11. Status of Higgs boson physics 1 11. Status of Higgs Boson Physics Revised September 2017 by M. Carena (Fermi National Accelerator Laboratory and the University of Chicago), C. Grojean (DESY, Hamburg, and Humboldt University, Berlin), M. Kado (Laboratoire de l’Acc´el´erateur Lin´eaire, Orsay), and V. Sharma (University of California, San Diego). I.Introduction . .3 II. The standard model and the mechanism of electroweak symmetry breaking . 5 II.1. The SM Higgs boson mass, couplings and quantum numbers ......7 II.2.TheSMcustodialsymmetry . 8 II.3.StabilityoftheHiggspotential . 8 II.4. Higgs production and decay mechanisms . 9 II.4.1. Production mechanisms at hadron colliders . .9 II.4.2. Production mechanisms at e+e− colliders . 16 II.4.3.SMHiggsbranchingratiosandtotalwidth . 16 III.TheexperimentalprofileoftheHiggsboson . 17 III.1. The principal decay channels to vector bosons . 18 III.1.1. H γγ .................... 19 → III.1.2. H ZZ∗ ℓ+ℓ−ℓ′+ℓ′− ............... 20 → → III.1.3.MeasurementoftheHiggsbosonmass . 21 III.1.4. H W +W − ℓ+νℓ−ν ............... 22 → → III.2.Decaystofermions . 23 III.2.1. H τ +τ − ................... 24 → III.2.2. H bb .................... 25 → III.3. Higgs production in association with top quarks or in topdecays . 27 III.3.1. The associated production with top quark pairs . ..... 27 III.3.2. The associated production with a single top quark . ...... 29 III.3.3. Flavor changing neutral current decays of the top quark . 29 III.4.Higgsbosonpairproduction . 30 III.4.1.SearchesforHiggsbosonpairproduction . 31 III.4.2.TheHiggsselfcoupling . 31 M. Tanabashi et al. (Particle Data Group), Phys. Rev. D 98, 030001 (2018) June 5, 2018 19:47 2 11. Status of Higgs boson physics III.5.SearchesforraredecaysoftheHiggsboson . 33 III.5.1. H Zγ .................... 33 → III.5.2. H µ+µ− ................... 33 → III.5.3. H e+e− ................... 34 → III.5.4. Lepton flavor violating (LFV) Higgs boson decays . 34 III.5.5. Probing charm- and light-quark Yukawa couplings . ...... 35 III.5.6.Raredecaysoutlook . 35 III.6. Searches for non-standard model decay channels . 36 III.6.1.InvisibledecaysoftheHiggsboson . 36 III.6.2.ExoticHiggsbosondecays . 37 IV.Combiningthemainchannels . 38 IV.1.Principlesofthecombination . 39 IV.2. Main decay modes and observation of Higgs decays to taus ..... 42 IV.3. Main production modes and evidence for VBF production ..... 42 V.MainquantumnumbersandwidthoftheHiggsboson . 43 V.1. Main quantum numbers J PC ............... 44 V.1.1.Chargeconjugation . 44 V.1.2.Spinandparity . 44 V.1.3. Probing fixed J P scenarios . 45 V.1.4. Probing CP-mixing and anomalous HVV couplings . 47 V.2.Off-shellcouplingsoftheHiggsboson . 49 V.3.TheHiggsbosonwidth . 50 V.3.1.Directconstraints . 50 V.3.2. Indirect constraints from mass shift in the diphoton channel . 51 V.3.3. Indirect constraints from on-shell rate in the diphoton channel . 51 V.3.4. Indirect constraints from off-shell couplings . 52 VI. Probing the coupling properties of the Higgs boson . 53 VI.1.EffectiveLagrangianframework . 54 VI.2.Probingcouplingproperties . 56 VI.2.1. Combined measurements of the coupling properties of H ..... 57 June 5, 2018 19:47 11. Status of Higgs boson physics 3 VI.2.2.Differentialcrosssections . 64 VI.2.3. Constraints on non-SM Higgs boson interactions in an effective Lagrangian 64 VI.2.4.SimplifiedTemplateCrossSections . 65 VII. New physics models of EWSB in the light of the Higgs boson discovery . 66 VII.1. Higgs bosons in the minimal supersymmetric standard model (MSSM) . 68 VII.1.1.MSSMHiggsbosonphenomenology . 71 VII.2. Supersymmetry with singlet extensions . 73 VII.3. Supersymmetry with extended gauge sectors . 75 VII.4.EffectsofCPviolation . 77 VII.5. Non-supersymmetric extensions of the Higgs sector . ...... 78 VII.5.1.Two-Higgs-doubletmodels . 80 VII.5.2.Higgstriplets . 82 VII.6.CompositeHiggsmodels. 84 VII.6.1.LittleHiggsmodels . 85 VII.6.2.Modelsofpartialcompositeness . 86 VII.6.3.MinimalcompositeHiggsmodels . 90 VII.6.4.TwinHiggsmodels . 91 VII.7. Searches for signatures of extended Higgs sectors . ...... 93 VII.7.1. Searches for non-standard production processes oftheHiggsboson . 103 VII.7.2.Outlookofsearchesforadditionalstates . 103 VIII.Summaryandoutlook . 104 I. Introduction Understanding the mechanism that breaks the electroweak symmetry and generates the masses of the known elementary particles has been one of the fundamental endeavors in particle physics. The discovery in 2012 by the ATLAS [1] and the CMS [2] Collaborations of a new resonance with a mass of approximately 125 GeV and the subsequent studies of its properties with a much larger data set have provided the first portrait of this mechanism. The mass of this boson has been precisely measured and its production and decay rates are found to be consistent, within errors, with the standard model (SM) predictions. Nevertheless, several channels are yet out of reach experimentally and the couplings of the Higgs boson to light fermions are yet to be proven. At the same time, many theoretical questions remain unanswered. New questions about what lies behind June 5, 2018 19:47 4 11. Status of Higgs boson physics the Higgs boson have come to fore. Nonetheless, five years since its discovery, the Higgs boson has turned into a new tool to explore the manifestations of the SM and to probe the physics landscape beyond it. In the SM [3] the electroweak interactions are described by a gauge field theory invariant under the SU(2)L U(1)Y symmetry group. The mechanism of electroweak symmetry breaking (EWSB)× [4] provides a general framework to keep untouched the structure of these gauge interactions at high energies and still generate the observed masses of the W and Z gauge bosons. The EWSB mechanism posits a self-interacting complex doublet scalar field, whose CP-even neutral component acquires a vacuum expectation value (VEV) v 246 GeV, which sets the scale of electroweak symmetry breaking. Three massless Goldstone≈ bosons are generated and are absorbed to give masses to the W and Z gauge bosons. The remaining component of the complex doublet becomes the Higgs boson – a new fundamental scalar particle. The masses of all fermions are also a consequence of EWSB since the Higgs doublet is postulated to couple to the fermions through Yukawa interactions. All measurements of the Higgs boson properties are so far indicating that the observations are compatible with a minimal EWSB sector. Nevertheless, within the current precision a more complex sector with additional states is not ruled out, nor has it been established whether the Higgs boson is an elementary particle or whether it has an internal structure like any other scalar particles observed before it. Without the Higgs boson, the calculability of the SM would have been spoiled. In particular, perturbative unitarity [5, 6] would be lost at high energies since the longitudinal W/Z boson scattering amplitude would grow with the increase in centre-of-mass energy. In addition, the radiative corrections to the gauge boson self-energies would exhibit dangerous logarithmic divergences that would be difficult to reconcile with EW precision data. With the discovery of the Higgs boson, the SM is a spontaneously broken gauge theory and as such it could a priori be consistently extrapolated well above the masses of the W and Z bosons. Hence, formally there is no need for new physics at the EW scale. However, as the SM Higgs boson is a scalar particle, at the quantum level it has sensitivity to high energy thresholds. Quite generally, the Higgs mass is affected by the presence of heavy particles and receives quantum corrections proportional to highest energy scale which destabilize the weak scale barring a large fine tuning of unrelated parameters. This is known as the hierarchy or naturalness problem [7]. There are two broad classes of models addressing the naturalness problem1: one is based on a new fermion-boson symmetry in nature called supersymmetry (SUSY) [9–11]. This is a weakly coupled approach to EWSB, and in this case, the Higgs boson remains elementary and the corrections to its mass are screened at the scale at which SUSY is broken and remain insensitive to the details of the physics at higher scales. These theories predict at least three neutral Higgs particles and a pair of charged Higgs particles [12]. One of the neutral Higgs bosons, most often the lightest CP-even Higgs, has properties 1 Another solution to the naturalness problem is to lower the fundamental scale of quantum gravity, like for instance in models with large extra-dimensions, see Ref. [8]. June 5, 2018 19:47 11. Status of Higgs boson physics 5 that resemble those of the SM Higgs boson. It is referred to as a SM-like Higgs boson, meaning that its couplings are close to the ones predicted in the SM. The other approach invokes the existence of strong interactions at a scale of the order of a TeV or above and induces strong breaking of the electroweak symmetry [13]. In the original incarnation of this second approach, dubbed technicolor, the strong interactions themselves trigger EWSB without the need of a Higgs boson. Another possibility, more compatible with the ATLAS and CMS discovery, is that the strong interactions produce four light resonances identified with the Higgs doublet and EWSB proceeds through vacuum misalignment [14] (see Refs. [15, 16] for recent reviews). The Higgs boson could also correspond to the Goldstone boson associated with the spontaneous breaking of scale invariance [17, 18]. However, this dilaton/radion scenario now requires jumbled model-building to be consistent with the constraints from the coupling measurements. Both approaches can have important effects on the phenomenology of the Higgs boson associated with EWSB. Also, in each case the Higgs role in unitarization of scattering amplitudes is shared by other particles that remain targets of experimental searches. The naturalness problem has been the prime argument for new physics at the TeV scale, and sizable effects on the Higgs boson properties were expected.