Discriminating between SUSY and Non-SUSY Higgs Sectors through the Ratio $H \to b \bar b / H \to \tau^+ \tau^-$ with a 125 GeV Higgs boson

It is still an open question whether the new scalar particle discovered at the LHC with a mass of 125 GeV is the SM Higgs boson or it belongs to models of new physics with an extended Higgs sector, as the MSSM or 2HDM. The ratio of branching fractions $R$ = BR($H \to b \bar b$)/BR($H \to \tau^+ \tau^-$) of Higgs boson decays is a powerful tool in order to distinguish the MSSM Higgs sector from the SM or non-supersymmetric 2HDM. This ratio receives large renormalization-scheme independent radiative corrections in supersymmetric models at large $\tan\beta$, which are insensitive to the SUSY mass scale and absent in the SM or 2HDM. Making use of the current LHC data and the upcoming new results on Higgs couplings to be reported by ATLAS and CMS collaborations and in a future linear collider, we develop a detailed and updated study of this ratio $R$ which improves previous analyses and sets the level of accuracy needed to discriminate between models.


Introduction
At present, it is still an open question in the high energy physics community whether the discovered new scalar particle at the Large Hadron Collider (LHC) [1] is actually the Higgs boson of the Standard Model of particle physics (SM). This new particle seems to behave as the SM Higgs boson, and the most recent combined measurement of its mass by the ATLAS and CMS collaborations set m H SM = 125.09 ± 0.21 (stat.) ± 0.11 (syst.) GeV [2]. However, many more measurements and data will be needed to extract reliable conclusions. It is worth noticing that the study of perturbativity and stability of the SM Higgs boson potential suggests that, given the measured Higgs boson mass, new physics must be present before the Planck scale [3]. Apart from the introduction of new particles, extensions of the SM scalar sector may affect the properties of the SM-like Higgs boson discovered at the LHC. Experimental data is being used to constrain these extensions. Among the minimal extensions of the SM is the inclusion of additional Higgs bosons. In the two-Higgsdoublet models (2HDM) one additional Higgs doublet is introduced and five physical Higgs bosons are obtained [4]: two CP-even scalars (h and H), one CP-odd scalar (A), and a charged Higgs pair (H ± ); being the lightest Higgs boson very similar to the SM one in the so-called decoupling limit [5]. The minimal supersymmetric standard model (MSSM) [6], one of the most-predictive frameworks beyond the SM, also contains two Higgs doublets with a light neutral scalar boson compatible with the existing measurements, including the recently discovered Higgs boson. In this letter we approach the question of the existence of an extended Higgs structure beyond the SM by investigating the neutral Higgs sector of various types of models.
We consider in this work the ratio of branching ratios of a neutral Higgs boson H [7], analyzing in detail the Yukawa-coupling effects and their phenomenological consequences. At leading order, in either the SM, the 2HDM or the MSSM, this ratio is given by just the ratio of squared (running) masses: However, this ratio receives large renormalization-scheme independent radiative corrections in supersymmetric (SUSY) models at large tan β, the ratio of the vacuum expectation values. These corrections are insensitive to the SUSY mass scale (M SUSY ) and absent in the SM or 2HDM. Therefore, this ratio is a discriminant quantity between SUSY and non-SUSY models. The leading radiative corrections to this ratio can be cast into an effective Yukawa SUSY coupling h f , and summarized in a simple correction factor ∆m f [7][8][9], thus for a down-type quark or a charged lepton one can write: Here m f (Q) is the running fermion mass, v 1 and v 2 are the vacuum expectation values (v.e.v.s) of the two Higgs doublets; being v 1 the one giving mass to down-type quarks and charged leptons, This expression includes all possible tanβ enhanced corrections of the type (α (s) tanβ) n [10] correctly resumed. The leading part of the (potentially) non-decoupling contributions proportional to the trilinear soft-SUSY-breaking coupling A f can be absorbed in the definition of the effective Yukawa coupling at low energies and only subleading effects survive [11]. Therefore, expression (3) contains all leading potentially large radiative effects. The resummation of the two-loop dominant corrections for large values of tan β has been calculated in [12].
The interplay between Higgs physics and SUSY, with the inclusion of radiative corrections, has been extensively discussed in the literature, see e.g. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. It is also well known that the SUSY radiative corrections to the couplings of the Higgs bosons to bottom quarks can be significant for large values of tan β, and that they do not decouple in the limit of a heavy supersymmetric spectrum [8-11, 14-20, 23], opposite to their behavior in electroweak gauge boson physics [25]. The partial decay width Γ(h → bb) of the lightest supersymmetric neutral Higgs particle has received particular attention. The complete one-loop corrections have been studied in [13], and comprehensive studies of the one-and two-loop SUSY-QCD corrections are also available in [14] and [21]. The effective Lagrangian description of the hbb vertex and the implications for Higgsboson searches from SUSY effects can be found in [8,10,11,17,18]. The decoupling properties of the SUSY-QCD corrections to Γ(h → bb) have been extensively discussed in [20]. On the other side, the analysis of BR(H → τ + τ − ) was presented in [22]. The observable R, as the ratio of the two last mentioned processes, has been also analyzed in [7] and [19]. Some recent analyses of these two branching ratios and other Higgs decay modes, confronting LHC data with the MSSM predictions, can be found, for example, in [26].
The ratio (1) is very interesting from both the experimental and the theoretical sides. It is a clean observable, measurable in a counting experiment, with only small systematic errors since most of them cancel in the ratio. The only surviving systematic effect results from the efficiency of τ -and b-tagging. From the theoretical point of view, it is independent of the production mechanism of the decaying neutral Higgs boson and of its total width. Therefore, new-physics effects affecting the production cross-section do not appear in the ratio and also this observable is insensitive to unknown higher order QCD corrections to Higgs boson production. Besides, since this ratio only depends on the ratio of the masses (2), there is no other parameter (e.g. tanβ) that could absorb the large quantum corrections.
As shown in [7], the ratio of the Higgs boson decay rates into b quarks and τ leptons (1) normalized to the Standard Model expectation R SM is a very efficient quantity to distinguish a general 2HDM from the MSSM, whose Higgs sector could be fully covered at the LHC [27]. This normalized value is a function depending only on tanβ, tan α, ∆m b , and ∆m τ , and encoding all the genuine SUSY corrections. The explicit form of ∆m b and ∆m τ at the one-loop level can be obtained approximately by computing the supersymmetric loop diagrams at zero external momentum (M SUSY m b , m τ ) [7]. These two quantities are independent of the SUSY mass scale M SUSY since they only depend on tanβ and the ratio A t /M SUSY [7,10,17]. Therefore, the conclusions about the sensitivity to the SUSY nature of the Higgs sector through the analysis of the ratio R are independent of the scale of the SUSY masses.
Nowadays, the experiments at the LHC become increasingly sensitive to the Higgs boson couplings. CMS and ATLAS have indeed performed a generic fit to Higgs-boson coupling ratios. In order to carry out this analysis, they define a set of Higgs boson couplings normalized to the SM ones, κ x ≡ g x /g SM x , and the production rates measurements give a measurement of the coupling ratios for two particles: In the present work, we are interested in the bottom-quark and τ -lepton measurements, for which CMS and ATLAS collaborations provide [28] λ CMS Besides, the expected accuracy for the measurement of the fundamental Higgs couplings Hbb and Hτ + τ − in future course of the LHC run corresponds to an uncertainty of 10-13% (b quarks) and 6-8% (τ leptons), going down to 4-7% and 2-5% for the high luminosity LHC (HL-LHC). At the Linear Collider (LC) the expected uncertainty is smaller, 0.6% for Hbb coupling and 1.3% for Hτ + τ − coupling [29]. In this paper we consider the present experimental results on the Higgs boson mass and couplings in the analysis of the ratio (1) as well as the expected future precision, and discuss the possibility to discriminate between models at various levels of future accuracy.
In section 2 we present the relevant expressions for our study and analyze the ratio R (eq. (1)) in view of the present LHC data on Higgs boson coupling ratios as given in (4). Section 3 is devoted to the analysis of the future sensitivities of this ratio at present and future colliders, and the study of the potential discrimination between SUSY or non-SUSY models. Finally, the conclusions of this work are summarized in section 4.

Analysis of present data
In this section we concentrate on the analysis of the ratio R defined in (1) for the cases of the lightest CP-even Higgs boson, h. For the sake of the discussion and the analysis it will be useful to introduce the ratio R (1) normalized to the SM value for equal values of the Higgs boson mass. For a Higgs boson φ we define: We can write this normalized ratio for each neutral MSSM Higgs boson in terms of the nondecoupling quantities ∆m b and ∆m τ as [7] In [7], by assuming a ±21% measurement of this ratio for the lightest Higgs boson at the LHC [30], it was found that one can be sensitive to the SUSY nature of the lightest Higgs boson h for M A up to ∼ 1.8 TeV in the most favorable scenario, being up to M A ∼ 500 GeV in some other regions. Nowadays, the combination of the LHC coupling measurements of eq. (4) provides an experimental determination of the normalized ratio (5) Using the values in eq. (4) we obtain: In this work we consider this experimental determination and we discuss their phenomenological consequences through the analysis of the normalized ratio X (5) in different SUSY scenarios. Besides, we also include in our numerical analysis a combined analysis of CMS and ATLAS results.
From the generic fit to Higgs coupling ratios given above one can determine the values of these coupling ratios to be We obtain these values by using the procedure for combination of results described in [31]. As a consequence we get a value for the ratio of The one-standard deviation (68% C.L.) favored bands on X (5) are: While the CMS result includes the SM value (X = 1) in its favored region, the ATLAS and our combined results disfavor the SM (at 68% C.L.). SUSY can provide the necessary corrections to bring the predicted theoretical value of X inside the ATLAS favored band.
For the theoretical numerical analysis, we consider different SUSY scenarios, by checking that those scenarios are compatible with the present experimental value of the Higgs boson mass, m H SM = 125.09 ± 0.21 (stat.) ± 0.11 (syst.) GeV [2]. The Higgs boson mass is computed by using FeynHiggs 2.11 [32]. For completeness, first we consider the four scenarios analyzed in [7] and we find that the SUSY spectra defined in these scenarios provide a Higgs boson mass value not compatible with the present experimental result. The only exception is the scenario with µ < 0 A t > 0, in which we obtain that m h is around 122 GeV. For the purpose of making contact with the previous results, we include this scenario in the following discussion. Besides, we choose SUSY spectra as defined in [33] for the m mod+  [35]. The CP-even mixing angle is computed including the leading corrections up to two-loop order by means of the program FeynHiggsFast [36]. The branching ratios of Higgs boson decays into bb and τ + τ − have been also computed with FeynHiggs 2.11 and we find a perfect agreement with our results for values of tan β 50. The difference between these two computations for larger values of tan β is around 10%.
In Fig. 1 we present numerical results for R MSSM (h) normalized to the SM value, as a function of (a) M A and (b) tan β, for various choices of SUSY scenarios with tan β = 50 and M A = 500 GeV, respectively. The horizontal lines show the one-standard deviation experimental upper limit for X (13) by ATLAS (in red), CMS (in blue), and our combined result (in black). The largest deviation with respect to the SM value emerges in the scenario µ < 0 A t > 0. Actually, the present analysis already excludes this scenario at 68% C.L., and only a small region with tanβ < 10 and M A = 500 GeV survives the CMS measurement (Fig. 1b). This shows the huge potential of the observable R in SUSY searches/exclusions. We note, however, that this scenario (µ < 0 A t > 0) is also disfavored by the constraints from the measurement of BR(B s → µ + µ − ) [37]. Actually, the sign of the dominant contribution to the corrections to R is proportional to −sign(µA t ), and since the experimental data on BR(B s → µ + µ − ) disfavors µA t < 0, it selects negative corrections to R. For this reason we will not further consider the µ < 0 A t > 0 scenario. The other scenarios provide a prediction for R MSSM (h) (6) smaller than in the SM, and then the CMS measurement alone can not exclude any of them (13). However, note that most scenarios have a prediction close the SM one, and therefore the ATLAS result disfavors them (at 68% C.L.). The m mod- is practically indistinguishable from the SM one, whereas the m mod+ h has a largest deviation of a 20% with respect to the SM value, and both of them are also disfavored by ATLAS. The light-stop and light-stau scenarios provide larger deviations, up to 40% for small M A , and this small region is not disfavored by ATLAS. The pMSSM scenario provides larger deviations, and thus has the largest allowed regions, for M A 500 GeV and tanβ 50.
We note in Fig. 1b the flat evolution of the normalized ratio X with respect to tanβ in the m mod+ h , m modh , light-stop, and light-stau scenarios. The reason is manifold: first of all, the resummation procedure softens the tanβ evolution; second, at M A 500 GeV the MSSM Higgs sector is already close to the decoupling limit, with tan α close to −1/ tan β and therefore providing a small effect of the ∆m f corrections to X(h) (8); thirdly, those scenarios use as input parameter in the squark sector the non-diagonal element of the squark-mass matrix X t[b,τ ] = A t[b,τ ] − µ cot β[tan β], and therefore the sfermion mass matrix is nearly flat as a function of tanβ, and so are also the sfermion masses. For the pMSSM scenario the first two conditions also apply, however here the input parameter in the sfermion sector is the soft-SUSY-breaking trilinear coupling A t[b,τ ] , therefore the sfermion-mass mixing terms changes strongly with tanβ, and so do also the physical sfermion masses.
As expected, the decoupling behavior with M A becomes apparent in Fig. 1a for all the SUSY scenarios. Notice that in all the above scenarios the gluino mass is around 1500 GeV. We have also examined numerically the decoupling behavior of the ratio X with the gluino mass, extrapolating the results up to M g ∼ 5000 GeV. Our results show that there is not decoupling, the ratio X tends to a constant value for all mentioned SUSY scenarios. Therefore, our conclusions are also valid for large values of the gluino mass, in perfect agreement with the present bounds for this mass at the LHC.
We finish this section by discussing the regions of the MSSM parameter space favored by the present experimental values of X (13). Of course, as already told, all the studied scenarios have X 1, and therefore all of them are allowed by CMS. Furthermore, the m modh scenario has very small deviations with respect to the SM value and it is practically indistinguishable from the SM.  Table 1 are also included. The sensitivity regions are the ones to the left of the corresponding curve. Shown in blue is the 95% C.L. allowed regions by the negative searches by ATLAS and CMS for neutral MSSM Higgs bosons decaying to a pair of τ leptons [38].   (13), the allowed region is the red area of the curve. We also show the 95% C.L. favored regions (shaded blue areas) by the negative searches by ATLAS and CMS for neutral MSSM Higgs bosons decaying into a pair of τ leptons [38]. We see that in the m mod+ h roughly the whole explored M A − tanβ plane is disfavored, whereas in the light-stop and light-stau scenarios a small corner of large tanβ and low M A is favored. The region favored in the pMSSM scenario is much larger, allowing large values of M A with large tanβ. In all the cases, the favored regions fall completely inside the excluded region for the CMS and ATLAS direct searches for Higgs bosons decaying into τ -lepton pairs, which means that there is a tension (albeit a very soft one) between the experimental determination of the Higgs boson couplings and the direct search for Higgs boson decaying into τ -lepton pairs.

Future prospects
In this section we study the prospects for finding deviations in the ratio R (1) in future colliders. In order to define the different sensitivity regions we show in Table 1 the expected accuracies with which the fundamental Higgs couplings Hbb and Hτ + τ − , and our derived observable R (1), can be measured at the LHC/HL-LHC, the LC, and in combined analyses of the HL-LHC and the LC [29]. Note that Table 1 shows the accuracy expected on absolute coupling measurements, whereas for the purpose of the present work relative coupling measurements, like the ones on eq. (4), are sufficient, and those have better accuracies.
We reanalyze, from the point of view of the sensitivity to the SUSY nature of the neutral MSSM Higgs bosons, the results of Fig. 2, where the regions in the M A − tanβ plane in which the MSSM prediction for the normalized ratio X (5) is larger than the expected sensitivities of Table 1 are depicted. Fig. 2 shows these sensitivity regions on X(h) (6) for the m mod+ h , light-stop, light-stau, and pMSSM scenarios, respectively, for 42%, 32%, 24%, 12%, 4%, and 3% accuracy measurements. The sensitive regions are the ones above and to the left of the corresponding curve. The sensitivity regions for the m modh scenario are not shown here, since as can be inferred from the results of Fig. 1, it is not possible to distinguish its predictions from the SM ones. Indeed, in order to measure a deviation with respect the SM value in this scenario, an accuracy of at least ∼ 0.5% would be required.
The SUSY nature of the discovered Higgs boson of 125 GeV is testable within these four scenarios with the expected accuracies for the current LHC runs or for its high luminosity phase. Unfortunately the corresponding sensitivity regions lie mainly outside the shaded blue areas and We turn now our attention to the heavy neutral Higgs bosons H and A. In case of these heavy states are found at the LHC, one still has to answer the question whether they belong to a simple 2HDM, or whether they belong to a SUSY extension of the SM. The ratio of branching ratios R (1) can be useful in this task. Fig. 3 shows the normalized ratio X(H/A) (5) as a function of tanβ for the m mod+ h , light-stop, light-stau, and pMSSM scenarios with M A = 500 GeV. Note that once we are close to the decoupling limit (M A M Z ) the couplings of H/A are indistinguishable, and, furthermore, the ratio R(H/A) becomes independent of M A . We show through different shaded regions the expected accuracies for the future measurement of R (1), ±32% (shaded gray area), ±12% (shaded green area), and ±4% (shaded orange area). For the sake of readiness, we only show the smallest accuracies reported in Table 1. We see that, given a large enough value of tanβ, all the scenarios (except the m modh ) provide a value for X(H/A) (5) larger than the expected experimental accuracies. Within the m mod+ h scenario, it would be possible to observe at the LHC 32% deviations with respect to the SM value for tan β 55. At the HL-LHC, we could be sensitive to SUSY within this scenario for a 12% deviation from values of tan β 20. The results for the light-stop, light-stau, and pMSSM scenarios are very similar and even more favorable in order to detect any SUSY deviation with respect to the SM value. The LHC could observe 32% deviations for values of tan β larger than 20 and the HL-LHC would be sensitive to SUSY with 12% deviations for tan β 5. If an accuracy of 4% is achieved at a future LC, it would be possible to probe the SUSY nature of H and A Higgs bosons for tan β 5 in any of these four scenarios. Therefore, if a new heavy Higgs scalar or pseudoscalar is discovered, and its couplings to bottom quarks and τ leptons are measured with a moderate level of precision, it would be possible to distinguish between SUSY and non-SUSY Higgs sectors at the LHC.

Conclusions
In this work, we have updated the analysis of the observable R = BR(H → bb)/BR(H → τ + τ − ) (1) in order to look for a strong evidence for, or against, the SUSY nature of the Higgs boson. We have considered more realistic MSSM scenarios with a lightest Higgs boson mass m h compatible with the current value of the Higgs boson mass m H SM 125 GeV. We have compared the theoretical prediction in the MSSM with the current experimental determination of Higgs boson couplings to fermions at the LHC (4). We find that the SM prediction for R agrees well with current CMS data, but using ATLAS data we obtain a (one-standard deviation) upper limit below the SM prediction. By contrast, the SUSY contributions can provide a prediction that agrees with the experiment at the one-standard deviation level. Current accuracy already allows to exclude portions of the parameter space, showing the potential of the observable R to discriminate among different models of new physics. It is also important to mention that the parameter space regions that are favored by the determination of the Higgs boson couplings to fermions are in tension with the direct searches for MSSM neutral Higgs boson decaying into τ -lepton pairs.
We have also looked at the prospects for future measurements of the Higgs boson couplings. We find that, in wide regions of the parameter space, a moderate accuracy of the couplings would signal the presence of SUSY in the Higgs boson data. This analysis allows the use of relative couplings, which can improve significantly the accuracy in the experimental determination of R.
Finally, we have moved our attention to the heavier Higgs bosons of the MSSM, H and A. If one or both of these heavy neutral Higgs bosons are discovered, one would still need to determine whether they belong to a generic 2HDM or to a SUSY model. A moderate accuracy determination of their couplings to b quarks and τ leptons, by means of the analysis of the ratio R, would be sufficient to discern the SUSY nature of such particles.