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The Higgs Boson in the Standard Model Abdelhak Djouadi

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The Higgs Boson in the Standard Model Abdelhak Djouadi The Anatomy of Electro-Weak Symmetry Breaking. I: The Higgs boson in the Standard Model Abdelhak Djouadi To cite this version: Abdelhak Djouadi. The Anatomy of Electro-Weak Symmetry Breaking. I: The Higgs boson in the Standard Model. 2005. hal-00004502v2 HAL Id: hal-00004502 https://hal.archives-ouvertes.fr/hal-00004502v2 Preprint submitted on 3 May 2005 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. LPT–Orsay–05–17 March 2005 The Anatomy of Electro–Weak Symmetry Breaking Tome I: The Higgs boson in the Standard Model Abdelhak DJOUADI Laboratoire de Physique Th´eorique d’Orsay, UMR8627–CNRS, Universit´eParis–Sud, Bˆat. 210, F–91405 Orsay Cedex, France. Laboratoire de Physique Math´ematique et Th´eorique, UMR5825–CNRS, Universit´ede Montpellier II, F–34095 Montpellier Cedex 5, France. E–mail : [email protected] Abstract This review is devoted to the study of the mechanism of electroweak symmetry breaking and this first part focuses on the Higgs particle of the Standard Model. The funda- mental properties of the Higgs boson are reviewed and its decay modes and production mechanisms at hadron colliders and at future lepton colliders are described in detail. ½¼¼ ½ ÏÏ · ´ÔÔ ! À · X µ ℄ ´e e ! ÀX µ ℄ Ô À Ô ½¼¼ g g ! À × ½ ÌÎ × ¼¼ Î ÅÊËÌ»ÆÄÇ ØØ ÀZ ¼º½ Ñ ½ Î Ø ½¼ · À e e ÀÕÕ ½¼ ¼º¼½ ÏÀ BÊ´À µ ZÀ ØØÀ ½ ­ ­ ½ ÀØØ ¼º¼¼½ ×× ÀÀZ Z ­ ¼º¼¼¼½ ¼º½ ¼º½ ½¼¼ ½¿¼ ½6¼ ¾¼¼ ¿¼¼ 5¼¼ 7¼¼ ½¼¼¼ ½¼¼ ½¼¼¼ ½¼¼ ½¿¼ ½6¼ ¾¼¼ ¿¼¼ 5¼¼ Å ℄ Å ℄ À À Å ℄ À The decay branching ratios of the Standard Model Higgs boson and its production cross sections in the main channels at the LHC and at a 500 GeV + collider. ccsd-00004502, version 2 - 3 May 2005 e e− Contents Pr´eambule 5 1 The Higgs particle in the SM 13 1.1 The SM of the strong and electroweak interactions . ......... 13 1.1.1 The SM before electroweak symmetry breaking . .... 13 1.1.2 TheHiggsmechanism .......................... 16 1.1.3 The SM Higgs particle and the Goldstone bosons . .... 21 1.1.4 TheSMinteractionsandparameters . .. 25 1.2 High–precisiontestsoftheSM. .... 31 1.2.1 ObservablesinZbosondecays. 32 1.2.2 The electroweak radiative corrections . ...... 35 1.2.3 Observables in W bosonproductionanddecay. 39 1.2.4 Approximating the radiative corrections . ...... 43 1.2.5 The electroweak precision data . .. 46 1.3 Experimental constraints on the Higgs boson mass . ......... 50 1.3.1 Constraintsfromhighprecisiondata . .... 50 1.3.2 Constraintsfromdirectsearches . .... 54 1.4 Theoretical constraints on the Higgs boson mass . ......... 59 1.4.1 Constraints from perturbativity and unitarity . ........ 59 1.4.2 Triviality and stability bounds . .... 64 1.4.3 Thefine–tuningconstraint . 69 2 Decays of the SM Higgs boson 73 2.1 Decaystoquarksandleptons . .. 74 2.1.1 TheBornapproximation . 74 2.1.2 Decays into light quarks and QCD corrections . ..... 75 2.1.3 Thecaseofthetopquark ........................ 76 2.1.4 Distinction between scalar and pseudoscalar Higgs bosons ...... 79 2.2 Decays into electroweak gauge bosons . ...... 82 2.2.1 Twobodydecays ............................. 82 2.2.2 Threebodydecays ............................ 83 2.2.3 Fourbodydecays............................. 84 2.2.4 CP properties and comparison with the CP–odd case . ..... 85 2.3 Loop induced decays into γγ,γZ and gg .................... 88 2.3.1 Decaysintotwophotons . .. .. 89 2.3.2 Decays into a photon and a Z boson .................. 92 2.3.3 Decaysintogluons ............................ 94 2 2.4 The electroweak corrections and QCD improvements . ........ 97 2.4.1 Thelowenergytheorem ......................... 99 2.4.2 EW corrections to decays into fermions and massive gaugebosons . 100 2.4.3 NNLO QCD and EW corrections to the loop induced decays . .... 104 2.4.4 Summary of the corrections to hadronic Higgs decays . ....... 108 2.5 The total decay width and the Higgs branching ratios . ......... 110 3 Higgs production at hadron colliders 115 3.1 Higgsbosonsathadronmachines . 115 3.1.1 Generalities about hadron colliders . ..... 115 3.1.2 Higgs production at hadron machines . 117 3.1.3 The higher–order corrections and the K–factors . 118 3.1.4 Thescaledependence. .. .. 119 3.1.5 The parton distribution functions . .... 120 3.2 The associated production with W/Z bosons . ...... 123 3.2.1 The differential and total cross sections at LO . ...... 123 3.2.2 TheQCDradiativecorrections . 125 3.2.3 The electroweak radiative corrections . ...... 129 3.2.4 The total cross section and the PDF uncertainties . ....... 131 3.3 Thevectorbosonfusionprocesses . ..... 133 3.3.1 The differential and total cross sections at LO . ...... 133 3.3.2 ThecrosssectionatNLO . .. .. 135 3.3.3 Kinematicsoftheprocess . 137 3.3.4 Dependence on the scale and on the PDFs at NLO . 140 3.3.5 The effective longitudinal vector boson approximation......... 143 3.4 The gluon–gluon fusion mechanism . .... 145 3.4.1 TheproductioncrosssectionatLO . 145 3.4.2 ThecrosssectionatNLO . .. .. 146 3.4.3 The cross section beyond NLO in the heavy top quark limit ..... 151 3.4.4 The distributions and Higgs + n jet production . ..... 157 3.5 Associated Higgs production with heavy quarks . ........ 161 3.5.1 The cross sections at the tree level . 161 3.5.2 ThettHcrosssectionatNLO . 164 3.5.3 ThecaseofthebbHprocess . 169 3.5.4 Associated Higgs production with a single top quark . ....... 170 3.6 Thehigher–orderprocesses. .... 172 3.6.1 Higgsbosonpairproduction . 172 3.6.2 Higgs production in association with gauge bosons . ........ 176 3 3.6.3 Moreonhigher–orderprocesses . 179 3.6.4 DiffractiveHiggsbosonproduction . 181 3.7 Detecting and studying the Higgs boson . ..... 184 3.7.1 Summary of the production cross sections . .... 184 3.7.2 Higgs signals and backgrounds at the Tevatron and the LHC..... 188 3.7.3 Discovery expectations at the Tevatron and the LHC . ...... 195 3.7.4 Determination of the Higgs properties at the LHC . ...... 199 3.7.5 Higher luminosities and higher energies . ...... 205 4 Higgs production at lepton colliders 209 4.1 Lepton colliders and the physics of the Higgs boson . ......... 209 + 4.1.1 Generalities about e e− colliders .................... 209 4.1.2 Thephotoncolliders ........................... 212 4.1.3 Futuremuoncolliders. 215 4.1.4 Higgs production processes in lepton collisions . ......... 217 + 4.2 The dominant production processes in e e− collisions . 219 4.2.1 The Higgs–strahlung mechanism . 219 4.2.2 TheWWfusionprocess . .. .. 224 4.2.3 The electroweak radiative corrections . ...... 226 + 4.3 The subleading production processes in e e− collisions . 230 4.3.1 TheZZfusionmechanism . 230 4.3.2 Associated production with heavy fermion pairs . ....... 233 4.3.3 Higgsbosonpairproduction . 237 + 4.3.4 Other subleading processes in e e− collisions. 241 + 4.4 Higgs studies in e e− collisions ......................... 247 4.4.1 Higgsbosonsignals............................ 247 4.4.2 Precision measurements for a light Higgs boson . ...... 253 4.4.3 Combined measurements and the determination of the couplings . 263 4.4.4 Measurements at higher and lower energies . ..... 265 4.5 Higgs production in γγ collisions ........................ 269 4.5.1 Higgs boson production as an s–channel resonance . ....... 269 4.5.2 Measuring the CP–properties of the Higgs boson . ...... 275 4.5.3 Other Higgs production mechanisms . 279 4.6 Higgsproductionatmuoncolliders . ..... 283 4.6.1 Higgs production in the s–channel.................... 283 4.6.2 Determination of the properties of a light Higgs boson ........ 288 4.6.3 Study of the CP properties of the Higgs boson . .... 291 References 295 4 Pr´eambule A short praise of the Standard Model The end of the last millennium witnessed the triumph of the Standard Model (SM) of the electroweak and strong interactions of elementary particles [1, 2]. The electroweak the- ory, proposed by Glashow, Salam and Weinberg [1] to describe the electromagnetic [3] and weak [4] interactions between quarks and leptons, is based on the gauge symmetry group SU(2) U(1) of weak left–handed isospin and hypercharge. Combined with Quantum L × Y Chromo–Dynamics (QCD) [2], the theory of the strong interactions between the colored quarks based on the symmetry group SU(3)C, the model provides a unified framework to de- scribe these three forces of Nature. The theory is perturbative at sufficiently high energies [2] and renormalizable [5], and thus describes these interactions at the quantum level. A cornerstone of the SM is the mechanism of spontaneous electroweak symmetry breaking (EWSB) proposed forty years ago by Higgs, Brout, Englert, Guralnik, Hagen and Kibble [6] to generate the weak vector boson masses in a way that is minimal and, as was shown later, respects the requirements of renormalizability [5] and unitarity [7]. An SU(2) doublet of complex scalar fields is introduced and its neutral component develops a non–zero vacuum expectation value. As a consequence, the electroweak SU(2) U(1) symmetry is sponta- L × Y neously broken to the electromagnetic U(1)Q symmetry. Three of the four degrees of freedom of the doublet scalar field are absorbed by the W ± and Z weak vector bosons to form their longitudinal polarizations and to acquire masses. The fermion masses are generated through a Yukawa interaction with the same scalar field and its conjugate field. The remaining degree of freedom corresponds to a scalar particle, the Higgs boson. The discovery of this new type of matter particle is unanimously considered as being of profound importance. The high–precision measurements of the last decade [8, 9] carried out at LEP, SLC, Tevatron and elsewhere have provided a decisive test of the Standard Model and firmly established that it provides the correct effective description of the strong and electroweak interactions at present energies.
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