PProceedings of the Second Annual LHCP
Higgs Physics Beyond the Standard Model
Margarete Muhlleitner
Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76128 Karlsruhe,Germany
ABSTRACTHiggs physics beyond the Standard Model (SM) is presented in the context of anunderlying strong dynamics of electroweak symmetry breaking (EWSB) as givenby composite Higgs models. Subsequently, the study of New Physics (NP) effectsin a more model-independent way through the effective Lagrangian approach isbriefly sketched before moving on to the investigation of NP through Higgscoupling measurements. Depending on the precision on the extracted couplings,NP scales up to the TeV range can be probed at the high-luminosity option ofthe LHC, if the coupling deviations arise from mixing effects or from someunderlying strong dynamics.PRESENTED ATThe Second Annual Conferenceon Large Hadron Collider PhysicsColumbia University, New York, U.S.AJune 2-7, 2014 a r X i v : . [ h e p - ph ] J a n Introduction
The announcement of the discovery of a new scalar particle by the Large Hadron Collider (LHC) experimentsATLAS and CMS [1, 2] has immediately triggered activities to determine the properties of this particle. Themeasurement of its couplings to other SM particles and the extraction of its spin and parity quantumnumbers are steps in order to establish the scalar as the
Higgs boson, i.e. the particle related to EWSB.Any deviations in these properties from the SM expectation would hint to physics beyond the SM (BSM).Although the Higgs boson looks very SM-like, there is still room for interpretations within BSM theories.In absence of any direct detection of NP particles, the Higgs sector becomes particularly interesting. Theprecise measurements of the Higgs properties help to reveal the underlying mechanism of EWSB and inparticular may shed light on the question if the underlying dynamics is strongly or weakly interacting. Anexample for the latter are supersymmetric (SUSY) extensions of the SM which remain weakly interacting upto high energies. The talk, that is summarised here, focuses on non-SUSY extensions of the SM. CompositeHiggs Models shall be presented as theories emerging from a strongly interacting sector, before moving on toeffective theory descriptions that allow for a more model-independent investigation of the Higgs sector. Thelast part finally is dedicated to specific (non-SUSY) models and how they can be probed through couplingmeasurements.
In composite Higgs models the Higgs boson arises as a pseudo Nambu-Goldstone boson from a strongly-coupled sector [3]. As result of the Goldstone nature of the Higgs boson, in the Strongly Interacting LightHiggs (SILH) scenario [4] there is a light narrow Higgs-like scalar, which is the bound state from some strongdynamics and which is separated by a mass gap from the other usual resonances of the strong dynamics. Atlow energy, the particle content is hence the same as in the SM. The Higgs couplings to the SM particles,however, are modified [4]. In composite Higgs models the problem of the generation of fermion masses issolved by the hypothesis of partial compositeness [5]. The SM fermions, which are elementary, couple linearlyto heavy states of the strong sector with the same quantum numbers, implying in particular the top quarkto be largely composite. The global symmetry of the strong sector is explicitly broken by these couplings,and the Higgs potential is generated from loops of SM particles with the dominant contribution comingfrom the top quark. As has been shown in Ref. [6] a low-mass Higgs boson of ∼
125 GeV can naturallybe accommodated only if the heavy quark partners are rather light, with masses below about 1 TeV. Froma phenomenological point of view, the modified Higgs couplings to the SM particles not only change theHiggs production and decay rates [7, 8], but notably lead to an increase of the cross section for doubleHiggs production in vector boson fusion with the energy [4, 9]. Furthermore, composite Higgs models arechallenged by electroweak precision tests (EWPTs) [4, 10]. The tension with the S and T parameters [11]Figure 1: Parameters passing the χ test of electroweak precision observables, which fulfill | V tb | > .
92, [13].1an be weakened through the contributions from new heavy fermions [12, 13]. This is shown in Fig. 1 fora model with composite bottom quarks, where the fermions are embedded in the , the smallest possiblerepresentation of SO (5) that allows for partially composite bottom quarks while being compatible with theEWPTs by implementing custodial symmetry. Performing a χ test, taking into account the EWPTs andthe measurement of V tb [14], it displays ∆ χ = χ − χ as a function of ξ for the points passing the testafter a scan over the model parameters. Here ξ = v /f , where v ≈
246 GeV is the vacuum expectationvalue and f the typical scale of the Goldstone bosons of the strong sector.As long as no heavy fermion partners have been detected directly, their influence on loop induced processeslike Higgs production through gluon fusion becomes particularly interesting. It has been shown, that theprocess computed by applying the Low-Energy Theorem (LET) [15] is insensitive to the details of thecouplings and masses of the strong sector [16, 17]. In double Higgs production, however, the LET is notreliable any more [18] and the cross section becomes sensitive to the properties of the strong sector [17, 19].Also the production of a boosted Higgs boson in association with a high-transverse momentum jet is sensitiveto the details of heavy fermions [20, 21] and can be exploited to measure the Higgs coupling to top pairs, asshown in Fig. 2 from Ref. [21]. (cid:45) (cid:45) (cid:45) Κ t Κ g (cid:82) .0 (cid:61) (cid:215) (cid:45) (cid:82) .0 (cid:61) (cid:215) (cid:45) (cid:82) .0 (cid:61) (cid:215) (cid:45) Μ (cid:61) (cid:177) (cid:37) (cid:247) Figure 2: The 95% confidence level (C.L.) contours from a χ test, in the plane of the top and effectivegluon coupling modifiers κ t and κ g for different values of the inclusive signal strength µ and the boostedobservable R . For details, see [21]. The plethora of NP extensions calls for an effective framework that captures NP effects in a model-independentway. The scale Λ at which NP becomes effective, proposed by natural mechanisms of EWSB, is not far fromthe TeV scale, so that a convenient framework for a model-independent analysis of deviations from the SM isgiven by an effective Lagrangian approach which enlarges the SM by including higher-dimensional operatorsbuilt from SM fields [22, 23]. At the dimension-6 level, there are 59 linearly independent operators, takinginto account only one fermion generation and allowing also for CP-odd operators [23, 24]. There has beensome discussion not only about the most appropriate basis to use but also about the minimum number ofoperators that should be applied to best capture the NP impact on Higgs physics. As it is impossible toreview in this short text all contributions in this field a few recent results shall be highlighted in the follow-ing. The authors of Ref. [25] found that for one family there are 8 CP-even operators that, at tree-level, canonly affect Higgs physics and no other SM processes. In a bottom-up approach, taking as starting point allpossible new interactions among SM fields, the authors of Refs. [26, 27] derived the set of independent new2nteractions at the dimension-6 level, that are presently best tested by the experiments and that give thebest way to constrain NP. They found 18 of these BSM primary effects, not taking into account four-fermiondeviations, minimal flavour violation suppressed deviations and those arising from CP violation. There are 8Higgs primaries, 7 EWPT primaries and 3 primaries affecting triple gauge boson couplings (TGC). All otherNP effects are not independent and are correlated with the BSM primaries, see also [24, 28]. In particularit is found, that large NP effects can still be revealed in the Higgs decay H → Zγ [29], while the deviationsfrom the SM in the differential distributions of Higgs decays into a vector boson and a fermion pair arealready constrained from TGC measurements [27]. The effective field theory approach has the advantage to allow for the study of a large class of models ina rather model-independent way. However, it cannot account for effects from light particles in the loopsor for Higgs decays into light non-SM particles. In order to give a complete picture of BSM effects in theHiggs sector the effective approach therefore has to be complemented by studies in specific models, thatideally capture these features. The subject of this section is the information that can be obtained from themeasurement of the Higgs couplings, in particular also on the scale of NP, both in the effective Lagrangianapproach and in specific models. For a review, see [30]. Deviations in the Higgs couplings due to NP canoccur from two effects. The couplings can be modified due to the mixing of the standard Higgs field withother scalar fields. This is e.g. the case in portal models, where the SM Higgs field is coupled with a hiddensector, or in extensions of the simplest Higgs sector by a second Higgs doublet. The second class of mixingeffects arises from vertex corrections of Higgs couplings to SM particles due to virtual contributions of newgauge bosons, scalars or fermions. Such loop effects can occur in various models like e.g. supersymmetry,extra dimensions, see-saw models, strong dynamics or extended gauge groups.Characterising NP effects by higher dimensional operators [22, 23], the deviations of the Higgs couplings g from the corresponding SM couplings g SM are of the order of g = g SM [1 + ∆] , with ∆ = O ( v / Λ ) , (1)where Λ (cid:29) v is the characteristic BSM scale. ∗ Depending on the precision ∆ with which the couplings aremeasured this allows then to probe mass scales of the order of Λ = v √ ∆ . For coupling modifications that aregenerated by loop effects, there is an additional loop suppression factor 1 / (16 π ) that adds to potentiallysmall couplings between the SM and the new particles, so that only scales up to Λ < v/ (4 π √ ∆) can beprobed. Loop effects are therefore less promising for the indirect exploration of NP scales than mixingeffects.Table 1 summarises the present precision on the couplings from measurements at the LHC [32, 33] andthe accuracy that can be achieved at the high-luminosity (HL) run of the LHC, at a future e + e − linearcollider (LC) [33, 34] and from the combination of the HL-LHC and HL-LC results. The extracted limits onthe effective scales Λ ∗ from the contributions of the dimension-6 operators taking into account these couplingprecisions are shown in Fig. 3. They have been obtained with SFitter [32] after defining the effective scalesΛ ∗ , that are obtained by factoring out from the operators typical coefficients like couplings and loop factors.Furthermore, in the loop-induced couplings to the gluons and photons only the contributions from the contactterms are kept. The effects of the loop terms are already disentangled at the level of the input values ∆.In the context of composite Higgs models, based on the estimates of potential deviations from SM Higgscouplings, bounds have been derived on the compositeness parameter ξ . These in turn translate into boundson the compositeness scale f and are summarised in Table 2. They are given for two different models, theMCHM4 and MCHM5. Built in a five dimensional warped space, they provide a resummation of the fullseries in ξ , while the SILH Lagrangian should be seen as an expansion in ξ and can describe composite Higgsmodels only in the vicinity of the SM limit. The bulk gauge symmetry SO (5) × U (1) X × SU (3) is brokendown to the SM gauge group on the ultraviolet boundary and to SO (4) × U (1) X × SU (3) on the infrared. Inthe MCHM4 [35] the SM fermions transform as spinorial representations, in the MCHM5 [36] as fundamental ∗ This does not hold in case the underlying model violates the decoupling theorem [31]. hW W hZZ htt hbb hτ τ hγγ hgg h invis — — 0.008 0.004 0.004Table 1: Expected accuracy at the 68% C.L. with which fundamental and derived Higgs couplings can bemeasured; the deviations are defined as g = g SM [1 ± ∆] compared to the Standard Model at the LHC/HL-LHC (luminosities 300 and 3000 fb − ), LC/HL-LC (energies 250+500 GeV / 250+500 GeV+1 TeV andluminosities 250+500 fb − / 1150+1600+2500 fb − ), and in combined analyses of HL-LHC and HL-LC. Forinvisible Higgs decays the upper limit on the underlying couplings is given. Taken from [30]. Λ * [ T e V ] LHCHL-LHCLCHL-LCHL-LHC+HL-LC 0 0.5 1 1.5 2 2.5 3 3.5 4 h WW h ZZ h tt hbb h ττ hgg h γγ Figure 3: Effective NP scales Λ ∗ extracted from the Higgs coupling measurements collected in Table 1. (Theordering of the columns from left to right corresponds to the legend from up to down.) For details, see [30].representations of SO (5). As a consequence in the MCHM4 the Higgs couplings are changed universally asfunction of ξ , while separately for SM vector bosons and fermions in the MCHM5. The limits that can beobtained on the compositeness scale f range from below 1 TeV up to 5 TeV. ξ LHC HL-LHC LC HL-LC HL-LHC+HL-LCuniversal 0.076 0.051 0.008 0.0052 0.0052non-universal 0.068 0.015 0.0023 0.0019 0.0019 f [TeV]universal 0.89 1.09 2.82 3.41 3.41non-universal 0.94 1.98 5.13 5.65 5.65Table 2: Estimates of the parameter ξ = ( v/f ) and the Goldstone scale f for various experimental set-upsand two different fermion embeddings (universal/MCHM4, non-universal/MCHM5); from Ref. [30].As a last example, the interpretation of the current Higgs coupling measurements in terms of a 2-Higgs-Doublet Model (2HDM) [37] is shown. The Yukawa couplings of the two Higgs doublets are taken to beproportional to each other in flavour space. At tree-level this aligned 2HDM has five free parameters, wherethe mass of the charged Higgs boson, which contributes to the effective Higgs-photon coupling, is already4ncluded. For simplicity, custodial symmetry is assumed to be fulfilled, i.e. the deviations of the Higgs-gaugecouplings from the SM couplings are ∆ Z = ∆ W ≡ ∆ V <
0. Figure 4 shows the comparison of the extractedfree couplings according to Eq. (1) with the corresponding fit to the aligned 2HDM parameters, translatedinto the SM coupling deviations. The central values and the error bars agree well between these two models.The observed small deviations are due to correlations between the couplings induced in the 2HDM. If thealigned 2HDM is realized in nature, additional constraints arise from non-standard Higgs searches, fromEWPTs and from flavour constraints. They are taken into account in the cyan bands. For recent work onHiggs coupling interpretations within the 2HDM with respect to wrong-sign Yukawa couplings, see e.g. [39]. -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 ∆ V ∆ t ∆ b ∆ τ ∆ γ measured data direct fitdirect fit ( ∆ V <0)aligned 2HDMaligned 2HDM (constr.) Figure 4: For the Higgs coupling measurement based on all currently available ATLAS and CMS data( (cid:82) L = 4 . − − − ): Comparison of the fits to the weak-scale couplings with a fitto the aligned 2HDM in terms of the light Higgs couplings. Figure from Ref. [38]. After the discovery of the Higgs boson it is important to reveal the true nature of the underlying dynamicsof EWSB and to answer the question if it is the Higgs boson of the SM or of some NP extension. In theabsence of any discovery of new particles pointing to BSM physics, the Higgs sector itself has to be exploredin great detail and may turn out to be the harbinger of NP. Composite Higgs models are examples of a Higgsboson emerging from a strongly interacting sector. Although challenged by EWPTs they are still a viableoption. A wide class of BSM Higgs sectors can be studied in a rather model-independent way through theeffective Lagrangian approach. New physics effects are encoded in higher dimensional operators that arebuilt from SM fields and suppressed by some high scale Λ at which NP becomes effective. Higgs couplingmeasurements prove useful to test such NP scales. In particular if deviations in the Higgs couplings aredue to mixings of the standard Higgs with other new scalars, scales in the TeV range can be constrainedby the LHC, while coupling deviations due to loop effects suffer from an additional loop suppression factorand are therefore less sensitive to Λ. Coupling fits performed within specific models, finally, complement theinterpretation within the effective Lagrangian approach. With the increasing accuracy in the measurementsat the next run of the LHC new exciting physics may wait for us to be discovered.
ACKNOWLEDGEMENTS
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