Precision phenomenology at the LHC and characterization of theoretical uncertainties Emanuele Angelo Bagnaschi To cite this version: Emanuele Angelo Bagnaschi. Precision phenomenology at the LHC and characterization of theoretical uncertainties. High Energy Physics - Phenomenology [hep-ph]. Université Paris Diderot - Paris 7, 2014. English. tel-01079886 HAL Id: tel-01079886 https://tel.archives-ouvertes.fr/tel-01079886 Submitted on 3 Nov 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Université Paris-Diderot (Paris 7) Sorbonne Paris Cité École Doctorale 560 STEP’UP Laboratoire de Physique Théorique et Hautes Énergies (LPTHE) Doctorat Physique Emanuele Angelo Bagnaschi Phénoménologie de Précision au LHC et caractérisation des incertitudes théoriques Precision phenomenology at the LHC and characterization of theoretical uncertainties Soutenu le 19 Septembre 2014 Thèse dirigée par Prof. Matteo Cacciari Jury PD. M. Grazzini Examinateur et Rapporteur Dr. JP. Guillet Examinateur et Rapporteur Prof. M. Cacciari Examinateur Dr. A. Djouadi Examinateur Dr. P. Slavich Examinateur Dr. R. Tanaka Examinateur “Quotation s a serviceable substitute for wit.” – Oscar Wilde CONTENTS Outline 1 Bibliography 5 i A B QCD 7 1 I 9 2 A B 11 2.1 The concept of probability . 11 2.2 Exemplification of the differences between the Bayesian and the frequentist approaches 12 2.3 Missing higher order uncertainties as a measurement problem in a Bayesian context . 16 3 E QCD 19 3.1 Uncertainty estimation by scale variation . 19 3.2 The Cacciari-Houdeau Bayesian approach . 21 3.3 The modified Cacciari-Houdeau approach (CH) . 23 4 G 29 4.1 Setup . 29 4.2 Results . 32 5 B 37 5.1 Higgs decays . 37 − 5.2 Hadroproduction process in e+e collisions . 43 5.3 The Drell-Yan process at the LHC . 45 5.4 tt¯ production at the LHC . 48 5.5 Higgs boson production at the LHC . 50 6 C 53 ii P H LHC 55 1 I 57 2 T H 59 2.1 The Standard Model . 59 2.1.1 Heavy quark effective Lagrangian for the Higgs-gluons coupling . 62 2.2 The Two Higgs Doublet Model . 62 2.3 The Minimal Supersymetric Standard Model . 66 3 H 71 3.1 Gluon fusion . 72 3.1.1 Standard model . 72 3.1.2 2HDM . 78 3.1.3 MSSM . 79 3.2 Bottom quark associated production . 82 i Contents 3.2.1 Standard Model . 82 3.2.2 2HDM . 83 3.2.3 MSSM . 84 4 T H MSSM 85 4.1 Higgs boson production in viable MSSM scenarios . 85 4.1.1 The tools . 85 4.1.2 The benchmark scenarios . 86 4.1.3 Cross section for Higgs production . 88 4.2 Sources of theoretical uncertainty . 96 4.2.1 Scale dependence of the cross section . 96 4.2.2 Definition of the Higgs-bottom coupling . 101 4.2.3 Uncertainties from the PDFs and αs . 106 4.2.4 Higher-order SUSY contributions to gluon fusion . 110 5 T H 115 5.1 Considerations on the resummed computation of the transverse momentum distribution 115 5.1.1 Analytic resummation and the collinear limit . 115 5.1.2 Numerical resummation in the NLO+PS framework . 116 5.2 POWHEG-BOX implementation of gg ϕ . 117 → 5.3 The transverse momentum spectrum of the Higgs boson in the SM . 120 5.3.1 Top-mass effects and inclusion of the bottom contribution . 121 5.4 The transverse momentum spectrum in the 2HDM . 124 5.5 The transverse momentum spectrum in the MSSM . 126 5.6 The choice of the resummation scale and uncertainty estimation . 127 5.6.1 The role of the damping factor h in the POWHEG-BOX framework . 127 5.6.2 The gg Hg subprocess . 129 → 5.6.3 SM phenomenology . 131 5.6.4 Bottom effects in the 2HDM . 135 6 C 137 O 141 CH 145 S λ 147 M 149 .1 Higgs production in gluon fusion at the LHC . 149 .2 The Drell-Yan process at the LHC . 150 A SM - POWHEG-BOX 153 C 155 Bibliography 159 iii Ŕ ́ F̧ 173 Plan de la thèse 175 Bibliographie 179 ii Contents 1 L ̀ CH ’ B́ ̀ ’ MHOU 181 1.1 Le modèle CH et ses développements . 182 1.1.1 Le modèle de Cacciari-Houdeau modifiée (CH ) . 183 1.1.2 Extension du modèle CH w observables avec des hadrons dans l’état initial . 184 1.2 Résultats . 186 1.2.1 Analyse globale . 186 1.2.2 Exemples des processus . 190 1.3 Conclusions . 193 2 Ć H 195 2.1 Production de bosons de Higgs dans de scénarios viables du MSSM . 195 2.1.1 Incertitudes théoriques de la section efficace . 196 2.2 L’impulsion transverse du boson de Higgs en fusion de gluons . 200 2.2.1 Résultats . 200 2.3 Conclusions . 200 Bibliographie 205 iii ACRONYMS 2HDM The two Higgs-doublet model. CH Cacciari-Houdeau Bayesian model. CH Modified Cacciari-Houdeau Bayesian model. DGLAP Dokshitezer-Gribov-Lipatov-Altarelli-Parisi equations for the evolution for parton densities. DoB Bayesian Degree of Belief. EW Electro Weak. HQEFT Heavy Quark Effective Field Theory – Effective field theory of the SM after the integration of the top quark degree of freedom. LHC The Large Hadron Collider at CERN. LHEF Les Houches Event File. LL Leading Logarithmic. LO Leading Order. MHO Missing Higher Order. MHOU Missing Higher Order Uncertainty due to uncomputed QCD corrections. MSSM The Minimal Supersymmetric Standard Model. NLL Next-to-Leading Logarithmic. NLO Next-to-Leading Order. NNLL Next-to-Next-to-Leading Logarithmic. NNLO Next-to-Next-Leading Order. PDF The Parton Distribution Function which describes the non-perturbative dynamic of the hadron. POWHEG POsitive WEight Hardest Emission Generator. POWHEG-BOX A Fortran77 implementation of the POWHEG method available at http://powhegbox. mib.infn.it/. v Acronyms PS Parton Shower Monte Carlo software. QCD Quantum Chromodynamics. RG Renormalization Group. SM The Standard Model of particle physics. SUSY Super Symmetry. SVN Subversion revision control system. vi OUTLINE Standard Model (SM) of the electroweak and strong interactions has been very successful in de- T scribing many different elementary particle processes at various energy scales, but suffers, on the other hand, from various severe problems. For instance, if one considers the interplay between particle physics and cosmology, it is immediately clear that the observed matter/antimatter asymmetry in the universe can not be explained only in terms of the fundamental interactions described by the Standard Model, but requires in general an extension that includes a larger particle spectrum. The latter is also needed to explain the observed dark matter content of the universe. Moreover the SM does not include neutrino masses and mixing and, on the more theoretical side, it suffers from the ”hierarchy problem” (i.e. the fact that quantum corrections to the Higgs boson mass have a quadratic dependence on the UV cutoff used in the computation) and from the fact that the gauge and Yukawa structure is not explained but assumed. Aside from these issues, now that the Higgs boson has been discovered a quest has started to under- stand if its properties are compatible with the predictions of the Standard Model. The Large Hadron Collider (LHC) has been designed to explore all these different questions, provid- ing the necessary tools to search and understand the Higgs boson and allowing the production of new particles in the TeV mass range, if they exist. The very successful first run of the accelerator has been accompanied by an already large amount of high-quality data. From the first analysis of these data, it seems that there are no apparent important deviations from the Standard Model. This in turn makes the use of this huge amount of data to perform precision physics the next logic step. Such a class of studies requires not only a very high accuracy in experimental measures but also a control over the uncertainties in theoretical computations. In light of this, during my graduate studies I have been involved in a series of projects whose aim was to improve either the accuracy of predictions, accounting for new effects, or the control over the uncertainties of theoretical calculations. Among the theoretical uncertainties, a prominent role is occupied by the always-present problem, in precise calculations in quantum field theory, of how to estimate the contributions from missing higher orders in the perturbative expansion, the so-called Missing Higher Order Uncertainty (MHOU). Tra- ditionally, these uncertainties have been estimated by varying the unphysical scales present in the result around their central values. Various prescriptions for this procedure are conventionally used by the com- munity, however all are based on arbitrary choices and fail in giving a statistical meaning to the inter- val they produce. With M. Cacciari (LPTHE) and A. Guffanti and L. Jenniches, both at the N. Bohr Institute in Copenhagen, we studied the extension of the Cacciari-Houdeau (CH) Bayesian model to hadronic observables, with the specific aim of giving a more consistent estimate of the MHOU for LHC observables in general, and Higgs-boson production in particular [1]. The CH model tries to address the shortcomings of the standard prescription used to evaluate MHOU, the scale variation procedure.