Updated Global Analysis of Higgs Couplings
KKCL-PH-TH/2013-10, LCTS/2013-05, CERN-PH-TH/2013-050
Updated Global Analysis of Higgs Couplings
John Ellis , and Tevong You Theoretical Particle Physics and Cosmology Group, Physics Department,King’s College London, London WC2R 2LS, UK TH Division, Physics Department, CERN, CH-1211 Geneva 23, Switzerland
Abstract
There are many indirect and direct experimental indications that the new particle H discovered by the ATLAS and CMS Collaborations has spin zero and (mostly) positiveparity, and that its couplings to other particles are correlated with their masses. Beyond anyreasonable doubt, it is a Higgs boson, and here we examine the extent to which its couplingsresemble those of the single Higgs boson of the Standard Model. Our global analysis of itscouplings to fermions and massive bosons determines that they have the same relative signas in the Standard Model. We also show directly that these couplings are highly consistentwith a dependence on particle masses that is linear to within a few %, and scaled by theconventional electroweak symmetry-breaking scale to within 10%. We also give constraintson loop-induced couplings, on the total Higgs decay width, and on possible invisible decaysof the Higgs boson under various assumptions.March 2013 a r X i v : . [ h e p - ph ] M a r Introduction and Summary
It has now been established with a high degree of confidence that the new particle H withmass ∼
126 GeV discovered by the ATLAS [1] and CMS [2] has spin zero and (mainly)positive-parity couplings, as expected for a Higgs boson [3]. Minimal spin-two alternativeswith graviton-like couplings have been disfavoured by measurements of the H couplings tovector bosons [4], and quite strongly excluded by constraints on the energy dependence of H production [5]. The graviton-like spin-two hypothesis has also been disfavoured strongly byanalyses of H decays into γγ [6], ZZ ∗ and W W ∗ final states [7, 8], and the positive-parityassignment is favoured by decays into ZZ ∗ , in particular . Beyond any reasonable doubt,the H particle is a Higgs boson.In this paper we make updated global fits to the H couplings to other particles withthe aim of characterizing the extent to which they resemble those of the Higgs boson ofthe Standard Model. There has been considerable progress since our previous analysis of H couplings [17], including updates at the Hadron Collider Physics conference in November2012 [11], the CERN Council in December 2013 [12], the Moriond Electroweak Confer-ence [13] and the Aspen ‘Quo Vadis Higgs’ Meeting in March 2013 [14], and most recentlyan update of the CMS H → γγ data at the Moriond QCD session [15].There have been many analyses of the H couplings [16, 17], some also including theMoriond 2013 data [18]. Many of these analyses, including those made by the differentexperimental Collaborations, assume simple parameterizations in which the couplings ofthe Standard Model Higgs boson to bosons and fermions are rescaled by factors a V and c f ,respectively (or equivalently by factors κ V,f ) [19]. Fits with non-minimal couplings to massivevector bosons have also been considered, as have fits in which the loop-induced couplings togluons and photons deviate by factors c g,γ from the values predicted in the Standard Model.The latter have been of interest in view of the possible excess of H → γγ decays relative tothe Standard Model prediction, particularly as reported by the ATLAS Collaboration [6].Since the Hγγ coupling could in principle receive contributions from new massive chargedparticles, and the
Hgg coupling from new massive coloured particles, these are particularlysensitive to new physics beyond the Standard Model. In this paper we make updated globalfits to the H couplings within such common phenomenological frameworks.We also revisit parameterizations of the H couplings to fermions and bosons that werefirst considered in [17], which are designed specifically to probe the dependence of the H It is also impressive that the mass of the H particle coincides with the best fit for the mass of the Higgsboson found in a global fit to precision electroweak data taking account of pre-LHC searches at LEP andthe TeVatron [9], and is also highly consistent with low-energy supersymmetry [10]. H couplings tofermions λ f and massive bosons g V of the form λ f = √ (cid:16) m f M (cid:17) (cid:15) , g V = 2 (cid:32) m (cid:15) ) V M (cid:15) (cid:33) , (1)which reduce to the couplings of the Standard Model Higgs boson in the double limit (cid:15) → , M → v = 246 GeV. This parameterization addresses explicitly the question the extentto which the H particle resembles a quantum excitation [3] of the Englert-Brout-Higgs fieldthat is thought to give masses to the particles of the Standard Model [3, 20–22].We find that, in the absence of contributions from any particles beyond the StandardModel, a combination of the Higgs signal strengths measured in different channels is nowvery close to the Standard Model value, within 13% at the 68% CL. We also find, for the firsttime, a strong preference for the couplings to bosons and fermions to have the same sign, alsoas expected in the Standard Model, driven largely by the new CMS result on H → γγ decay.This also means that there is no significant evidence of additional loop contributions to the Hγγ beyond those due to the top quark and the W boson. Using the parameterization (1),we find that the dependence of the Higgs couplings to different particle species is within a few% of a linear dependence of their masses. Within the parameterization (1), or marginalizingover the H couplings to Standard Model bosons and fermions, we find that the total Higgsdecay rate lies within 20% of the Standard Model value at the 68% CL. If the couplings ofthe Higgs Boson to Standard Model particles have their Standard Model values and there areno non-standard contributions to the Hgg and
Hγγ amplitudes, the upper limit on invisibleHiggs decays is 10% of the total Higgs decay rate.
The analysis of this paper is based mainly on the material presented by the LHC and TeVa-tron experimental Collaborations at the March 2013 Moriond Conferences in La Thuile [13,15]. The following are some of the main features of interest among the new results: • The H → ¯ bb signal strength reported by the TeVatron experiments has reduced from2 . ± . . ± .
75 times the Standard Model value. • A new H → τ + τ − result of 1 . ± . . ± .
5. 2
The H → γγ signal strength reported by ATLAS has reduced somewhat from 1 . +0 . − . to 1 . +0 . − . times the Standard Model value. Most importantly, CMS has reported anew result of 0 . +0 . − . for the signal strength using an MVA approach. • The H → W W ∗ signal strength reported by ATLAS has reduced from 1 . ± . . ± .
31 times the Standard Model value.All the latest available results from ATLAS, CMS and TeVatron are incorporated intoour global fit. The experimental data are used to reconstruct the likelihood in a combinationof three possible ways according to the available information: 1) using the official best-fitcentral value of µ with its 1- σ error bars, 2) using the given number of signal, backgroundand observed events with their respective errors, or 3) reconstructing the central value of µ from the 95% CL expected and observed µ . Specifically, the data inputs are as follows: • The TeVatron H → ¯ bb, τ + τ − , W W ∗ , γγ combined best-fit µ and 1- σ error bars from [23]. • The likelihood for the CMS 8 TeV
W W ∗ W W ∗ W W ∗ data. The ATLAS Collaboration provides 0,1-jet and 2-jet µ central val-ues and 1- σ ranges for a combination of 7- and 8-TeV, which we treat effectively as8 TeV. The percentages of the vector-boson fusion (VBF) production mode contribu-tions to the signals in the 0,1 and 2-jet channels are taken to be 2%, 12% and 81%,respectively [27]. • For H → b ¯ b in CMS we used the 7- and 8-TeV best-fit values from [26] and [28], whilefor ATLAS the likelihood was reconstructed from the 95% CL expected and observedvalues of µ at 7 and 8 TeV given in [29]. • The CMS H → τ + τ − and ZZ ∗ and ZZ ∗ dijet rates were taken from the central valuesgiven in [7]. Since no separate 7- and 8-TeV numbers are given for these, we treatthem effectively as 8 TeV. Numbers of events for the ATLAS H → ZZ ∗
7- and 8-TeV analyses are provided separately in [7], while the ATLAS H → τ + τ − likelihoodis reconstructed using the 95% expected and observed values of µ given in [30]. TheVBF τ + τ − efficiencies are taken from [31]. • The CMS γγ central values are given for six (five) different subchannels at 8 (7) TeV in[7], along with the percentage contributions from all production mechanisms in Table3 in [32]. The same information can be found for ATLAS at 7 TeV in [1] and at 8 TeVin [7], broken down into eleven subchannels including two VBF-dominated ones. TheCMS update is reported for a cut-based and MVA analysis; we use the MVA result,which has the greater sensitivity.For each individual experiment we have checked that our combinations of the likelihoodsfor the various subchannels agree with official combinations with only slight exceptions, forexample the CMS 7-TeV γγ analysis ( µ = 1 . +0 . − . instead of the official value of 1 . . − . ).When combined with the CMS 8-TeV data (for which we reproduce the official central value)we calculate for the combined CMS γγ data a value of µ = 0 . +0 . − . (to be compared withthe official value of 0 . +0 . − . ). This difference of a fraction of the quoted error does notimpact significantly our overall results.As a preliminary to our analysis, we compile in Fig. 1 the overall signal strengths in theprincipal channels, as calculated by combining the data from the different experiments. Thus,for example, in the first line we report the V + ( H → ¯ bb ) signal strength found by combiningthe data on associated V + H production from the TeVatron and LHC. As can be seen inthe second line, so far there is no significant indication of associated ¯ tt + H production. Thethird line in Fig. 1 combines the experimental information on the H → ¯ bb signal strengthsin these two channels. Signals for H → τ + τ − decay have now been reported in variousproduction channels, as reported in the next three lines of Fig. 1, and the combined signalstrength is given in the following line. As we have discussed, data are available on H → γγ final states following production in gluon-gluon collisions and via vector-boson fusion. Thecentral values of the corresponding signal strengths are now only slightly larger than theStandard Model predictions, and we return later to a discussion of the significance of thesemeasurements. The signal strengths in the H → W W ∗ and ZZ ∗ final states are very muchin line with the predictions of the Standard Model. These dominate the determination of thecombined signal strength reported in the last line of Fig. 1, together with the γγ final state.It is striking that the available data already constrain the combined Higgs signal strengthto be very close to the Standard Model value: µ = 1 . +0 . − . . (2)We present separately the combined signal strength in the VBF and VH channels withoutthe loop-induced γγ final state, which lies slightly (but not significantly) above the StandardModel value. To the extent that a signal with direct Higgs couplings in both the initialand final state is established, this combination disfavours models that predict a universal4uppression of the Higgs couplings .Figure 1: A compilation of the Higgs signal strengths measured by the ATLAS, CDF, D0and CMS Collaborations in the ¯ bb , τ + τ − , γγ , W W ∗ and ZZ ∗ final states. We display thecombinations of the different channels for each final state, and also the combination of allthese measurements, with the result for the VBF and VH channels (excluding the γγ finalstate) shown separately in the bottom line. Our first step in analyzing the implications of these data uses the following effective low-energy nonlinear Lagrangian for the electroweak symmetry-breaking sector [33]: L eff = v (cid:0) D µ U D µ U † (cid:1) × (cid:20) a Hv + . . . (cid:21) − v √ f ¯ f L λ f f R (cid:20) c f Hv + . . . (cid:21) + h.c. , (3)where U is a unitary 2 × W ± and Z bosons, H is the physical Higgs boson field and v ∼
246 GeV isthe conventional electroweak symmetry-breaking scale. The coefficients λ f are the StandardModel Yukawa couplings of the fermion flavours f , and the factors a and c f characterize the We address later in a full fit of the effective couplings of the Higgs to photons and gluons the ques-tion whether an enhancement of the loop-induced gluon fusion production could compemsate for this bycontaminating the VBF cut selection. H couplings to massivevector bosons and the fermions f , respectively. The couplings of the Higgs boson to masslessboson pairs gg and γγ are described by the following dimension-5 loop-induced couplings: L ∆ = − (cid:104) α s π c g b g G aµν G µνa + α em π c γ b γ F µν F µν (cid:105) (cid:18) HV (cid:19) , (4)where the coefficients b g,γ are those found in the Standard Model, and the factors c g,γ char-acterize the deviations from the Standard Model predictions for the H couplings to masslessvector bosons.One specific model for a common rescaling factor of all fermion and vector boson Higgscouplings is a minimal composite Higgs scenario [33], the MCHM4, in which the composite-ness scale f is related to ( a, c ) by a = c = (cid:115) − (cid:18) vf (cid:19) . A similar universal suppression is found in pseudo-dilaton models. A variant of this minimalmodel with a different embedding of the Standard Model fermions in SO(5) representationsof the new strong sector, the MCHM5, has separate vector and fermion rescalings: a = (cid:115) − (cid:18) vf (cid:19) , c = 1 − (cid:16) vf (cid:17) (cid:114) − (cid:16) vf (cid:17) . In the following we confront the data with these specific models, as well as an ‘anti-dilaton’scenario in which c = − a .Fig. 2 compiles the constraints imposed by the data summarized in Fig. 1 on the factors( a, c ) in the effective Lagrangian (3), assuming universality in the fermion factors c f ≡ c ,and assuming that no non-Standard-Model particles contribute to the anomaly factors c g,γ ,which therefore are determined by a combination of the factors c t = c and a W = a . In eachpanel of Fig. 2 and similar subsequent figures, the more likely regions of parameter spacehave lighter shading, and the 68, 95 and 99% CL contours are indicated by dotted, dashedand solid lines, respectively.We see again in the top row of panels of Fig. 2 that the data on H → ¯ bb decays(left) and τ + τ − decays (right) are entirely consistent with the Standard Model predictions( a, c ) = (1 , a, c ) plane favoured by the ¯ bb data manifests a correlationbetween a and c that arises because the dominant production mechanism is associated V + X production, which is ∝ a . On the other hand, the region of the ( a, c ) plane favoured by the6igure 2: The constraints in the ( a, c ) plane imposed by the measurements in Fig. 1 in the ¯ bb final state (top left), in the τ + τ − final state (top right), in the γγ final state (middleleft), in the W W ∗ final state (middle right) and in the ZZ ∗ final state (bottom left). Thecombination of all these constraints is shown in the bottom right panel. + τ − data exhibits a weaker correlation between a and c , reflecting the importance of dataon production via gluon fusion in this case. As was to be expected from the compilation inFig. 1, the γγ data displayed in the middle left panel of Fig. 2 are now compatible with theStandard Model prediction ( a, c ) = (1 , H → W W ∗ (middle right panel of Fig. 2) and ZZ ∗ decays (bottom left panel) arealso entirely consistent with ( a, c ) = (1 , c ∼
0. This effect is very visible in the γγ and W W ∗ results displayed in the middle plots. On the other hand, in the ZZ ∗ case theCMS dijet analysis is less powerful, so there is a weaker suppression of the likelihood around c ∼ H → γγ decay or the Hgg coupling. We note that the global fit is not symmetric between the two possibilities forthe sign of c relative to a , a feature visible in the middle left panel of Fig. 2, and traceableto the interference between the t quark and W boson loops contributing to the H → γγ decay amplitude. In the past it has been a common feature of such global fits that theyhave exhibited two local minima of the likelihood function with opposite signs of c that,because of this asymmetry, were not equivalent but had similar likelihoods [34]. We see inthe bottom right panel of Fig. 2, for the first time a clear preference for the minimum with c >
0, i.e., the same sign as in the Standard Model.This feature is also seen clearly in Fig. 3, where we display in the left panel the one-dimensional likelihood function χ for the boson coupling parameter a obtained by marginal-izing over the fermion coupling parameter c , and in the right panel the one-dimensionallikelihood function for c obtained by marginalizing over a . We see that the fit with c > c <
0, with ∆ χ ∼
9. The parameters of the globalminimum of the χ function and their 68% CL ranges are as follows: a = 1 . ± . , c = 0 . ± . . (5)This preference for c > γγ data.The yellow lines in the bottom right panel of Fig. 2 correspond to various alternatives tothe Standard Model, as discussed above. We see that fermiophobic models (the horizontalline) are very strongly excluded, as are anti-dilaton models in which c = − a . On the otherhand, dilaton/MCHM4 models with a = c are compatible with the data as long as theircommon value is close to unity. Likewise, MCHM5 models lying along the curved line are8igure 3: The one-dimensional likelihood functions for the boson coupling parameter a (leftpanel) and the fermion coupling parameter c (right panel), as obtained by marginalizing overthe other parameter in the bottom right panel of Fig. 2. also compatible with the data if their parameters are chosen to give predictions close to theStandard Model.The fact that, whereas all the direct measurements of H couplings to fermions andmassive vector bosons are very compatible with the Standard Model, the coupling to γγ wasformerly less compatible, has given rise to much speculation that additional virtual particlesmay be contributing to the factor c γ in (4). However, the motivation for this speculationhas been largely removed by the recent re-evaluation of the H → γγ decay rate by theCMS Collaboration, which is quite compatible with the Standard Model prediction. Theleft panel of Fig. 4 shows the results of a global fit to the anomaly factors ( c γ , c g ), assumingthe Standard Model values ( a, c ) = (1 ,
1) for the tree-level couplings to massive bosons andfermions. Under this hypothesis, any deviation from ( c γ , c g ) = (1 ,
1) would be due to newparticles beyond the Standard Model. We see explicitly in Fig. 4 that, while there may stillbe a hint that c γ >
1, the value of c g is completely compatible with the Standard Model.Thus, any set of new particles contributing to c γ should be constructed so as not to contributesignificantly to c g .The right panel of Fig. 4 is complementary, showing the constraints in the ( a, c ) plane aftermarginalizing over ( c γ , c g ). Thus it represents the constraints on a and c if no assumptionis made about the absence of new particle contributions to the loop amplitudes. In thiscase, the symmetry between the solutions with c > < H → γγ decay rate no longer discriminates between them. In this case, the Standard Model values a = c = 1 are well inside the most favoured region of the ( a, c ) plane.9igure 4: Left: The constraints in the ( c γ , c g ) plane imposed by the measurements in Fig. 1,assuming the Standard Model values for the tree-level couplings to massive bosons andfermions, i.e., a = c = 1 . Right: The constraints in the ( a, c ) plane when marginalizingover c γ and c g . We display in the left panel of Fig. 5 the one-dimensional likelihood function χ forthe factor c γ obtained by marginalizing over c g , and in the right panel the one-dimensionallikelihood function for c g obtained by marginalizing over c γ . The central values and the 68%CL ranges of c γ and c g are as follows: c γ = 1 . ± . , c g = 0 . ± . , (6)and the likelihood price for c γ = 1 is ∆ χ = 2, whereas the price for c g = 1 is ∆ χ = 1. We now turn to the results of a global fit using the (
M, (cid:15) ) parameterization (1) that probesdirectly the extent to which the current measurements constrain the H couplings to otherparticles to be approximately linear: (cid:15) ∼
0, and the extent to which the mass scalingparameter M ∼ v . The left panel of Fig. 6 shows the result of combining the measurementsshown in Fig. 1 in the ( M, (cid:15) ) plane. The horizontal and vertical yellow lines correspond to (cid:15) = 0 and M = v , respectively, and the data are quite compatible with these values. Thecentral values and the 68% CL ranges of M and (cid:15) are as follows: M = 244 +20 − GeV , (cid:15) = − . +0 . − . , (7)and the likelihood price for M = 246 GeV and (cid:15) = 0 is ∆ χ = 0 .
12. It is remarkable thatthe data already constrain the mass dependence of the H couplings to other particles to be10igure 5: The one-dimensional likelihood functions for c γ (left panel) and c g (right panel), asobtained by marginalizing over the other variable in the bottom right panel of Fig. 4, assumingthe Standard Model values for the tree-level couplings to massive bosons and fermions. linear in their masses to within a few %, and that the mass scaling parameter M is within10% of the Standard Model value v = 246 GeV. We display in the left panel of Fig. 7 the one-dimensional likelihood function χ for the factor (cid:15) obtained by marginalizing over M , andin the right panel the one-dimensional likelihood function for M obtained by marginalizingover (cid:15) .The right panel of Fig. 6 displays the mass dependence of the H couplings in a differentway, exhibiting explicitly the constraints on the couplings of H to other particles withinthe parameterization (1). The solid red line is the prediction of the Standard Model, (cid:15) = 0and M = v , the black dashed line corresponds to the best-fit values in (7), and the dottedlines correspond to their 68% CL ranges. The black points and vertical error bars are thepredictions of the ( M, (cid:15) ) fit for the couplings of H to each of the other particle species: thepoints lie on the best-fit dashed line and the error bars end on the upper and lower dottedlines. Also shown (in blue) for each particle species is the prediction for its coupling to H if the data on that particular species are omitted from the global fit. In other words, theblue points and error bars represent the predictions for the H coupling to that particle, asderived from the couplings to other particles. We now discuss the total Higgs decay rate in the two classes of global fit discussed above,assuming that the Higgs has no other decays beyond those in the Standard Model [35].11igure 6:
The constraints in the ( M, (cid:15) ) plane imposed by the measurements in Fig. 1 (leftpanel) and the strengths of the couplings to different fermion flavours and massive bosonspredicted by this two-parameter ( M, (cid:15) ) fit (right panel). In the latter, the red line is theStandard Model prediction, the black dashed line is the best fit, and the dotted lines are the68% CL ranges. For each particle species, the black error bar shows the range predictedby the global fit, and the blue error bar shows the range predicted for that coupling if itsmeasurement is omitted from the global fit. Figure 7:
The one-dimensional likelihood functions for (cid:15) (left panel) and M (right panel), asobtained by marginalizing over the other variable in the left panel of Fig. 6. The left panel of Fig. 8 displays contours of the Higgs decay rate relative to the StandardModel prediction in the ( a, c ) plane discussed in Section 3. The local χ minimum with c > c < M, (cid:15) ) plane, where we again see12hat the best fit has a total decay rate very close to the Standard Model value. We displayin Fig. 9 the one-dimensional likelihood function for the total Higgs decay width relativeto its Standard Model value assuming no contributions from non-Standard-Model particles.The solid line is obtained assuming that a = c (or, equivalently, that (cid:15) = 0 but M is free),the dashed line is obtained marginalizing over ( a, c ), and the dot-dashed line is obtained bymarginalizing over ( M, (cid:15) ).Figure 8:
Contours of the total Higgs decay rate relative to the Standard Model prediction inthe ( a, c ) plane shown in the bottom right panel of Fig 2 (left) and the ( M, (cid:15) ) plane shown inthe left panel of Fig. 6 (right). One may also use the current Higgs measurements to constrain the branching ratio forHiggs decays into invisible particles, BR inv [36]. This invisible branching ratio factors outof the total decay width asΓ Tot = Γ
Vis + Γ
Inv = (cid:18) R Vis − BR Inv (cid:19) Γ SMTot , (8)where R Vis = Γ
Vis / Γ SMTot is the rescaling factor of the total decay width in the absence ofan invisible contribution. Thus we see that an invisible branching ratio acts as a generalsuppression of all other branching ratios, which could be compensated by non-standardvisible Higgs decays.The left panel of Fig. 10 displays the χ function for BR inv under various assumptions.The solid line was obtained assuming the Standard Model couplings for visible particles, i.e.,( a, c ) = (1 ,
1) or equivalently (
M, (cid:15) ) = ( v, BR inv = 0, andthat the 68 and 95% CL limits are 0.04 and 0.13, respectively. The dot-dashed line wasobtained by marginalizing over ( a, c ), where the shallow minimum at BR inv ∼ . The one-dimensional likelihood function for the total Higgs decay width relative toits value in the Standard Model, R ≡ Γ / Γ SM , assuming decays into Standard Model particlesalone and assuming a = c or equivalently (cid:15) = 0 (solid line), marginalizing over ( a, c ) (dashedline) and marginalizing over ( M, (cid:15) ) (dot-dashed line). require a >
1. Finally, the dashed line was obtained fixing ( a, c ) = (1 ,
1) (or equivalently(
M, (cid:15) ) = ( v, c γ , c g ). Conversely, the right panelof Fig. 10 displays the constraint in the ( c γ , c g ) plane obtained by marginalizing over BR inv .Figure 10: Left: The branching ratio for Higgs decay into invisible particles obtained assumingthe Standard Model decay rates for all the visible Higgs decays (solid), marginalizing over ( c γ , c g ) (dashed) and (a,c) (dot-dashed). Right: The constraints in the ( c γ , c g ) plane whenmarginalizing over the invisible branching ration BR inv . Conclusions
The recent installments of data from the LHC experiments announced in March 2013 imposestrong new constraints on the properties and couplings of the H particle, which is beyonddoubt a Higgs boson. The data now constrain this particle to have couplings that differby only some % from those of the Higgs boson of the Standard Model. In particular, therelative sign of its couplings to bosons and fermions is fixed for the first time, its couplingsto other particles are very close to being linear in their masses, and strong upper limits oninvisible Higgs decays can be derived.The data now impose severe constraints on composite alternatives to the elementaryHiggs boson of the Standard Model. However, they do not yet challenge the predictionsof supersymmetric models, which typically make predictions much closer to the StandardModel values. We therefore infer that the Higgs coupling measurements, as well as its mass,provide circumstantial support to supersymmetry as opposed to these minimal compositealternatives, though this inference is not conclusive.It is likely that the first LHC run at 7 and 8 TeV has now yielded most of its Higgssecrets, and we look forward to the next LHC run at higher energy, and its later runs atsignificantly higher luminosity. These will provide significant new information about the H particle and constrain further its couplings, as well as providing opportunities to probedirectly for other new physics. The LHC will be a hard act to follow. Acknowledgements
The work of JE was supported partly by the London Centre for Terauniverse Studies (LCTS),using funding from the European Research Council via the Advanced Investigator Grant267352. The work of TY was supported by a Graduate Teaching Assistantship from King’sCollege London. JE thanks CERN for kind hospitality.
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