1 Introduction

LAPTH-061/12

LPSC12350

LPT Orsay 12-119

NSF-KITP-12-236

Higgs Couplings at the End of 2012

G. Bélanger111Email: belanger@lapp.in2p3.fr, B. Dumont222Email: dumont@lpsc.in2p3.fr, U. Ellwanger333Email: Ulrich.Ellwanger@th.u-psud.fr, J. F. Gunion444Email: jfgunion@ucdavis.edu, S. Kraml555Email: sabine.kraml@lpsc.in2p3.fr

LAPTH, Université de Savoie, CNRS, B.P.110, F-74941 Annecy-le-Vieux Cedex, France

[1mm] Laboratoire de Physique Subatomique et de Cosmologie, UJF Grenoble 1, CNRS/IN2P3, INPG, 53 Avenue des Martyrs, F-38026 Grenoble, France

[1mm] Laboratoire de Physique Théorique, UMR 8627, CNRS and Université de Paris–Sud, F-91405 Orsay, France

[1mm] Department of Physics, University of California, Davis, CA 95616, USA

[1mm] Kavli Institute for Theoretical Physics, University of California, Santa Barbara,

CA 93106-4030, USA

Performing a fit to all publicly available data, we analyze the extent to which the latest results from the LHC and Tevatron constrain the couplings of the Higgs boson-like state at . To this end we assume that only Standard Model (SM) particles appear in the Higgs decays, but tree-level Higgs couplings to the up-quarks, down-quarks and vector bosons, relative to the SM are free parameters. We also assume that the leptonic couplings relative to the SM are the same as for the down-quark, and a custodial symmetry for the couplings. In the simplest approach, the effective Higgs couplings to gluons and photons are computed in terms of the previous parameters. This approach is also applied to Two-Higgs-Doublet Models of Type I and Type II. However, we also explore the possibility that the net Higgs to and couplings have extra loop contributions coming from Beyond-the-Standard Model physics. We find that the SM -value is more than away from fits in which: a) there is some non-SM contribution to the coupling of the Higgs; or b) the sign of the top quark coupling to the Higgs is opposite that of the W coupling. In both these cases -values can be achieved. Since option b) is difficult to realize in realistic models, it would seem that new physics contributions to the effective couplings of the Higgs are preferred.

1 Introduction

The recent discovery [1, 2] of a new particle with properties consistent with a Standard Model (SM) Higgs boson is clearly the most significant news from the Large Hadron Collider (LHC). This discovery was supported by evidence for a Higgs boson found by the CDF and D0 collaborations at the Tevatron [3] and completes our picture of the SM. However, the SM leaves many fundamental questions open—perhaps the most pressing issue being that the SM does not explain the value of the electroweak scale, i.e. the Higgs mass, itself. Clearly, a prime goal after the discovery is to thoroughly test the SM nature for this Higgs-like signal.

The SM makes precise predictions for the production cross sections of the Higgs boson (via gluon-gluon fusion (ggF), vector boson fusion (VBF), associated production with an electroweak gauge boson (VH) and associated production with a pair (ttH)), and its decay branching fractions into various final states (, , , , and ) as a function of its unpredicted mass . The observation of the Higgs boson at the LHC is based primarily on the [4, 5], [6, 7] and [9, 10] decay modes. The Higgs boson mass, , is quite precisely measured to be in the 125–126 GeV range using the high resolution and final states [11, 12].111Although ATLAS finds a lower value of  GeV in the channel, the combined value from ATLAS is  GeV, in very good agreement with  GeV measured by CMS. We find it reasonable to assume that the lower value from the ATLAS measurement is due to a statistical fluctuation or unknown systematics. The evidence for the Higgs boson at the Tevatron is based principally on the decay mode [13, 3, 14], the observed enhancements being consistent with a large range of possible Higgs masses.

With the measurements in various channels, a comprehensive study of the properties of the Higgs-like state becomes possible and has the potential for revealing whether or not the Higgs sector is as simple as envisioned in the SM. In particular it is crucial to determine the Higgs couplings to gauge bosons and to fermions as defined by the Lagrangian

(1)

where the are scaling factors for the couplings relative to their SM values, introduced to test possible deviations in the data from SM expectations. In principle all the are independent, in particular the can be different for up- and down-type quarks and/or leptons. A significant deviation of any from unity would imply new physics beyond the SM.

While fits to various combinations of ’s are performed by the experimental collaborations themselves [15, 12], we find it important to develop our own scheme in order to bring all results from ATLAS, CMS and the Tevatron experiments together and test not only the SM but also specific models beyond. Such fits by theorists, using various parametrizations, were performed previously in [16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43]. Here, we go beyond these works by including all publicly available data as of the end of 2012. In particular we take into account the updates presented at the Hadron Collider Physics Symposium in Nov. 2012 (HCP2012) [44] and at the Open Session of the CERN Council in Dec. 2012 [45].

Our parametrization is as follows. We treat the couplings to up-type and down-type fermions, and , as independent parameters (but we only consider the case , and we assume that the are family universal). Moreover, we assume a custodial symmetry in employing a single in Eq. (1). The structure we are testing thus becomes

(2)

In general, the can take on negative as well as positive values; there is one overall sign ambiguity which we fix by taking . Even in this restricted context, various types of deviations of these three from unity are possible in extended theories such as Two-Higgs-Doublet Models (2HDMs), models with singlet-doublet mixing, and supersymmetric models such as the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM).

In addition to the tree-level couplings given above, the has couplings to and that are first induced at one loop and are completely computable in terms of , and if only loops containing SM particles are present. We define and to be the ratio of these couplings so computed to the SM (i.e. ) values. However, in some of our fits we will also allow for additional loop contributions and from new particles; in this case and . The largest set of independent parameters in our fits is thus

(3)

In this study, we focus on models in which the Higgs decays only to SM particles, in particular not allowing for invisible (e.g. , where is the lightest SUSY particle) or undetected decays (such as , where is a light CP-odd, perhaps singlet scalar). This approach, when we allow in the most general case for the , , , and couplings to be fully independent, encompasses a very broad range of models, including in particular those in which the Higgs sector consists of any number of doublets + singlets, the only proviso being the absence of decays of the observed state to non-SM final states. (A fit for invisible Higgs decays was performed early on in [46].) This approach however does not cover models such as composite models and Higgs-radion mixing models for which the coupling has a more complicated tensor structure than that given in Eq. (2). Our procedure will also be inadequate should the observed signal at actually arise from two or more degenerate Higgs bosons (see e.g. [47, 48]). Although the success of our fits implies that there is no need for such extra states, the explicit tests for degenerate states developed in [49] should be kept in mind as a means to test directly for two or more Higgs bosons contributing to the signal at 125–126 GeV.

This paper is organized as follows. The experimental inputs and our fitting procedure are described in Section 2. The results of three generic fits are presented in Section 3 together with the results of a fit in Two-Higgs-Doublet models. Section 4 contains our conclusions.

2 Experimental inputs and fitting procedure

We perform fits employing all production/decay channels for which results are available from the ATLAS and CMS collaborations at the LHC, as well as the Tevatron CDF+D0 Higgs results. The experimental results are given in terms of signal strengths , the ratio of the observed rate for some process relative to the prediction for the SM Higgs. Often it is the case that several production processes contribute to a given experimental channel. For example, both vector boson fusion and gluon fusion can contribute to the “VBF” channels (or “categories”) that are defined by a given set of experimental cuts. In comparing theory to experiment it is thus important to incorporate the estimates from the experiments of the relative contributions of the theoretically distinct production/decay processes. The values for the signal strengths in the various (sub)channels as reported by the experiments and used in this analysis, together with the estimated decompositions into production channels are given in Tables 13.

We adopt the simple technique of computing the associated with a given choice of the input parameters following the standard definition:

(4)

where runs over all the experimentally defined production/decay channels employed, is the observed signal strength for channel , is the value predicted for that channel for a given choice of parameters and is the experimental error for that channel. The associated with each experimentally defined channel is further decomposed as

(5)

where the give the amount of contribution to the experimental channel coming from the theoretically defined channel and is the prediction for that channel for a given choice of , , and (for fits where treated as independent) and . For the computation of the including NLO corrections we follow the procedure recommended by the LHC Higgs Cross Section Working Group in [60]. In particular we include all the available QCD corrections for using HIGLU [61, 62] and for using HDECAY [62, 63], and we switch off the electroweak corrections. The depend on the specific analysis and hence differ from experiment to experiment. Often, the are determined from simulations of a SM Higgs signal. In some cases, the experiments have done the unfolding of theoretical vs. experimental channels from the data and provide directly experimental results for the theoretically relevant ’s and the correlations between them.

Channel Signal strength (GeV) Production mode
ggF VBF VH ttH
( at 7 TeV + at 8 TeV) [4]
126.6 100%
126.6 60% 40%
( at 7 TeV + at 8 TeV) [6, 11]
Inclusive 125 87% 7% 5% 1%
at 8 TeV) [8, 11]
125.5 95% 3% 2%
( at 7 TeV + at 8 TeV) [50, 11]
VH tag 125.5 100%
( at 7 TeV + at 8 TeV) [51]
125 100%
125 60% 40%
Table 1: ATLAS results as employed in this analysis. The correlations included in the fits are for the and for the channels.
Channel Signal strength (GeV) Production mode
ggF VBF VH ttH
( at 7 TeV + at 8 TeV) [2, 5, 12]
125.8 100%
125.8 60% 40%
( at 7 TeV + at 8 TeV) [12, 7]
Inclusive 125.8 87% 7% 5% 1%
(up to at 7 TeV + at 8 TeV) [52, 10, 12]
0/1 jet 125.8 97% 3%
VBF tag 125.8 17% 83%
VH tag 125.8 100%
(up to at 7 TeV + at 8 TeV) [54, 53, 12]
VH tag 125.8 100%
ttH tag 125.8 100%
(up to at 7 TeV + at 8 TeV) [56, 55, 12]
0/1 jet 125.8 76% 16% 7% 1%
VBF tag 125.8 19% 81%
VH tag 125.8 100%
Table 2: CMS results as employed in this analysis. The correlation included for the channel is .
Channel Signal strength (GeV) Production mode
ggF VBF VH ttH
 [59]
Combined 125 78% 5% 17%
 [59]
Combined 125 78% 5% 17%
 [14]
VH tag 125 100%
Table 3: Tevatron results for up to at  TeV, as employed in this analysis.

With this framework programmed, our fitting procedure is as follows. We first scan over a fine grid of the free parameters of the scenario considered, for example, , , with as computed from the SM-particle loops (this will be Fit II below). We obtain the value of associated with each point in the grid and thus determine the values of the parameters associated with the approximate minimum (or minima). To get the true minimum , , and the associated “best-fit” values and the one-standard deviation () errors on them we employ MINUIT [64]. (The errors on parameters which are not input, i.e.  and , are determined from the grid data.) For plotting distributions of as a function of any one variable, we use the above grid data together with the best fit value, to profile the minimal value with respect to the remaining unconstrained parameters. The 68%, 95% and 99.7% confidence level (CL) intervals are then given by , and , respectively. Two-dimensional distributions are obtained analogously from a grid in the two parameters of interest, profiling over the other, unseen parameters; in this case, we show contours of corresponding to the 68% (), 95% () and 99.7% () confidence levels for 2 parameters treated jointly.

Before presenting our results, a couple of comments are in order. First of all, we stress that in models of new physics beyond-the-SM (BSM), both the branching ratios and the production cross sections and distributions (and indeed the number of Higgs particles) may differ from SM expectations. For any BSM interpretation of the Higgs search results it is absolutely crucial to have as precise and complete channel-by-channel information as possible [65]. Unfortunately, not all the experimental analyses give all the necessary details. Below we comment on how we use the currently available information from the experiments. The ideal case would of course be that the experiments consistently do the unfolding of theoretical vs. experimental channels from the data as mentioned above and always provide directly the experimental results for the theoretically relevant ’s (see Eq. (5)) and the correlations between them.

Atlas

  • : we take our information from Fig. 4 of [4]. This figure shows the results after unfolding to obtain the experimental results for the ’s as defined theoretically. Fig. 4 does make the approximation that VBF and VH can be lumped together (i.e. have the same efficiencies after cuts) and that ggF and ttH can be similarly lumped together (note that ttH contributes less than ). We fit the 68% CL contour assuming that the follows a bivariate normal distribution.222We thank Guillaume Drieu La Rochelle for providing this fit, cf. Table 4 in version 2 of [39]. With this, the correlation between the ggF and VBF+VH channels is automatically taken into account. We also note that while Fig. 4 of [4] is for 126.6 GeV, Fig. 12 (right) in the same paper shows that there is a broad “plateau” as a function of the mass when the energy scale uncertainty is taken into account, implying that the results should not depend too much on the mass.

  • : the signal strength in this channel reported by ATLAS [6, 11] is with a best fit mass of  GeV. At  GeV, the signal strength is , see Fig. 10 in [11]. Assuming that the discrepancy in the Higgs mass determined from the and the 4 lepton final states is due to a statistical fluctuation (rather than unknown systematics) we use at  GeV, i.e. close to the combined best fit mass from ATLAS, in our fits.

    Alternatively, one could rescale the value of at  GeV for a Higgs mass of 125 GeV. This would give at  GeV (or at  GeV). We checked that taking this alternative approach has only marginal influence on our results.

    Regarding the decomposition in production modes, no statement is made in the conference note or paper. However, as it is an inclusive analysis, we take the relative ratios of production cross sections for a SM Higgs as a reasonable approximation. To this end, we use the ratios given by the LHC Higgs Cross Section Working Group [57].

  • : we adopt relative contributions of 95% ggF and 5% VBF [8]. We do not include any result for 7 TeV because the update presented at HCP is a combination of 7 and 8 TeV.

  • : ATLAS provides only an overall signal strength with no information on the decomposition with respect to production modes. However, the conference note [51] contains the results of unfolding to the theory-level ’s via a plot (Fig. 19) of the experimental results for versus at  GeV. We fit the contours with the same procedure as for . The correlation (included in the fit) is .

Cms

  • : we follow the same procedure as for ATLAS , using Figure 11 from [12]. The correlation (included in the fit) is .

  • : no decomposition with respect to production modes is given in the conference note or paper. As it is a fully inclusive analysis, we use the relative ratios of production cross sections given by the LHC Higgs Cross Section Working Group [57] as a good approximation [58].

  • : the information provided in the conference note and papers is incomplete; our decomposition into production modes is based on [58]. Our combination (weighted mean) agrees within 9% with that given by CMS ( instead of ).

  • : as there is no information on possible contaminations by other production modes, we assume 100% VH or 100% ttH production for the respective categories.

  • : for the 0/1 jet and VBF tag categories we extract the decomposition into production modes from [56], assuming that there is no significant change in the efficiencies between  GeV and  GeV. We use the efficiencies from the first three categories (, and ) because they are the most sensitive ones; they lead to very similar decompositions which we use in our analysis. Our combination (weighted mean) agrees within 6% with that given by CMS ( instead of ).

Tevatron

  • and : no decomposition into production modes is given by the experiments. We assume that the analyses are inclusive and we thus employ the ratios of the theoretical predictions for the (SM) Higgs production cross sections.

  • : we use the new results from HCP2012 [14] assuming 100% VH.

3 Results

3.1 General coupling fits

Fit I: , and free

For a first test of the SM nature of the observed Higgs boson, we take (i.e. quark, lepton and vector boson couplings to the Higgs are required to be SM-like) but we allow for additional new physics contributions to the and couplings, parameterized by and , coming from loops involving non-SM particles or from anomalies. This fit, which we refer to as Fit I, is designed to determine if the case where all tree-level Higgs couplings are equal to their SM values can be consistent with the data. For example, such a fit is relevant in the context of UED models where the tree-level couplings of the Higgs are SM-like [66, 67].

Figure 1 displays the results of this fit in the versus plane. The best fit is obtained for , , and has for 19 degrees of freedom (d.o.f.), giving a -value of . The results of this fit are summarized in Table 4, together with the results of the other fits of this section.

Figure 1: Two parameter fit of and , assuming (Fit I). The red, orange and yellow ellipses show the 68%, 95% and 99.7% CL regions, respectively. The white star marks the best-fit point , .

We note that the SM (i.e. , ) has and is hence more than away from the best fit in Fig. 1. The number of degrees of freedom for the SM fit is 21, implying a -value of . The largest contributions come from the channels from ATLAS (), CMS () and Tevatron (), followed by the VBF result for from CMS with .

Fit II: varying , and ()

Next, we let , , vary, assuming there are no new particles contributing to the effective Higgs couplings to gluons and photons, i.e. we take implying , as computed from the SM-particle loops. The results for the one-dimensional and two-dimensional distributions are shown in Figs. 2 and 3. The value of is rather well determined to be close to unity. It is intriguing that the best fit of is indeed just slightly below 1, as any model with only Higgs doublets or singlets requires . The best fit values for and are SM-like in that they have magnitudes that are close to one. However, the best fit value is opposite in sign to the SM Higgs case. The preference for is at the level of — see the first plot in Fig. 2. This results from the fact that an enhanced rate (as observed in the experimental data) is obtained by changing the sign of the top-loop contribution so that it adds, rather than subtracts, from the -loop. In contrast, in the case of almost equally good minima are found with and . Details on the minima in different sectors of the (, ) plane are given in Table 5. Note that, for the best fit point, the resulting and are in good agreement with the result of Fit I above, for which and . Here, however, the enhanced value derives from rather than from . The best fit results are again tabulated in Table 4.

Figure 2: One-dimensional distributions for the three parameter fit, Fit II, of , , with and as computed in terms of .
Figure 3: Two-dimensional distributions for the three parameter fit, Fit II, of , , with and as computed in terms of . The red, orange and yellow ellipses show the 68%, 95% and 99.7% CL regions, respectively. The white star marks the best-fit point. Details on the minima in different sectors of the (, ) plane can be found in Table 5.

A negative sign of —while maintaining a positive sign of —is actually not easy to achieve. (A sign change of both and would have no impact on the top quark induced loop amplitudes.) It would require that is induced dominantly by the vev of a Higgs boson which is not the Higgs boson considered here. Hence, we have in most models, implying that it is important to study the impact of this constraint on our fits. The fit results when requiring are shown in the left two plots of Fig. 4 and the top row of Fig. 5; see also Table 5. We observe that for this quadrant the results are consistent with SM expectations (i.e. within ). Interestingly the fit is not better than the SM itself: for  d.o.f., corresponding to .

Figure 4: One-dimensional distributions for the three parameter fit, Fit II, but imposing , ; the left two plots allow for (), while in the right two plots ().
Figure 5: Two-dimensional distributions for the three parameter fit, Fit II, as in Fig. 3 but with , , . The upper row of plots allows for , while in the lower row of plots is imposed.

Another possible model constraint is to require (recall that by convention). This constraint applies to any model containing only Higgs doublets and singlets. The 1d results for the combined requirement of and are shown in the right two plots of Fig. 4, and in the bottom-row plots of Fig. 5. We observe that the best fit values for and are only slightly shifted relative those found without constraining , and that accordingly the and at the best fit point are only slightly shifted. However, the constraint does severely change the upper bound on , which for and mostly depends on the -boson loop contribution. The apparent sharpness of the boundary in the vs.  plane is a result of the fact that these two quantities really only depend on for .

Finally note that it has been shown in [69, 68] that single top production in association with a Higgs is greatly enhanced when , have opposite signs. Thus, the possibility of should be further scrutinized by precision measurements of the single top production cross section at the LHC.

Fit I II III, 1st min. III, 2nd min.
Table 4: Summary of results for Fits IIII. For Fit II, the tabulated results are from the best fit, cf. column 1 of Table 5.
Sector
11.95 12.06 18.66
0.66 0.67 1.04
Table 5: Results for Fit II in different sectors of the (, ) plane.

Fit III: varying , , , and

Finally, in Fit III, we allow the and additions to and , fitting therefore to five free parameters: , , , , and . The associated 1d and 2d plots are given in Figs. 6 and 7. There are two main differences as compared to Fit II. On the one hand, the preference for does does not necessarily imply a negative value for , since a positive value for can contribute to an increase in even when the top-quark loop interferes destructively with the loop. (This is obviously already expected from Fit I.) On the other hand, both and feed into the effective , and if one of them is large the other one has to be small to result in a near SM-like cross section. This anti-correlation between and can be seen in the center-top plot in Fig. 7. The best fit is actually obtained for , with in order to compensate for the very suppressed top-loop contribution to ggF. However, it is also apparent that the minimum at is quite shallow (cf. the top left plot in Fig. 6) and that a fit with with small is well within the contour (as should indeed be the case for consistency with Fits I and II).

We also note that at the best fit, i.e. that with , one finds by virtue of the fact that the loop is not partially cancelled by the top loop and only a small is needed to further enhance the final state and bring into agreement with observations; see top-right and bottom-right plots of Fig. 7. If we move to the SM value of then is needed to fit the rate. The best fit results are tabulated in Table 4.

A way to lift the degeneracy in and would be to have an independent determination of . This might be achieved by an accurate measurement of the channel, as illustrated in Fig. 8. This figure assumes that will eventually be measured with 30% accuracy — more concretely, the figure assumes . This is certainly a very challenging task. For comparison, CMS currently gives  [12]. Finally, as mentioned above, may also be constrained by the associated production of a single top and a Higgs [69, 68].

Figure 6: One-dimensional distributions for the five parameter fit of , , , and (Fit III). Details regarding the best fit point are given in Table 4.
Figure 7: Two-dimensional distributions for the five parameter fit of , , , and (Fit III). Details regarding the best fit point are given in Table 4.
Figure 8: Lifting of the degeneracy in and in Fit III when is measured to 30% accuracy (). These two plots should be compared to the top left and top middle plots of Fig. 7. See text for details.

3.2 Two-Higgs-Doublet Model

So far our fits have been model-independent, relying only on the Lagrangian structure of Eq. (2). Let us now turn to the concrete examples of Two-Higgs-Doublet Models (2HDMs) of Type I and Type II. In both cases, the basic parameters describing the coupling of either the light or heavy CP-even Higgs boson are only two: (the CP-even Higgs mixing angle) and , where and are the vacuum expectation values of the Higgs field that couples to up-type quarks and down-type quarks, respectively. The Type I and Type II models are distinguished by the pattern of their fermionic couplings as given in Table 6. The SM limit for the () in the case of both Type I and Type II models corresponds to (). In our discussion below, we implicitly assume that there are no contributions from non-SM particles to the loop diagrams for and . In particular, this means our results correspond to the case where the charged Higgs boson, whose loop might contribute to , is heavy.

Type I and II Type I Type II
Higgs VV up quarks down quarks & up quarks down quarks &
leptons leptons
0
Table 6: Tree-level vector boson couplings () and fermionic couplings normalized to their SM values for the Type I and Type II two-Higgs-doublet models.

The results of the 2HDM fits are shown in Fig. 9 for the case that the state near 125 GeV is the lighter CP-even . The figure also applies for the case of the heavier being identified with the state with the replacement rules given in the figure caption.333Since the state clearly couples to we do not consider the case where the is the only state at . We also do not consider the cases where the peak comprises degenerate , or pairs. Note that the convention implies for the and for the . Moreover, the requirement restricts . The best fit values and ranges for and , together with the corresponding values for , , , and , are listed in Table 7. These numbers are again for the case of being the state near 125 GeV. Replacing by amounts to a shift in ; thus we find () for the 2HDM-I and () for the 2HDM-II, while the values for , , , , etc. do not change.

Figure 9: 2HDM fits for the in the Type I (left) and Type II (right) models. The upper row shows the fit results in the vs.  plane, while the lower row shows the vs.  plane. The dashed lines indicate the SM limit. The same results are obtained for the heavier with the replacements and (, ).
Fit 2HDM-I 2HDM-II 2HDM-I, 2HDM-II,
[rad]
[rad]
12.20 11.95 19.43 19.88
Table 7: Summary of fit results for the in 2HDMs of Type I and Type II.

Note that for both the Type I and the Type II model, the best fits are quite far from the SM limit in parameter space. In particular, since we do not include any extra loop contributions to , we end up with negative close to as in Fit II. Demanding (i.e.  for , for ), one ends up in a long ‘valley’ along the decoupling limit where the Higgs couplings are SM like, see Fig. 9; this is however always more than away from the best fit. Furthermore, solutions with very small are preferred at more than . Since such small values of are rather problematic (in particular is problematical for maintaining a perturbative magnitude for the top-quark Yukawa coupling) we also give in Table 7 the corresponding fit results requiring . These results come quite close to the SM limit, and accordingly have a of about 19–20 (recall that for the SM we find ). 2HDMs with hence do not provide a better fit than the SM itself.

A couple of more comments are in order. First, an important question that we leave for future work is whether other — e.g. stability, unitarity, perturbativity (SUP) and precision electroweak (PEW) — constraints are obeyed at the best-fit points, or the 68% CL regions. Here we just note that according to Fig. 1 of [70], the SUP and PEW constraints do not seem problematic for Type II, but may play a role for Type I models at low .

Second, the best fits correspond to very small (small ) values that are potentially constrained by limits from B-physics, in particular from and . The B-physics constraints are summarized in Figs. 15 and 18 of [71] for Type II and Type I, respectively. Figure 18 for Type I places a lower bound on as a function of the charged Higgs mass which excludes small unless the charged Higgs is very heavy, something that is possible but somewhat unnatural. Figure 15 for Type II places a substantial lower bound on the charged Higgs mass for all , but such a constraint does not exclude the 68% CL region.

Third, we remind the reader that in the 2HDMs, the soft -symmetry-breaking and the other Higgs masses (, and ) are independent parameters. It is thus possible to have either or without violating constraints from direct searches for the charged Higgs whose mass is related to . However, in the case of , one has to avoid the LEP limits for the lighter , which severely constrain the coupling to in case of  [72]. So either for , or needs to be small (e.g.  for , or for ). The distributions of for Type I and Type II with are shown in Fig. 10. Interestingly, around the best fit the coupling to is sufficiently suppressed to allow for of the order of (or lower in Type II).

Figure 10: distribution of in the Type I (left) and Type II (right) models for the case that is the observed state near 125 GeV.

4 Summary and Conclusions

We assessed to which extend the currently available data on the Higgs-like scalar constrain the Higgs couplings. To this end we performed fits to all public data from the LHC and the Tevatron experiments.

First, we employed a general parametrization of the Higgs couplings based on a SM-like Lagrangian, but allowing for extra contributions to the loop-induced couplings of the Higgs-like scalar to gluons and photons. While the SM does not provide a bad fit (), it is more than away from our best fit solutions. The main pull comes from the enhanced rates observed by ATLAS and CMS, as well as from the Tevatron experiments. The best fits are thus obtained when either (i.e. opposite in sign to the SM expectation) or there is a large BSM contribution to the coupling of the Higgs. In short, significant deviations from the SM values are preferred by the currently available data and should certainly be considered viable. Since having (in the convention) is not easy to achieve in a realistic model context, and leads to unitarity violation in scattering at scales that can be as low as 5 TeV [73, 74], it would seem that new physics contributions to the effective couplings of the Higgs to gluons and photons are the preferred option. (The possibility of a second, degenerate Higgs boson contributing to the observed signal remains another interesting option, not considered here.)

Second, we examined how well 2HDM models of Type I and Type II fit the data. We found that it is possible to obtain a good fit in these models with (), in the () cases, respectively, not far from . However, the best fit values for the individual , , and parameters lie far from their SM values. Further, the best fits give , which is disfavored from the theoretical point of view if we want perturbativity up to the GUT scale. Requiring (or simply ) pushes the fit into the SM ‘valley’ and no improvement over the pure SM solution is obtained. In particular the obtained in this region is substantially larger than that for the best fit, and not far from the found for the SM.

We once again refer the reader to Tables 4, 5 and 7 which summarize the best fit values and errors for the parameters for the various cases considered. In Fig. 11 we show some of these results graphically. Moreover, in order to assess the physics associated with our best fit points, we give in Tables 8 and 9 the values of the derived (theory level) signal strengths , , , , , and for the best fit point in the various fits we have considered. (These are a complete set since for the models we consider , and .) We see that in the general case both and are enhanced by factors 1.7–2.1 (1.8–1.9 in 2HDMs), while the other signal strengths tend to be . When demanding without allowing for extra contributions from new particles, then only very small enhancements of and of the order of 1.2–1.3 are found.

Last but not least, we strongly encourage the experimental collaborations to make as complete as possible channel-by-channel information (including the important decomposition into production modes) available, in order to allow for reliable tests of non-standard Higgs scenarios. The information currently given by ATLAS and CMS for the signal is an example of good practice and should become the standard for the presentation of results for all channels. This would immensely help interpretation efforts such as attempted in this paper. The ideal case would of course be if the full likelihood distributions were made available.

Figure 11: Graphical representation of the best fit values for , , , and of Table 4. The labels refer to the fits discussed in the text. The dashed lines indicate the SM value for the given quantity. The ’s indicate cases where the parameter in question was fixed to its SM value.
Fit I II, II, III
Table 8: Summary of results for Fits IIII. For Fit II, the tabulated results are for the best fit with , column 1 of Table 5, and for the case , column 3 of Table 5.
Fit 2HDM-I 2HDM-II 2HDM-I, 2HDM-II,