Constraints on Higgs Couplings and Physics Beyond the Standard Model
CConstraints on Higgs Couplings and Physics Beyond the Standard Model
Herm`es B´elusca-Ma¨ıto, Adam Falkowski
Laboratoire de Physique Th´eorique, CNRS – UMR 8627,Bˆat. 210 Universit´e de Paris-Sud 11 F-91405 Orsay Cedex France.
We summarize current constraints on the couplings of the Higgs boson in the framework of aneffective theory beyond the Standard Model.
Article prepared for the proceedings of the 9thRencontres du Vietnam “Windows on the Universe” Quy Nhon Vietnam, August 11-17 2013.
The discovery of the Higgs boson at the LHC was a spectacular confirmation of the centralprediction of the Standard Model (SM). Nevertheless, it is possible that precision studies of theHiggs boson will reveal new physics beyond the SM. The effective theory framework offers amodel-independent approach to address this issue. The underlying assumption is that there areno new particles (beyond those of the SM) with masses near the weak scale. In this talk wepresent up-to-date constraints on the parameters of the leading effective theory operators thatgovern the Higgs couplings to matter. We assume that the Higgs boson h is a part of the Higgs field H that transforms as the ( , ) / representation under the SM SU (3) C × SU (2) L × U (1) Y gauge group and obtains an expectationvalue v . Then one can organize the effective Lagrangian as an expansion L eff = L SM + L D =5 + L D =6 + . . . , where each term consists of gauge invariant local operators of canonical dimension D constructed out of the SM fields. The leading term is the SM Lagrangian which containsoperators up to dimension 4. The only operators at dimension 5 are of the form ( LH ) ; theygive masses to neutrinos but have no observable impact on Higgs phenomenology. At dimension6, the minimal non-redundant set of operators was given by Grzadkowski et al. ; we use theequivalent basis written down in Contino et al. . We assume L D =6 contains no new sources offlavor, CP and baryon number violation. Then the dimension 6 operators lead to the following a r X i v : . [ h e p - ph ] N ov ouplings of a single Higgs boson to pairs of SM fields: L h = hv c V m W W + µ W − µ + c V,Z m Z Z µ Z µ − c u (cid:88) f = u,c,t m f ¯ f f − c d (cid:88) f = d,s,b m f ¯ f f − c l (cid:88) f = e,µ,τ m f ¯ f f + 14 c gg G aµν G aµν − c W W W + µν W − µν − c γγ γ µν γ µν − c ZZ Z µν Z µν − c Zγ γ µν Z µν + κ Zγ ∂ ν γ µν Z µ + κ ZZ ∂ ν Z µν Z µ + ( κ W W ∂ ν W + µν W − µ + h . c . ) , (1) L D =6 contains also the so-called vertex and dipole operators that modify Higgs couplings to3 or more SM fields, but we ignore them here. The 13 real couplings in Eq. (1) map to 11operators in the dimension 6 Lagrangian (one constraint on c ii and one on κ ii follow froman accidental custodial symmetry in L D =6 3 ). Given the current precision of experiment andtheoretical predictions, the effective operators of dimension greater than 6 are not relevant.It would be desirable to obtain constraints on all these coefficients using the Higgs data.However, the data publicly available so far leave important degeneracies, in particular they havea very limiting power of discriminating between different tensor structures of the Higgs couplingto vector bosons. Therefore we make further assumptions demanding that the combinationsof couplings leading to power-divergent corrections to electroweak precision observables vanish.This leads to the constraints c V,Z = c V , c W W = c γγ + g L g Y c Zγ , c ZZ = c γγ + g L − g Y g L g Y c Zγ , κ Zγ = κ W W = κ ZZ = 0 , (2)where g L and g Y are the gauge couplings of SU (2) L × U (1) Y . Only 2 combinations of theseconstraints follow automatically from L D =6 . The remaining ones have to be imposed by handand represent an assumption about the underlying UV theory. In the following we work withthe effective Lagrangian of Eq. (1) subject to the constraints of Eq. (2). The Higgs couplings tomatter thus depend on 7 free parameters: c V , c u , c d , c l , c gg , c γγ , c Zγ . (3)The SM Higgs is the limiting case where c V = c f = u,d,l = 1 and c gg = c γγ = c Zγ = 0. Movingaway from the SM point, one effect is that the partial decay widths of the Higgs boson aremodified. For m h = 125 . cc Γ SM cc (cid:39) | c u | , Γ bb Γ SM bb (cid:39) | c d | , Γ ττ Γ SM ττ (cid:39) | c l | , (4)Γ ZZ ∗ → l Γ SM ZZ ∗ → l (cid:39) c V + 0 . c V c Zγ + 0 . c V c γγ , Γ W W ∗ → l ν Γ SM W W ∗ → l ν (cid:39) c V + 0 . c V c Zγ + 0 . c V c γγ , (5)Γ gg Γ SM gg (cid:39) | ˆ c gg | | ˆ c gg, SM | , ˆ c gg = c gg + 10 − [1 . c u − (0 . − . i ) c d ] , | ˆ c gg, SM | (cid:39) . , Γ γγ Γ SM γγ (cid:39) | ˆ c γγ | | ˆ c γγ, SM | , ˆ c γγ = c γγ + 10 − (0 . c V − . c u ) , | ˆ c γγ, SM | (cid:39) . , Γ Zγ Γ SM Zγ (cid:39) | ˆ c Zγ | | ˆ c Zγ, SM | , ˆ c Zγ = c Zγ + 10 − (1 . c V − . c u ) , | ˆ c Zγ, SM | (cid:39) . . (6)The relative branching fraction is given by Br( h → XX )Br( h → XX ) SM = Γ XX Γ XX, SM Γ tot , SM Γ tot , where Γ tot is the sumof all partial decay widths. Furthermore, the Higgs production cross-section via the gluon fusion able 1: The LHC Higgs search results used in our fit. ATLAS
Production Decay ˆ µ Ref.2D γγ . +0 . − .
29 5 , ZZ . +0 . − .
33 5 , W W . +0 . − .
26 5 , τ τ . +0 . − .
62 9 VH bb . +0 . − . ttH bb . ± . γγ − . ± . inclusive Zγ . ± . µµ . ± . CMS
Production Decay ˆ µ Ref.2D γγ . +0 . − .
26 15 ZZ . +0 . − .
24 16
W W . +0 . − .
19 16 τ τ . +0 . − .
41 16 VH bb . ± . VBF bb . ± . ttH bb . +1 . − . γγ − . +2 . − . τ τ − . +6 . − . multi- (cid:96) . +1 . − . inclusive Zγ − . ± . µµ . +2 . − . gg → h (ggH), top pair associated production gg → ht ¯ t (ttH), vector boson fusion qq → hqq (VBF), and vector boson associated production q ¯ q → hW/Z (VH) are modified as σ ggH σ SM ggH (cid:39) | ˆ c gg | | ˆ c gg, SM | , σ ttH σ SM ttH (cid:39) c u , σ V BF σ SM V BF (cid:39) c V + 0 . c V c Zγ + 0 . c V c γγ , (7) σ W H σ SM W H (cid:39) c V − . c V c Zγ − . c V c γγ , σ ZH σ SM ZH (cid:39) c V − . c V c Zγ − . c V c γγ . (8)The LHC collaborations typically quote the relative rate ˆ µ Y HXX = σ Y H σ SM Y H
Br( h → XX )Br( h → XX ) SM in a numberof channels. Comparing the measured rates with the SM predictions we can constrain theparameters of the effective Lagrangian. We will show that the current Higgs and electroweakprecision data constrain in a non-trivial way all the 7 parameters in Eq. 3. The LHC Higgs data we included in our fit are collected in Table 1. We used 2-dimensional(2D) likelihoods in the ˆ µ ggH + ttH / ˆ µ V BF + V H plane whenever those are provided by experiments.In these cases the value of ˆ µ is given for illustration only; in the fit we always use the full2D likelihood function which captures non-trivial correlations between the rates measured forvarious production modes. In the channels where only 95% CL limits are given we reconstructˆ µ assuming the errors are Gaussian. We also include the combined Tevatron measurements :ˆ µ incl .γγ = 6 . +3 . − . , ˆ µ incl .W W = 0 . +0 . − . , ˆ µ V Hbb = 1 . +0 . − . , ˆ µ incl .ττ = 2 . +2 . − . . Furthermore, we use elec-troweak precision measurements from LEP, SLC, and Tevatron collected in Table 1 of Falkowski et al. . To evaluate logarithmically divergent corrections from the Higgs loops to electroweakprecision observables we assume Λ = 3 TeV. We fit the 7 parameters in Eq. 3 to the available Higgs and electroweak precision data assumingthe errors are in various channels are Gaussian and uncorrelated, except in the cases whereorrelations are known (as in the case of 2D likelihood or some electroweak precision data). Weinclude the uncertainty on the prediction of the SM ggH production cross-section by introducinga nuisance parameter with a Gaussian distribution around the central value. For the LHC at √ s = 8 TeV we take the scale error (+7.2%, -7.8%) and the PDF error (+7.5%, -6.9%) andadd those two linearly. We obtain the following central values and 68% CL intervals for theparameters: c V = 1 . +0 . − . , c u = 1 . +0 . − . , c d = 1 . +0 . − . , c l = 1 . +0 . − . ,c gg = − . +0 . − . , c γγ = 0 . +0 . − . , c Zγ = 0 . +0 . − . . (9)We find χ − χ = 3 . all c V is dominated by electroweak precision observables, and can be relaxedin the presence of additional tuned contributions to the S and T parameter that could arise fromintegrating out heavy new physics states. Ignoring the electroweak precision data in the fit oneobtains the weaker constraint c V = 1 . +0 . − . .The fit displays an approximately flat direction along c gg +0 . c u , which is the combinationthat sets the strength of the gluon fusion production mode. This is clearly visible in Fig. 1(a)where a 2D fit in the c u – c gg plane is performed, with the other couplings fixed to their SMvalues. This flat direction is lifted by the ttH production mode which depends on c u only. Therecent CMS results in the ttH channel put interesting constraints on c u independently of c gg :unlike in the previous fits, c u = 0 is now disfavored at the 2 σ level. Furthermore, the fit showsa strong preference for c d (cid:54) = 0 even though the h → b ¯ b decay has not been clearly observed. Thereason is that c d determines Γ bb which dominates the total Higgs decay width and the latter isindirectly constrained by the Higgs rates measured in other decay channels. The least stringentconstraint is currently that on c Zγ which reflects weak experimental limits on the h → Zγ decayrate. It is interesting to note that there are good prospects of probing c Zγ using differentialcross section measurements in the h → ZZ ∗ → (cid:96) channel. (cid:43)(cid:43) (cid:43) Best fitSM point (cid:45) (cid:45) c u c gg c u vs. c gg correlation (a) Σ Σ Σ Σ Σ Σ Br inv (cid:68) Χ c f (cid:61) c V (cid:61) c gg (cid:61) c ΓΓ (cid:61) c Z Γ (cid:61) (b)Figure 1 – Left: A fit in the c u - c gg plane with the other couplings fixed at their Standard Model values. Right: χ − χ min of the fit for the Higgs with SM-size couplings to the SM matter and an invisible branching fraction. Constraints on invisible width
Going beyond the effective Higgs Lagrangian in Eq. 1, it is interesting to consider the possibilityof an invisible Higgs width. This may arise in models with new weakly interacting light degreesof freedom that have a significant couplings to the Higgs boson, for example in Higgs-portalmodels of dark matter or in supersymmetric models. The invisible decays have been directlysearched for at the LHC. The current 95% CL limits on the invisible branching fraction areBr inv <
65% in the ZH production mode in ATLAS , Br inv <
75% in the ZH production modein CMS , and Br inv <
69% in the VBF production mode in CMS . Stronger limits on theinvisible Higgs width can be obtained indirectly from a global fit to the Higgs couplings. In thecase when the couplings of the Higgs to the SM matter take the SM values the invisible widthleads to a universal reduction of the decay rates in all the visible channels. This possibility isstrongly constrained, given the Higgs is observed in several channels with the rate close to theSM one. From Fig. 1(b) one can read off the limit Br inv <
16% at 95% CL. This bound can berelaxed if one allows new physics to modify the Higgs couplings such that the Higgs productioncross-section is enhanced, so as to offset the reduction of the visible rates. For example, if c gg is allowed to float freely in the fit, the weaker limit Br inv <
40% is obtained. Note that theseindirect limits apply to any other exotic (but not necessarily invisible) contribution to the Higgswidth.
Acknowledgments
AF thanks Dean Carmi, Erik Kuflik, Francesco Riva, Alfredo Urbano, Tomer Volansky andJure Zupan for collaboration on closely related projects. AF also thanks the organizers of theconference
Windows on the Universe for the invitation and support.
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