Is the resonance at 125 GeV the Higgs boson?

The recently discovered resonance at 125 GeV has properties remarkably close to those of the Standard Model Higgs boson. We perform model-independent fits of all presently available data. The non- standard best-fits found in our previous analyses remain favored with respect to the SM fit, mainly but not only because the {\gamma}{\gamma} rate remains above the SM prediction.


Introduction
New searches for the Higgs boson [1,2,3,4,5] based on 5 fb −1 data per experiment collected in 2012 by the Large Hadron Collider (LHC) have been recently presented by the ATLAS [6] and CMS [7] experiments at CERN. The excess at 125 GeV that was evident already in the 2011 data has been consistently observed in γγ, ZZ * , W W * channels by both experiments. In addition, CMS presented updated Higgs boson searches also in bb and ττ channels. As a result, when combining the 7 TeV and 8 TeV data, both experiments separately have reached the sensitivity to the SM-like Higgs with a significance of 5σ.
One must make sure that the discovered new resonance is, indeed, the Higgs boson that induces the electroweak symmetry breaking and gives masses to both the SM vector bosons and to fermions. The SM has definite predictions for the gauge boson and fermion couplings with the Higgs boson. Those affect both the Higgs boson production mechanism at the LHC as well as its dominant decay modes. Fortunately for a Higgs boson mass of 125 GeV the LHC experiments do have sensitivity to test these couplings in all interesting final states γγ, ZZ * , W W * , bb and ττ taking into account different Higgs boson productions mechanisms.
The aim of this paper is to perform a fit to the available Higgs boson data in order to determine its preferred couplings to the SM states as well as to an invisible channel. Our main goal is to study whether the Higgs boson is SM-like or is there any indication for new physics beyond the SM. The later possibility is motivated by numerous multi-Higgs boson, supersymmetric, composite Higgs boson, dark matter, exotic scalar, etc models. In the absence of direct signal of new physics, the Higgs boson couplings might indirectly indicate a portal to new physics. To achieve this goal we allow the Higgs boson gauge and Yukawa couplings to be free parameters and modify the the Higgs tree level couplings hW W, hZZ, hff as well as the loop level processes such as the Higgs production in gluon-gluon fusion gg → h and Higgs decays to h → γγ, gg, accordingly. We also allow for an invisible branching fraction.
The new LHC data on Higgs boson tree level decays to W W * , ZZ * are in a better agreement with the SM expectations than the 2011 year data, proving that the observed state indeed participates in the electroweak symmetry breaking, and is likely the Higgs boson. We recall that the 2011 data indicated significant deficit in all W W * channels in both LHC experiments. Concerning the loop induced observables, the excess in h → γγ observed in 7 TeV data, in particular the large excess in exclusive di-jet tagged events, decreased in the 8 TeV data. However, the combination of all data still shows an excess in h → γγ.
While our fits are in general model independent, we demonstrate usefulness of our results for constraining new physics beyond the SM using some well known models as examples. These examples show that already in the present stage of accuracy the LHC data constrains models severely.
In the next section we proceed along the lines of [16] and briefly present updated results; for technical details of our fitting procedure and motivations of the scenarios we consider we refer the reader to our previous paper [16].

Reconstructing the Higgs boson properties
In the left panel of figure 1 we summarize all data points [6,7,8,9,10,11,12,13,14,15] together with their 1σ error-bars. The grey band shows the ±1σ range for the weighted average of all rates: Measured Higgs rate SM prediction = 1.10 ± 0.15 (1) It lies along the SM prediction of 1 (green horizontal line) and is 7σ away from 0 (red horizontal line). Thus the combination of all data favours the existence of Higgs boson with much higher significance than any of the experiments separately.

Higgs boson mass
In the right panel of Fig. 1 we show our approximated combination of all Higgs boson data, finding that the global best fit for the Higgs boson mass is The Higgs boson mass values preferred by the two experiments are compatible, and the uncertainty is so small that in the subsequent fits we can fix m h to its combined best-fit value. The analysis proceeds along the lines of our previous work [16] (for similar older fits see [17]), with the following modifications: 1) whenever possible we use the central values and the uncertainties on Higgs boson rates as reported by the experiments, rather than inferring them from published observed and expected bounds; 2) we take into account uncertainties on the production cross sections: ±14% for σ(gg → h) and for σ(pp → htt), ±3% for vector boson fusion, and ±5% for σ(pp → V h). Only the first uncertainty is presently significant, as illustrated in the left panel of Fig. 2 where we show the theoretical and the experimental determination of the production cross sections, assuming that the resonance at 125.5 GeV is the SM Higgs boson.
While we always perform a full global fit, in Fig. 3 we combine the 16 rates into 7 categories according to the final state. This allows to more clearly see the main features in the data; in particular the γγ rate is 1.6 ± 0.3 higher than the SM prediction [18,19], compatibly with the γγjj rate.
In Fig. 3 we also show the rates predicted by a few new physics scenarios. The SM Higgs boson (green horizontal line) gives a fit of good quality. However, a scalar coupled to the trace of the SM energy-momentum tensor (and thereby called "dilaton" or "radion" [20]) gives a fit of overall quality comparable to the SM Higgs boson: the dilaton fits better the enhanced γγ rates but it predicts a bbV rate below the value preferred by experiments. Allowing for a mixing between the dilaton and the Higgs boson , all intermediate possibilities give fits with comparable quality, as shown in the right panel of Fig. 2. Fig. 3 also shows that even better fits can be achieved by the non-standard scenarios discussed that we shall discuss in the following.

Higgs boson branching ratios
In the left panel of Fig. 4 we allow for free values of the rates that in the SM occur at loop level: h → γγ and gg → h. The latter process is related to h → gg by the well known Breit-Wigner formula here written in the relevant narrow-width approximation. As a consequence we use a common notation BR(h ↔ gg) for those observables when studying their deviations from the SM predictions. We see that, like in our previous fit, data favour non-standard values Such a best-fit is shown in Fig. 3. It allows for quite significant reduction of the global χ 2 , in agreement with our previous analysis [16]. When we fix BR(h ↔ gg) to the SM values, the preferred enhancement of BR(h → γγ) is is good agreement with the ATLAS and CMS results.

Higgs boson invisible width
Next, we allow for a Higgs boson invisible width, as motivated e.g., by models of Dark Matter coupled to the Higgs boson [21]. We perform two fits.
1. We just add an additional invisible component to the SM Higgs boson width, finding that present data imply BR inv = 0 ± 0.15, as seen in the right panel of Fig. 4. 2. In addition to the latter we also allow for non-standard values of h → γγ and h → gg, finding a weaker constraint on BR inv , also shown in the right panel of Fig. 4.
An invisible Higgs boson width also gives unseen missing-energy signatures, which presently provide less stringent constraints [22] on Higgs boson properties than do global fits [16,23].

Higgs boson couplings
Next we extract from data the Higgs boson couplings to vectors and fermions, in order to test if they agree with the SM predictions. We recall that the SM predicts a negative interference between the W -loop and the top-loop contributions to h → γγ. In general this rate depends on the relative sign of these two contributions that depends on the relative sign of the gauge and top Yukawa couplings.
In the left panel of Fig. 5 we assume a common rescaling of the Higgs boson coupling to the W, Z bosons and a common rescaling of the Higgs boson couplings to all fermions, denoted by a and c, respectively. We find two preferred solutions, that both allow for an enhancement of h → γγ. The first solution has the Higgs boson coupling to fermions, thus also to the top and bottom quarks, reduced with respect to the SM predictions, thereby reducing the negative interference in h → γγ and increasing its branching fraction. This solution prefers somewhat enhanced Higgs boson couplings to vectors that enhances also the W -loop contribution to h → γγ. The second solution has the Higgs boson coupling to the top quark with opposite sign with respect to the SM prediction, thereby making the interference constructive and, again, increasing the branching fraction. In this region smaller than SM gauge couplings are preferred.
While the allowed regions in a are quite large and the SM prediction a = 1 is well within 90% CL region, the Yukawa couplings show more non-standard behaviour. This is demonstrated in the right panel of Fig. 5, where we fix the Higgs boson coupling to vectors to the SM value as predicted by gauge invariance and allow the couplings to fermions to top quark and to bottom quark/tau lepton to vary independently. We again find the same two best-fit solutions previously discussed. Notice that for positive Yukawa couplings one significant reduction of all of them is preferred. Yukawa couplings of order 30% of the SM values give as good fit as the SM itself. Although the purely fermiophobic Higgs boson is excluded with high significance, the question of the origin of reduced Yukawa couplings and, consequently, the question of the new physics contribution to the top/bottom masses remains open. If the present trends in the LHC data persist, this is one of the most clear signal of physics beyond the SM.
To demonstrate the usefulness of our fits for constraining models of new physics we consider two Higgs doublet model of type II [24], which allows independent for a modification of the t coupling, and for a common modification of the b and τ couplings, although one of them is predicted be reduced and the other enhanced by the model. We also allow for a modification in the Higgs boson coupling to vectors. The results are presented in Fig. 6 where we plot our best fits to the Yukawa couplings together with the theoretically forbidden regions of the parameter space. One sees that in this model the negative Yukawa couplings are strongly preferred. For the case of the SM gauge couplings the positive Yukawa region is allowed only at 99% CL. This example demonstrates that multi Higgs models may be in difficulties to explain present data and mode exotic new physics scenarios must be used.
Finally, in Fig. 7 we allow four Higgs boson couplings, the ones to gauge bosons, to top quark, to bottom quark and to tau lepton to vary independently. The global fit shows no preference for non-standard gauge couplings, we once again find the two solutions for Yukawas. Notice that present data are not sensitive to the Higgs boson coupling to the τ . While a tau-phobic Higgs boson is still allowed (and actually mildly favored), present data significantly disfavor the pure fermio-phobic or top-phobic or bottom-phobic Higgs boson. As before, the top Yukawa coupling is the most constrained one and shows significant preference for non-standard values. More data should confirm that new physics beyond the SM is discovered indirectly due to non-standard Yukawa couplings.

Conclusions
The new particle with mass 125.5 ± 0.5 GeV discovered at the LHC looks like the Higgs boson. We performed a fit to all available collider data in order to test its couplings. We find that the couplings to the W and the Z are in reasonable agreement with the SM Higgs boson expectations, suggesting that the discovered state is, indeed, the Higgs boson. However, the excess in γγ indicates potential non-standard physics in the loop level process h → γγ (see e.g. [25]). Combining all γγ channels and all experiments, this enhancement is at the 2.5σ level.
As long as this excess persists, it can be fitted by a non-standard (possibly negative) Yukawa We considered two main classes of scenarios: a) modified h → γγ, gg, which can be obtained by effective operators of the form HH † F 2 µν ; b) modified Higgs boson couplings to tops and other fermions, which can be obtained by effective operators of the form QU HH † H. In case the anomalies will persist, it will be interesting to explore observables, like σ(gg → htt), that can discriminate among them.
Our general fits were illustrated with some example models. While models with reduced Yukawa couplings were used to improve the fit, dilaton (or radion) scenarios and two Higgs doublet model of type II are shown to be well constrained already with the present data.