The universal Higgs fit

We perform a state-of-the-art global fit to all Higgs data. We synthesise them into a 'universal' form, which allows to easily test any desired model. We apply the proposed methodology to extract from data the Higgs branching ratios, production cross sections, couplings and to analyse composite Higgs models, models with extra Higgs doublets, supersymmetry, extra particles in the loops, anomalous top couplings, invisible Higgs decay into Dark Matter. Best fit regions lie around the Standard Model predictions and are well approximated by our 'universal' fit. Latest data exclude the dilaton as an alternative to the Higgs, and disfavour fits with negative Yukawa couplings. We derive for the first time the SM Higgs boson mass from the measured rates, rather than from the peak positions, obtaining $M_h = 125.0 \pm 1.8$ GeV.


Introduction
After the discovery of a new particle around 125.5 GeV announced by the ATLAS [1] and CMS [2] LHC collaborations during 2012, all LHC and TeVatron collaborations presented at the Moriond 2013 conference the new results based on the full collected data. These include the most important γγ, ZZ * and W W * channels as well as updates to the fermionic channels. Such results will stay with us for next two years until LHC with full energy starts operating. Therefore it is the right moment to analyse their implications.
We want to know if the new particle is the long-waited Standard Model (SM) Higgs boson [3,4,5,6]. On one side, the experimental collaborations are measuring its discrete quantum numbers to check if it is a scalar. On the other side, various theoretical groups [7,8,9] started to approximatively reconstruct from data its production cross section and its decay modes and consequently its couplings to check if they agree with the SM predictions or with other models beyond the SM. Clearly, this is a more significant test that can be precisely done only by the experimental collaborations, which indeed started to present analyses along these lines. However these experimental fits, presented in the form of likelihood plots within a few specific beyond-the-SM models, are of little use to theorists who are interested in different models.
We here propose how experimental collaborations could report their results in a modelindependent and useful way, such that these results would be readily and reliably used by theorists who want to test any desired model. The new ingredient that we introduce and that allows for this simplification is the assumption that new physics can be approximated as a first-order perturbation with respect to the SM predictions. We find that this assumption is increasingly supported by data, that agree with the SM with precisions around the 20% level.
Such results, obtained after two years of LHC operation and with only 25/fb data per experiment, implies severe constraints on models where the Higgs boson is a portal to new physics. We analyse several models and rule out alternative scenarios to the Higgs boson.
The paper is organised as follows. In section 2 we present the data and our fitting procedure. In section 3 we derive the first measurement of the Higgs mass from the rates, rather than from the position of the peaks in the γγ and ZZ invariant mass distributions. In section 4 we present the 'universal' format for data mentioned above. Next, in section 5 we present fits in various specific models, updating our previous results and comparing the full fit to the simplified 'universal' fit to verify that it is a good approximation. We fit Higgs cross sections in section 5.1, Higgs couplings in 5.2, composite Higgs models in 5.3, new physics in loops in 5.4, two Higgs doublet models in 5.5, the MSSM in 5.6, the dilaton in 5.7, the Higgs invisible width in 5.8 and models where DM couples to the Higgs in 5.9. In section 6 we summarise the results and draw our conclusions.

The data
Searches for the SM Higgs boson have been carried out in proton-proton collisions at √ s = 7 (2011 data) and 8 TeV (2012 data) with about 25/fb of total integrated luminosity.
There are four main production modes for Higgs boson from pp collisions at √ s ∼ 8 TeV. The gluon-gluon fusion production mode has the largest cross section, followed in turn by vector boson fusion (VBF), associated W h and Zh production, and production in association with top quarks, tth. The cross sections for the Higgs boson production modes and the decay branching fractions, together with their uncertainties, are taken from [10].
For a given Higgs boson mass, the search sensitivity depends on the production cross section of the Higgs boson, its decay branching fraction into the chosen final state, the signal selection efficiency, the mass resolution, and the level of standard model backgrounds in the same or a similar final state. For low values of the Higgs boson mass, the h → γγ and h → ZZ * → 4 channels play a special role due to the excellent mass resolution for the reconstructed diphoton and four-lepton final states, respectively. The h → W W * → ν ν channel provides high sensitivity but has relatively poor mass resolution due to the presence of neutrinos in the final state. The sensitivity in the bb and τ + τ − decay modes is reduced due to the large backgrounds and poor mass resolutions.
We include in our data-set all exclusive γγ and τ τ sub-categories described by the experimental collaborations by telling how much each Higgs production channel in the SM contributes to the various rates. Such information is fully included in our analysis. We adopt the Multi-Variate Analysis (MVA) γγ analysis from CMS and we combine all experiments, such that we find an average γγ rate very close to the SM prediction. Consequently our results differ from previous analyses performed without including the latest CMS γγ data [7]. This is an important issue because, while most of the presented LHC results are well consistent with the SM predictions within experimental errors, there are few unexpected new developments that need commenting. The most important of them is the discrepancy between the ATLAS and CMS results in the h → γγ channels. With full luminosity, ATLAS finds an overall rate of 1.65 ± 0.34, higher than the SM prediction of 1, and higher than the CMS result of 0.80 ± 0.30. The two measurements are compatible within 2σ. In addition, the two CMS γγ analyses (MVA and cut based) show different signal rates. Finally, the two Higgs boson mass determinations in ATLAS, from the peaks in the γγ and ZZ channels, differ by 2σ. Both experiments have cross checked their analyses and reached conclusions that those deviations are due to statistical fluctuations of both signal and background. This conclusion implies that: (i) combining all data in a global fit is meaningful and increases the precision; (ii) selecting instead any single measurement, for example the ATLAS excess in γγ, is not justified and introduces a bias in the data.
The experimental collaborations report Higgs boson rates R in units of the central value of the SM prediction. Their results could be fully encoded in a likelihood L(R, M h ), but only a limited amount of information is reported by the experiments. Often the experimental collaborations report the measured rates as R exp ± R err : we use the results in this form whenever available. Sometimes collaborations only report the upper bounds on rates at 95% C.L., R limit observed , and the expected upper bound at 95% C.L. in absence of a Higgs boson signal, R limit expected , as function of the Higgs boson mass m h . Assuming that the χ 2 = −2 ln L has a Gaussian form in R, these two experimental informations allow one to extract the mean R exp and the standard deviation R err as R exp = R limit observed − R limit expected and R err = R limit expected /1.96, where 1.96 arises because 95% confidence level corresponds to about 2 standard deviations [8]. 1 The χ 2 is approximated as where the sum runs over all measured Higgs boson rates I. The theoretical uncertainties on the Higgs production cross sections σ j start to be nonnegligible and affect the observed rates in a correlated way. We take into account such correlations in the following way. We subtract from the total uncertainty R err I the theoretical component due to the uncertainty in the production cross sections, obtaining the purely experimental uncertainty, R err−exp I . The theoretical error is reinserted by defining a χ 2 which depends 1 A similar procedure was described by Azatov et al. in [7]. on the production cross sections σ j , and marginalising it with respect to the free parameters σ j , constrained to have a central value σ th j and an uncertainty σ err j given by See also [25]. We neglect the relatively small uncertainties on the SM theoretical predictions for Higgs branching ratios, dominated by a 4% uncertainty on the h → bb width. We summarise all data in fig. 1 together with their 1σ error-bars. The grey band shows the ±1σ range for the naive weighted average of all rates: 0.98 ± 0.10. It lies along the SM prediction of 1 (horizontal green line) and is almost 10 σ away from 0 (the horizontal red line is the background-only rate expected in the absence of a Higgs boson). (4)

Reconstructing the Higgs mass
These measurements are mutually compatible, and the uncertainty is so small that in the subsequent fits to rates we can fix M h to its combined best-fit value. We combined all uncertainties in quadrature, using the standard Gaussian error propagation and neglecting correlations among systematic uncertainties. The averages within each experiment agree with those reported by the experiments. The ATLAS collaboration reports the combined value for the Higgs mass, based on the γγ and ZZ channels, as M h = 125.5 ± 0.2 stat +0.5 −0.6 syst (best fit signal strength R = 1.43 ± 0.16 stat ± 0.14 syst ) [26], whereas CMS gives M h = 125.7 ± 0.3 stat ± 0.3 syst based on γγ, ZZ, W W , τ τ and bb (best fit signal strength R = 0.80 ± 0.14) [27].
We here discuss how the Higgs mass can be independently measured, with a bigger uncertainty, by requiring that the measured rates agree with their SM predictions. Such predictions have a dependence on the Higgs mass that, around 125 GeV, can be approximated as In table 1 we list the values of the coefficients c X and of the measured rates for the various processes averaging all experiments, as well as the Higgs mass indirectly derived from such 6.4%/ GeV 7.8%/ GeV −1.5%/ GeV −5.4%/ GeV −4.1%/ GeV Measured rate/SM 0.82 ± 0.16 1.08 ± 0.20 1.07 ± 0.19 0.93 ± 0.36 1.13 ± 0.28 Higgs mass in GeV 122.8 ± 2.5 126.5 ± 2.5 121 ± 12 127 ± 7 123 ± 7 Table 1: Determinations of the Higgs mass from the measured Higgs rates, assuming the SM predictions for such rates. We do not use here the independent determination of the Higgs mass from the peak positions in the γγ and ZZ energy spectra.
rates. We see that the single best indirect determination of M h comes from the h → W W rates, that presently have no sensitivity to M h if one wants to measure it from a mass peak.
On the other hand, the h → γγ signal that offers the best peak measurement of M h has very little indirect sensitivity to M h , because the γγ rate happens to have a weak dependence on M h . Averaging over all channels we find M h = 124.5 ± 1.7 GeV (Higgs mass extracted from the rates, assuming the SM) (6) which is compatible with the determination of the pole Higgs mass obtained in a modelindependent way from the positions of the peaks.

The universal Higgs fit
We perform the most generic fit in terms of a particle h with couplings to pairs of t, b, τ, W, Z, g, γ equal to r t , r b , r τ , r W , r Z , r g , r γ in units of the SM Higgs coupling. This means, for example, that the coupling to the top is given by r t (m t /V )htt, where r t = 1 in the SM and V = 246 GeV is the Higgs vacuum expectation value. Similarly, the hγγ coupling is assumed to be r γ times its SM prediction. In the SM this couplings first arises at one loop level. Experiments are starting to probe also the hμµ and the hZγ effective couplings, so that also the corresponding r µ and r Zγ parameters will start to be measured. This discussion can be summarized by the following effective Lagrangian: The various SM loop coefficients c SM are summarised in appendix A. This Lagrangian is often written in a less intuitive but practically equivalent form by either using SU(2) L ⊗ U(1) Yinvariant effective operators, or assuming that the Higgs is the pseudo-Goldstone boson of a spontaneously broken global symmetry and writing its chiral effective theory [7]. We do not consider a modified Higgs coupling to charm quarks, given that h → cc decays at LHC are hidden by the QCD background. While we cannot exclude that new physics affects h → cc much more than all other Higgs properties, for simplicity we proceed by discarding this possibility. Furthermore, we take into account the possibility of Higgs decays into invisible particles X (such as Dark Matter or neutrinos [28]) with branching ratio BR inv . In almost all measured rates BR inv is equivalent to a common reduction r of all the other Higgs couplings, BR inv 1 − r 2 , such that BR inv is indirectly probed by data [8]. The only observable that directly probes an invisible Higgs width is the pp → Zh → + −X X rate measured by ATLAS [29], which implies Any possible new-physics model can be described as specific values of the r i parameters. Several examples are provided in section 5.
Following the procedure described in the previous section, we approximatively extract from data the function which describes all the information contained in Higgs data. We find χ 2 = 58.8 at the best fit (56 data points, 10 free parameters), marginally better than the SM fit, χ 2 SM = 61.7 (no free parameters).

Universal fit to small new physics effects
The universal χ 2 of eq. (9) has a too complicated form to be reported analytically, and depends on too many variables to be reported in numerical form, like plots or tables. For these reasons, previous analyses [7,8,9] focused on particular BSM models with a reduced number of parameters. For example, fig. 2 shows the fit as function of each r i , setting all others to their SM values of unity: we see that the χ 2 are approximately parabolic.
We here observe that Higgs data are converging towards the SM predictions with small errors, thereby it is time to start making the approximation and BR inv = inv . The observable rates R I are computed at first order in i , and consequently the χ 2 is expanded up to second order in i . As well known, this Gaussian approximation is a great simplification; for example marginalisations over nuisance parameters just becomes minimisation, which preserves the Gaussian form. Fig. 2 suggests that this approximation already seems reasonably good. For LHC at 8 TeV the main observables are approximated as where these expressions have been obtained by performing a first-order Taylor expansion in all the parameters of the full non-linear expressions. For all observables but the last one, we have assumed the total Higgs production cross section. When fitting the many real observables, we take into account the relative contribution of each production cross section, as determined by experimental cuts. The full χ 2 can now be reported in a simple form. Indeed the χ 2 is a quadratic function of the i , and it is usually written as in terms of the mean values µ i of each parameter i , of its error σ i and in terms of the correlation matrix ρ ij . We believe that this is the most useful form in which experimental collaborations could report their results. From our approximated analysis of LHC and TeVatron [14] data we obtain: We have not reported the central value of r t = 1 + t , of Zγ and of µ because they presently are known only up to uncertainties much larger than 1. Future searches for tth production, for h → Zγ and for h → µ + µ − will improve the situation.
In many models the Higgs couplings to vectors satisfy W = Z , because of SU(2) L invariance. Furthermore, in many models LEP precision data force W and Z to be very close to 0. This restriction can of course be implemented by just setting these parameters to be equal or vanishing in the quadratic χ 2 .
Since the uncertainties on the i parameters are now smaller then 1, the universal approximation starts to be accurate. In the next sections, where we analyze several specific models, we will systematically compare our full numerical fit (plotting best fit regions in yellow with continuous contours at the 90 and 99% C.L.) with the universal approximation (best fit ellipsoidal regions in gray with dotted contours, at the same confidence levels).

Higgs production cross sections
Assuming the SM predictions for the Higgs decays, we extract from the data the Higgs production cross sections. Given that measured rates of various exclusive and inclusive Higgs channels agree with their SM preditctions, we find that production cross sections too agree with SM predictions, as shown in fig. 3a. As expected, the most precisely probed cross section is the dominant one, σ(pp → h). At the opposite extremum σ(pp → jjh) is still largely unknown. The uncertainties on the reconstructed cross sections are correlated, altought we do not report the correlation matrix.

Higgs couplings
We here extract from data the Higgs boson couplings to vectors and fermions, assuming that only the SM particles contribute to the h → gg, γγ, γZ loops. This amounts to restrict the universal fit in terms of the r i parameters by setting the parameters for loop couplings to These numerical expressions are obtained by rescaling the expressions for the SM loops summarised in appendix A. In particular, the W loop (rescaled by r W ) and the top loop (rescaled by r t ) contribute to h → γγ with a negative interference. Under this assumption the top coupling of the Higgs, r t , becomes indirectly probed via the loop effects. The fit to the couplings is shown in fig. 3b and agrees with the SM predictions (diagonal line), signalling that the new boson really is the Higgs. The correlation matrix can be immediately obtained by inserting eq. (14) into the universal χ 2 of eq. (12).
We allow the SM prediction to vary in position and slope by assuming that the Higgs couplings to particles with mass m are given by (m/v ) p . Taking into account all correlations, we find that data imply parameters p and v close to the SM prediction of m/v (diagonal line in fig. 3b): with a 27% correlation. bosons and a common rescaling of the Higgs boson couplings to all fermions. These rescalings are usually denoted as a and c, respectively:

Composite Higgs models
The resulting fit is shown in fig. 4a. We see that our approximated universal fit (dotted contours) reproduces very well our full fit (continuous contours). The best fit converged towards the SM; in particular data now disfavour the solution with c < 0 which appeared in previous fits. Similar fits by the ATLAS and CMS collaborations are given in [30]. The CMS result is similar to ours, while ATLAS has c/a = 0.85 +0.23 −0.13 , due to their larger h → V V rates, which is compatible with our result at 1σ level.
The reason is visualised in fig. 4b, where we show the bands favoured by the overall rates for Higgs decay into heavy vectors (W W and ZZ, that get affected in the same way within the model assumptions), into fermions (bb and τ τ , that get affected in the same way within the model assumptions) and into γγ. We see that these bands only cross around the SM point, a = c = 1. The full fit to all exclusive rates contains more information than this simplified fit.
In fig. 4c we show the full χ 2 restricted along the trajectories in the (a, c) plane (plotted in the left panel) predicted by simple composite pseudo-Goldstone Higgs models in terms of the parameter ξ = (V /F π ) 2 , where F π is the scale of global symmetry breaking.

New physics only in the loop processes
We here assume that only the loop processes are modified with respect to the SM predictions, summarized in appendix A. This amounts to restrict our universal fit setting with BR inv = 0 and r Zγ = 1. The latter assumption is at present justified because of the large experimental error in the h → Zγ rate, even though in general new physics in the loop processes would induce deviation from unity in both r Zγ and r γ . The result is shown in the left panel of fig The resulting loop effects are summarised in appendix A. The solid and dashed curves in fig. 5b are respectively the upper bounds at 90% (solid) and 99% (dashed) C.L. More stringent limits are obtained on the top and bottom partners than on the τ partner.
One can also use the universal fit with the assumption of eq. (17) to derive indirect constraints on the top quark magnetic and chromomagnetic dipole moments [32,33], which in the SM are expected to be respectively g t ≈ 2 and k t ≈ 2. Allowing g t and k t to vary freely, the h → γγ and h → gg amplitudes are modified with respect to the SM as: where the quantities c  Fig. 6 shows the 90% and 99% C.L. allowed regions for g t and k t . The uncertainty on k t is comparable to the one from its direct measurement, while the one for g t is even smaller [34].
Eq. (19) was computed by [32,33] at the weak scale, in the phase with broken electroweak symmetry. An analogous computation was performed in [35], promoting the dipoles to full SU(2) L ⊗ U(1) Y -invariant effective operators with a non-renormalizable dimension d > 4, suppressed by a factor 1/Λ d−4 , Λ being the cutoff of the theory. The result [35] is that the dipole operators before electroweak symmetry breaking contribute, via RGE mixing, to other one-loop suppressed operators affecting the h → γγ and h → gg decay rates [36]. Finite parts are not computed. Because of the RGE running from Λ down to m h , the effect is proportional to ln Λ/m h , differently from eq. (19). Using the operator mixing result of [35] and parametrizing the d = 6 dipole operators at Λ via quantities analogous to g t and k t but defined at Λ, the decay rates [36] can be written as where the quantity c

Models with two Higgs doublets
There are four types of two Higgs doublets models (2HDM) where tree level flavour-changing neutral currents (FCNCs) are forbidden by a Z 2 symmetry [37] and both doublets H 1 and H 2 get a vacuum expectation value: • type I [38,39] where only one doublet couples to all quarks and leptons; • type II [39,40], where up-type quarks couple to H 2 and H 1 couples to down-type quarks and leptons. The Higgs sector of the MSSM is a type II 2HDM; • type X (lepton-specific or leptophilic) where H 2 couples only to quarks and H 1 couples only to leptons; • type Y (flipped) [41], where H 2 couples to up-type quarks and H 2 to down-type quarks, and (contrary to the type II HDM) leptons couple to H 2 .
For an extensive review see [42] and for some previous fits see [43]. The modification to Yukawa couplings to up-type and down-type quarks and leptons in the four 2HDMs are: Type I Type II Type X (lepton-specific) Type Y (flipped) r t cos α/ sin β cos α/ sin β cos α/ sin β cos α/ sin β r b cos α/ sin β − sin α/ cos β cos α/ sin β − sin α/ cos β r τ cos α/ sin β − sin α/ cos β − sin α/ cos β cos α/ sin β As usual, tan β = v 2 /v 1 is the ratio of the VEVs of the two doublets and α is the mixing angle of the CP-even mass eigenstates. The SM limit corresponds to β − α = π/2. In all of the models the vector couplings are also modified as The results of our fits are presented in fig. 7 in terms of the fermion couplings r t , r b , r τ , restricted by the 2HDM models to lie within the green regions. We find that in each case, it is r t that dominates the fit and the bottom contributions to gluon fusion and h → γγ are negligible. The type II 2HDM (upper panel) allows for independent modification of the t coupling r t , and for a common modification of the b and τ couplings, r b = r τ . The former is predicted be reduced and the latter enhanced by the model. The modification of eq. (21) of the vector couplings can be equivalently written as r W = r Z = (1+r t r b )/(r t +r b ) 1+ t b /2, showing that it is a small second order effect. In this model a negative t Yukawa coupling is still allowed at slightly more than 99% CL. The red line in the same panel shows the parameter space allowed by type I 2HDM, where all the couplings scale uniformly.
In the flipped 2HDM (middle panel) the τ Yukawa coupling changes in the same way as the t coupling and the region with negative coupling is disfavoured by data. Finally, in the leptophilic 2HDM (lower panel) the t and b couplings vary in the same way, while the τ coupling is independent.
The universal fit provides a good approximation to the full fit in all 2HD models.

Supersymmetry
Supersymmetry can affect Higgs physics in many different ways, such that it is difficult to make general statements. We here focus on the two most plausible effects: • The stop squark loop affect the h ↔ gg, γγ, Zγ rates. Given that the stop has the same gauge quantum numbers of the top, such effects are correlated and equivalent to a modification of the Higgs coupling to the top (as long as it is not directly measured via the tth production cross section) by an amount given by in the limit of heavy stop masses, mt 1,2 m t . Notice that Rt can be enhanced or reduced with respect to one, depending on the latter mixing term.
• The type II 2HDM structure of supersymmetric models modifies at tree level the Higgs couplings, as already discussed in section 5.5.
All of this amounts to specialise the universal χ 2 inserting the following values of its parameters Furthermore, the parameters r g , r γ , r Zγ relative to loop processes are fixed as in eq. (14). We trade the α parameter (mass mixing between Higgses) for the pseudo-scalar Higgs mass m A using Finally, we assume a large tan β, as motivated by the observed value of the Higgs mass. Fig. 8a shows the resulting fit. Once again, the universal fit approximates well the full fit. Of course, supersymmetry can manifest in extra ways not considered here, e.g. very light staus or charginos could enhance h → γγ [44].

Data prefer the Higgs to the dilaton
As another example of a model where both the tree level and the loop level Higgs couplings are modified, we consider the dilaton. The dilaton is an hypothetical particle ϕ, that, like the Higgs, couples to SM particles with strength proportional to their masses [45]. More precisely the dilaton has a coupling to the trace of the energy-momentum tensor T µν , suppressed by some unknown scale Λ: The dilaton couplings to gg and γγ differ from the corresponding Higgs boson couplings, because eq. (25) contains the latter two quantum terms, that are present in T µ µ because scale invariance is anomalous and broken at quantum level by the running of the couplings. Indeed b 3 and b γ are the β-function coefficients of the strong and electromagnetic gauge couplings. In the SM they have the explicit values b 3 = −7 and b γ = 11/3: we call 'pure dilaton' this special model, which gives a significant enhancement of h ↔ gg. Models where a dilaton arises usually often contain also new light particles, such that b 3 and b γ can differ from their SM values. Thereby we perform a generic fit where b 3 and b γ are free parameters in addition to Λ. Then, our universal fit is adapted to the case of the generic dilaton by setting where V = 246 GeV. In our previous analyses [8,9], the dilaton gave fits of comparable quality to the SM Higgs, despite the significantly different predictions of the dilaton: enhanced γγ rates and reduced vector boson fusion rates. The first feature is no longer favoured by data, and the second feature is now disfavoured: so we find that present data prefer the Higgs to the 'pure dilaton' at about 5σ level. We then consider the generic dilaton, showing in fig. 8b that the allowed part of its parameters space is the one where it mimics the Higgs, possibly up to a sign difference in r g and/or r γ . The linear couplings of the dilaton in eq. (25) become identical to those of the SM Higgs in the limit b 3 = b γ = 0 and Λ = V . This situation is not easily realisable in models, given that adding extra charged particles increases b γ rather than reducing it; one needs to subtract particles by e.g. assuming that that 3rd generation particles are composite [48].

Higgs boson invisible width
Next, we allow for a Higgs boson invisible width, for example into Dark Matter. We perform two fits.
1. In the first fit, the invisible Higgs width is the only new physics. We find (blue curves in fig. 9a) that present data imply BR inv = −0.07 ± 0.15. The one-sided upper bound, computed restricting to 0 ≤ BR inv ≤ 1, is 2. In addition to the invisible width we also allow for non-standard values of h → γγ and h ↔ gg, finding a weaker constraint on BR inv (red curves in fig. 9a) The reason is that an enhanced gg → h production rate can partially compensate for an invisible Higgs width, but a full compensation would be possible only by enhancing all production rates by the same amount. The Higgs coupling to vectors is independently measured to agree with SM predictions from electroweak precision data.
Notice that the main constraint con BR inv does not come from the direct search for pp → Zh → / E T (included in our data-set) but from the global fit [8,46].

Dark Matter models
The invisible Higgs boson decay width [46] [47], where DM is assumed to be either a scalar S, or a Majorana fermion f or a vector V coupled to the Higgs as The partial Higgs decay width into dark matter Γ(h → DM DM) and the spin-independent DM-proton elastic cross section σ SI can be calculated in terms of the parameters of the above Lagrangian. Both are proportional to the square of the DM-Higgs coupling, so that the ratio µ ≡ σ SI /Γ(h → DM DM) depends only on the the unknown DM mass and on the known masses and couplings of the relevant SM particles (see for instance the expressions provided in [47]). This allows us to relate the invisible Higgs branching fraction to the DM direct detection cross section: where Γ SM h = 4.1 MeV is the total Higgs decay width into all SM particles, that we fix to its SM prediction. For a given DM mass, an upper bound on the Higgs invisible branching fraction implies an upper bound on the DM scattering cross section on nucleons. The relation between the invisible branching fraction and the direct detection cross section strongly depends on the spinorial nature of the DM particle, in particular, the strongest (weakest) bound is derived in the vectorial (scalar) case.
Imposing the upper bounds on BR inv derived in section 5.8, fig. 9 shows the corresponding upper limits on the spin-independent DM cross section on nucleons as a function of the DM mass, in the case of scalar (green), Majorana fermion (red) and vector (blue) DM candidates.
In all cases, the derived bounds are stronger than the direct one from XENON100 as long as the mass of DM is lighter than M h /2. This conclusion does not rely on the assumption that DM is a thermal relic that reproduces the observed cosmological DM abundance. The limit on σ SI crucially depends on the assumption that DM directly couples to the Higgs. Larger values of σ SI remain possible in different models, where DM couples to the Z or directly to nucleons via loops of supersymmetric or other particles.

Discussion and Conclusions
The LHC experiments reported their measurements of Higgs boson properties at the Moriond 2013 conferences, based on the full collected luminosity during 2011 and 2012. At the same time, TeVatron reported their final Higgs results. With the crucial inclusion of the full CMS γγ data (missing in previous analyses), at this stage all main Higgs results from TeVatron and from the first phase of LHC have been basically presented. Those results will drive our understanding of particle physics, until new 13 TeV LHC data will be available.
Motivated by these results, we have performed a state-of-the-art global fit to Higgs boson data, including all sub-categories studied by the experimental collaborations, for a total of 56 data-points, as summarised in fig. 1. We found that the average Higgs rate is 1.00 ± 0.10 in SM units, supporting the SM Higgs boson hypothesis. The Higgs boson mass is usually determined from the peaks in the invariant mass distribution of ZZ and γγ. We performed the first measurement of the Higgs boson mass from the rates, finding that the two determinations are compatible: 125.66 ± 0.34 GeV from the peaks, 124.5 ± 1.7 GeV from the rates.
The LHC physics program has been successful: with only ≈ 25/fb of data per experiment the Higgs boson has been discovered and several of its properties determined within ≈ ±20% precision. We are now entering into the era of precision Higgs physics -deviations from the SM due to new physics no longer can dominate the data. This observation allowed us to propose a 'universal' form in which experiments could report their results allowing theorists to easily test any desired model. The new assumption that makes possible this significant simplification is that new physics is a small correction to the SM. While we present our own global combination in 'universal' form in eq. (??), we stress that only the experimental collaborations can perform a fully precise analysis.
We studied several new physics scenarios beyond the SM. We determined from data the production cross sections (assuming standard Higgs decays) and the Higgs decays widths (assuming standard productions), finding that they lie along the SM predictions. In a more general context, we allowed all possible Higgs boson couplings to any SM particle to deviate from its SM value, finding that couplings to the W, Z, t, b, τ must lie around their SM predictions up to uncertainties of about ±20% (see fig. 3b). In particular, non-standard Higgs boson couplings to vectors, predicted by composite Higgs models, are most stringently constrained. The scenario of negative Higgs coupling to fermions ('dysfermiophilia') that gave the best fit with early LHC data is now disfavoured at more than 2σ.
We considered various specific new physics models: new scalars, 2HDM, supersymmetry, dilaton, composite Higgs, invisible Higgs decays, possibly into Dark Matter particles, anomalous couplings of the top, etc. The results of those fits are presented in numerous figures throughout the paper. Qualitatively, all reach to the same conclusions: i) best fit regions lie along SM predictions, imposing constraints on new physics; ii) our simple 'universal' approximation to the full fit is adequate.
In particular we find that, with the latest data, the dilaton alternative to the Higgs is now excluded at 5σ, with the exception of the special non-minimal dilaton tuned to exactly reproduce the Higgs (section 5.7).
We will update this paper at the light of future results.