is 120 GeV. Note that the pseudoscalar Higgs has been displaced down by 20% to allow the two curved to be distinguished. These curves are for the LHC with the cuts described in the text. 58 ix 2.4 Normalized integrated moment α[a1] for the scalar and pseudo- scalar Higgs plus two jets. The center curve shows what the observable would look like if both of the processes were to be measured at the same time with degenerate masses. The split- ting between the two different production channels is clear at all mass scales with a statistical uncertainty of about 5%. These curves are for the LHC with the cuts described in the text. 60 √ 3.1 The ratio R in Eq. (3.46) plotted as a function of pT for S = 2 2 2 2 14 TeV and µ = pT + mB with mH = mA0 = 120 GeV/c ; LO LO R (Mt = ∞) (dotted line), R (Mt = 173.4) (solid line) NLO NLO R (mt = ∞) (dot-dashed line) R (Mt = 173.4) (dashed line). 75 2 2 3.2 The transverse momentum distribution dσA√/dpT with µ = pT + 2 2 M , M 0 = 91.9 GeV/c , tan β = 0.5; S = 14 TeV (solid A0 √ A line), S = 2 TeV (dashed line). 76 3.3 The rapidity distribution dσA0 /dy calculated from the integral 2 of d σA0 /(dpT dy) between 8 pT,min > pT > pT,min and pT,min = 2 2 2 30 GeV/c. Input parameters are µ = p + M , M 0 = √ T,min A0 √A 91.9 GeV/c2, tan β = 0.5; S = 14 TeV (solid line), S = 2 TeV (dashed line). 77 4.1 Sample Higgs plus one jet diagrams. Figures 4.1a,b are the gg diagrams, 4.1c is the qg channel, and 4.1d is the qq¯ channel. All quarks contribute to the loops. The crossed and charge conjugate diagrams are not shown. There are a total of 12 gg diagrams and 2 for each of the qg and qq¯ sub-processes. 81 2 2 4.2 The squared matrix elements, |M| , evaluated ats ˆ = 4mΦ and uˆ = tˆ for the three different channels, (gg, qg, qq¯), normalized to the squared matrix elements in the HQET for scalar and pseudoscalar (with gA = 1) Higgs plus jet production. We in- clude only the top quark loops. The solid line is the scalar, whereas the dashed line is the pseudoscalar. 84 4.3 Transverse momentum distributions for the SM Higgs boson 2 plus one jet production at the LHC with MH = 120 GeV/c for the different channels. The curves labeled ‘Top’ (‘Bot’) include only the top (bottom) quark loops. 89 4.4 Transverse momentum distributions for the SM Higgs (H) plus one jet and for a pseudoscalar (A0) plus one jet in the full theory with only the top-quark loops included and in the HQET at the 2 LHC for MΦ = 120 GeV/c . We assume gA = 1.
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