Interpreting the LHC Higgs Search Results in the MSSM

Recent results reported by the ATLAS and CMS experiments on the search for a SM-like Higgs boson both show an excess for a Higgs mass near 125 GeV, which is mainly driven by the \gamma\gamma\ and ZZ^* decay channels, but also receives some support from channels with a lower mass resolution. We discuss the implications of this possible signal within the context of the minimal supersymmetric Standard Model (MSSM), taking into account previous limits from Higgs searches at LEP, the Tevatron and the LHC. The consequences for the remaining MSSM parameter space are investigated. Under the assumption of a Higgs signal we derive new lower bounds on the tree-level parameters of the MSSM Higgs sector. We also discuss briefly an alternative interpretation of the excess in terms of the heavy CP-even Higgs boson, a scenario which is found to be still viable.


Introduction
The Higgs boson [1] has for a long time been considered as the only missing piece in the Standard Model (SM) of particle physics. Therefore, finding this particle has been one of the main tasks of experimental high-energy physics. However, the main results from the published searches so far have been exclusion limits (see e.g. the results from LEP [2], the Tevatron [3], and the LHC [4,5]). Combining the experimental limits, the only allowed region (before the latest results which will be discussed below) a relatively small window for the Higgs mass: 114 GeV < M SM H < 141 GeV. This low mass region is also the one favoured by electroweak precision tests, see e.g. [6].
A low Higgs mass is predicted in supersymmetric extensions of the SM, where the quartic Higgs couplings are related to gauge couplings. Exclusion of a heavy SM-like Higgs [3,4,5] can therefore be considered as being in line with the predictions of supersymmetry (SUSY). Besides predicting a light Higgs boson, SUSY protects scalar masses from the large hierarchy of scales, it allows for gauge coupling unification, and it can provide a dark matter candidate [7]. The minimal supersymmetric extension of the SM (MSSM) [8] has two complex Higgs doublets. Following electroweak symmetry breaking, the physical spectrum therefore contains five Higgs bosons. Assuming CP conservation, these are denoted h, H (CP-even), A (CP-odd), and H ± (charged Higgs). At the tree-level the MSSM Higgs sector can be described by two parameters (besides the SM parameters), commonly chosen as the mass of the CP-odd Higgs boson, M A , and tan β, the ratio of the two vacuum expectations values. In the decoupling limit, M A > ∼ 2M Z (where M Z denotes the mass of the Z boson), all MSSM Higgs bosons except the lightest CP-even scalar h become heavy, whereas h has SM-like properties. In this limit it would be difficult to separate hints for a SM Higgs boson from a potential MSSM counterpart. It is also in the decoupling limit where M h reaches its maximal value, M h ≃ 135 GeV [9].
The LHC experiments recently extended their exclusion regions for a SM-like Higgs boson down to M SM H 127 GeV, with the lowest limit coming from CMS (M SM H < 131 GeV for ATLAS). In addition, ATLAS reported exclusion of the range 114 GeV < M SM H < 115.5 GeV, which is a region where sensitivity was not expected. Most interestingly, both experiments also reported about an excess over the background expectation close to M SM H = 125 GeV [10]. Since this Higgs mass lies in the range compatible with supersymmetry, we report in this letter on a first analysis and interpretation of these results in an MSSM context. The result is driven by an observed excess of events over SM background expectations in primarily the γγ and ZZ * channels, which provide relatively good resolution for the Higgs boson mass. The local significance for the combined result is 3.6 σ for ATLAS and 2.6 σ for CMS. However, when interpreted in a global search containing many mass bins, the local significance is washed out by the look-elsewhere 1 Another excess at M SM H ≃ 119 GeV was reported by CMS, but not confirmed by ATLAS. Consequently, we will not consider this value in our analysis. effect (LEE). This effect compensates for the higher probability of random fluctuations generating an excess anywhere when searching in more than one place. Taking this into account, the significance of the reported result is reduced to 2.5 σ (1.9 σ) for ATLAS (CMS) when interpreted as a SM Higgs search over the mass range from 110 GeV to 146 GeV. On the other hand, one could argue that when interpreting these results in a model where the allowed range for M h is constrained to a smaller range by the theory (as in the MSSM), the LEE does not apply to the same degree as for the SM interpretation. These new results are therefore even somewhat more interesting in an MSSM context.

Experimental Higgs search results
For the remainder of this paper, encouraged by the excess reported by ATLAS and CMS, we investigate a scenario where we assume the observation of a state compatible with a SM-like Higgs boson with mass M h = (125 ± 1) GeV. We will discuss the implications that such an assumed signal would have for the MSSM. While the current statistical significance does not allow yet to draw firm conclusions on the validity of the above assumption, our analysis is in fact somewhat more general, as possible implications of observing (or excluding) a state compatible with a SM-like Higgs elsewhere in the allowed mass window 115.5 GeV < M h < 127 GeV [10] can also be inferred.

MSSM Interpretation
For calculating the Higgs masses in the MSSM we use the code FeynHiggs [9,11,12] (v. 2.8.5). The status of higher-order corrections to the masses (and mixing angles) in the neutral Higgs sector is quite advanced. 2 The complete one-loop result within the MSSM is available and has been supplemented by all presumably dominant contributions at the two-loop level, see Ref. [9] for details. Most recently leading three-loop corrections have been presented [14], where the leading term is also included in FeynHiggs. Following Ref. [9], we estimate the (intrinsic) theory uncertainty on the lightest Higgs mass from missing higher-order corrections to be ∆M intr h ∼ ±2 GeV. The intrinsic M h uncertainties are also somewhat smaller for a SM-like Higgs than in the general case, which makes this estimate conservative. Concerning the parametric uncertainty from the experimental errors of the (SM-) input parameters, ∆M param h , the main effect arises from the experimental error of the top-quark mass. We incorporate this uncertainty explicitly in our results below by allowing m t to vary within the range m t = 173.2 ± 0.9 GeV [17]. Parametric uncertainties in M h from α s are smaller than the m t uncertainties and will be neglected. Adding the intrinsic theory uncertainty (conservatively) linearly to the assumed experimental uncertainty, we arrive at the allowed interval which will be used for the MSSM interpretation of the assumed Higgs signal. While for most of this paper we investigate the case where the assumed signal is interpreted as the lighter CP-even Higgs boson, h, of the MSSM, we comment below also on the possibility of associating the assumed signal with the second-lightest CP-even Higgs boson, H. Since the observed excess includes W W * and ZZ * final states, an interpretation in terms of the CP-odd Higgs boson, A, appears to be highly disfavoured. For our discussions of the possible interpretations of the assumed signal, we use a phenomenological description of the (CP-conserving) MSSM with all parameters given at the electroweak scale. In order to determine the radiative corrections to the Higgs masses it is necessary to specify, besides the treelevel parameters M A and tan β, also the relevant SUSY-breaking parameters entering at higher orders. In particular, the parameters in the stop and sbottom sector have a large impact in this context. Since for the case where we interpret the assumed signal as the lighter CP-even Higgs h we are interested in particular in determining lower bounds on the most relevant parameters, we fix those with smaller impact on M h to their values in the m max h scenario [15], so that conservative lower bounds are obtained for the other parameters. In Eq. (2) M 1,2 and mg are the soft SUSY-breaking gaugino masses corresponding to the SM gauge group, and µ is the Higgs mixing parameter. This choice ensures that the corresponding contributions to M h are such that one obtains (approximately) the highest value for M h . In addition to varying the tree-level parameters, we allow for variation in the overall SUSY mass scale M SUSY and the stop mixing parameter X t ≡ A t − µ cot β, where A t,b denotes the trilinear coupling of the Higgs to scalar tops or bottoms. We furthermore set A b = A t . The scalar top masses will be denoted as mt 1 and mt 2 below, with mt 1 ≤ mt 2 . It should be noted that when we discuss relatively low values of M SUSY this refers only to squarks of the third generation (which give rise to the relevant Higgs mass corrections). The experimental bounds reported from squark searches at the LHC [16], on the other hand, apply only to squarks of the first two generations, which are essentially irrelevant for Higgs phenomenology. We also do not apply a lower bound on the gluino mass, which leads to more conservative lower limits on the parameters from the Higgs sector than e.g. a bound mg > 700 GeV [16] would do. We comment further on this point below. As mentioned above, for the top quark mass we use the latest Tevatron combination m t = 173.2 ± 0.9 GeV [17], taking the uncertainty into account by varying m t over its ±1 σ interval. Besides constraints from the Higgs sector, which we will discuss shortly, one could also consider indirect constraints on the MSSM parameter space coming from other measurements, such as the anomalous magnetic moment of the muon, (g − 2) µ , or from B-physics observables such as BR(b → sγ). The former requires in general that µ > 0, while the latter is often in better agreement with experimental data for µX t ≈ µA t < 0 (for a recent analysis see [18] and references therein). We will not apply any indirect constraints here, but when presenting the results below we sometimes distinguish between positive and negative X t , where the bounds obtained for X t < 0 could be regarded as experimentally preferred. However, one should keep in mind that a small admixture of non-minimal flavour violation could bring the BR(b → sγ) results into agreement with experimental data without changing (notably) the Higgs sector predictions [19].

A light CP-even SM-like Higgs boson
We begin the MSSM interpretation by associating the assumed LHC signal with the light CP-even Higgs boson h. By choosing the relevant parameters such that the radiative corrections yield a maximum upward shift to M h , it is possible to obtain lower bounds on the parameters M A and tan β governing the tree-level contribution. The situation where the radiative corrections to M h are maximized in this way is realised in the m max h scenario with a stop mixing of X t = 2M SUSY . In Fig. 1 we show the result of varying the tree-level parameters in this scenario (with M SUSY = 1 TeV as originally defined). Constraints on the parameter space from direct Higgs searches at colliders are taken into account by using HiggsBounds [20]. 3 Since we are interpreting an assumed signal, we do not include the updated exclusion bounds from [10]. Fig. 1 shows separately the regions excluded by LEP [22] (blue), and the Tevatron/LHC (red). The gray area is the allowed parameter space before including the bound from Eq. (1), and the green band corresponds to the mass interval compatible with the assumed Higgs signal of 122 GeV < M h < 128 GeV. The brighter green is for the central value for m t , while including also the dark green band corresponds to a ±1 σ variation of m t .
The assumed Higgs signal, interpreted as the lighter CP-even MSSM Higgs mass, implies in particular that M h > 122 GeV (including theoretical uncertainties), which is significantly higher than the limit observed for a SM-like Higgs at LEP of M h > 114.4 [2]. From Fig. 1 it is therefore possible to extract lower (one parameter) limits on M A and tan β from the edges of the green band. As explained above, by choosing the parameters entering via radiative corrections such that those corrections yield a maximum upward shift to M h , the lower bounds on M A and tan β that we have obtained are general in the sense that they (approximately) hold for any values of the other parameters. To address the (small) residual M SUSY dependence of the lower bounds on M A and tan β, we extract limits for the three different values M SUSY = {0.5, 1, 2} TeV. The results are given in Table 1, where for comparison we also show the previous limits derived from the LEP Higgs searches [22], i.e. before the incorporation of the new LHC results reported in Ref. [10]. The bounds on M A translate directly into lower limits on M H ± , which are also given in the table. A phenomenological consequence of the bound  For deriving the conservative lower bounds on M A and tan β it was unnecessary to impose constraints on the production and decay rates of the assumed Higgs signal in the relevant search channels at the LHC. One might wonder whether it would be possible to improve the bound on M A by requiring that the rate in the relevant channels should not be significantly suppressed as compared to the SM case. Such an improvement would be scenario-dependent, however, i.e. the result would depend on the specific choice made for the other MSSM parameters. We will therefore not study this issue in further detail.
It might look tempting to extract also an upper limit on tan β from the green band in Fig. 1, but in contrast to the lower bound which is scenario-independent, this limit will only apply to the specific case of the m max h scenario. In fact, the allowed range for tan β depends sensitively on the other parameters, as can be seen from Fig. 2, where we show the (X t , tan β) plane for M A = 400 GeV, but the results are qualitatively similar for other values of M A in the decoupling limit. The main difference is the LHC exclusion limit (in red), which goes down to lower values of tan β for lower M A . On the other hand, for M A in the non-decoupling regime, even before the new results tan β was already quite restricted, from above by the the LHC limits, and from below by the LEP limits, which can also be seen from Fig. 1. The m max h value of X t = +2M SUSY turns out to be quite special, since this parameter region (at least for M SUSY = 1 TeV and M SUSY = 2 TeV) actually shows the highest sensitivity to variations of tan β when M h ∼ 125 GeV. This would result in only a narrow allowed tan β region. For other regions of X t , however, tan β values all the way up to the LHC bound are compatible with an assumed signal at M h ∼ 125 GeV. Further progress could obviously be made if direct information on the stop sector became available from the LHC or a future Linear Collider.
Having established lower limits on the tree-level parameters M A and tan β, we now investigate instead what can be inferred from the assumed Higgs signal about the higher-order corrections in the Higgs sector. Similarly to the previous case, we can obtain an absolute lower limit on the stop mass scale M SUSY by considering the maximal tree-level contribution to M h . We therefore perform this analysis in the decoupling limit (fixing M A = 1 TeV, tan β = 20). The resulting constraints for M SUSY and X t are shown in Fig. 3 (left) using the same colour coding as before.
Several favoured branches develop in this plane, centred around X t ∼ −1.5M SUSY , X t ∼ 1.2M SUSY , and X t ∼ 2.5M SUSY . The minimal allowed stop mass scale is M SUSY ∼ 300 GeV with positive X t The colour coding is as in Fig. 1. and M SUSY ∼ 500 GeV for negative X t (which is in general preferred by BR(b → sγ), see above). The results on the stop sector can also be interpreted as a lower limit on the mass mt 1 of the lightest stop squark. This is shown in Fig. 3 (right). It is interesting to note from the figure that without the assumed Higgs signal, there is essentially no lower bound on the lightest stop mass coming from the Higgs sector. Taking the new results into account, we obtain the lower bounds mt 1 > 100 GeV (X t > 0) and mt 1 > 250 GeV (X t < 0). These bounds can be compared to those from direct searches, where the LEP limit mt 1 > ∼ 95 GeV is still valid [23]. Results from stop searches at the Tevatron can also be found in this reference. No new stop limits have been established so far from the SUSY searches at the LHC [16]. It should be noted that our stop mass bound is rather conservative, since the low mass scales discussed here correspond to a gluino mass mg = 0.8 M SUSY < 300 GeV, which is experimentally disfavoured [16, 23,24]. Since the low gluino mass contributes towards a higher value of M h , a lower bound on mg would lead to a stronger bound on mt 1 . As an example, in a simplified model consisting just of the gluino, the squarks of the first two generations and a massless lightest supersymmetric particle, the ATLAS Collaboration has inferred a lower bound of about 700 GeV on mg [16]. Imposing such a bound on mg in our analysis would shift the lower limit on mt 1 to mt 1 200 GeV (mt 1 350 GeV) for positive (negative) X t . It should be noted, however, that in the presence of a light stop decays of the gluino into a top and a scalar top would open up,g →t 1 t, which are expected to weaken the bound on mg as compared to the analysis in the simplified model where this decay mode is assumed to be absent.

A heavy CP-even SM-like Higgs boson
All results presented up until this point apply only if we interpret the assumed signal as corresponding to the light CP-even MSSM Higgs h. We now discuss briefly the alternative possibility that the heavier CP-even H has a mass M H ∼ 125 GeV (with the same experimental and theoretical uncertainties as before, see Eq. (1)) and SM-like properties.
In order to investigate whether there is a region in the MSSM parameter space that admits this solution we performed a scan over the relevant free parameters (M A , tan β, M SUSY , X t ), keeping  Fig. 4, indicating the region where M H fulfills Eq. (1) by cyan colour to distinguish it from the case discussed above (similarly to above, the darker region corresponds to the variation of m t ). As we can see from this figure, it is possible to obtain M H in the right range in a region with low M A and moderate tan β (left plot) where we have set M SUSY = 1 TeV, X t = 2.3 TeV. In the right plot we set M A = 100 GeV, tan β = 10 and show the regions compatible with a heavier CP-even Higgs having a mass M H ∼ 125 GeV in the plane of the stop sector parameters M SUSY and X t . We find that such an interpretation is possible over extended regions of the (M SUSY , X t ) parameter plane. Requiring in addition that the production and decay rates into γγ and vector bosons are at least 90% of the corresponding SM rates, a smaller allowed region is found (yellow) with large values for the stop mixing (X t 1.5 TeV). In the yellow region enhancements of the rate of up to a factor of three as compared to the SM rate are possible. Concerning the mass of the lighter CP-even Higgs boson h in this kind of scenario we we find in our scan allowed values for M h only below the SM LEP limit of 114.4 GeV [2] (with reduced couplings to gauge bosons so that the limits from the LEP searches for non-SM like Higgs bosons are respected [22]). A particularly intriguing option could be M H ≃ 125 GeV, M h ≃ 98 GeV, in view of the fact that LEP observed a certain excess at M h ≃ 98 GeV [22] (whose interpretation is of course subject to the look-elsewhere effect). This combination of Higgs masses is realized (with H SM-like), for instance, for M SUSY = 1 TeV, X t = 2.4 TeV, µ = 1 TeV, M A = 106 GeV, and tan β = 7. For this scenario we find a reduced coupling (g hZZ /g SM HZZ ) 2 = 0.1 of the lightest Higgs boson to a pair of Z bosons.
Despite the available parameter space, it should be noted that the scenario where the heavier CP-even Higgs is SM-like and has a mass of M H ∼ 125 GeV appears somewhat more contrived than the h interpretation. In particular, we find that simultaneously large values for the µ parameter and a large mixing in the stop sector are required in order to obtain a SM-like rate of production and decay of the heavy CP-even Higgs in the relevant channels. We leave a more detailed investigation of this scenario for future work.

Conclusions
An excess in the SM-like Higgs searches at ATLAS and CMS has recently been reported [10] around M SM H ≃ 125 GeV, which within the experimental uncertainties appears to be remarkably consistent between ATLAS and CMS and is supported by several search channels. While it would be premature to assign more significance to this result than regarding it as a possible (exciting) hint at this stage, it is certainly very interesting to note that this excess has appeared precisely in the region favoured by the global fit within the SM, and within the range predicted in the MSSM. Concerning the MSSM, it is remarkable that the mass region above the upper MSSM bound on a light SM-like Higgs is meanwhile ruled out [10]. Observing a state compatible with a SM-like Higgs boson with M SM H > 135 GeV would have unambiguously ruled out the MSSM (but would have been viable in the SM and in non-minimal supersymmetric extensions of it). We therefore regard the reported results as a strong motivation for studying the possible interpretation of an assumed (still hypothetical, of course) signal at 125 GeV ± 1 GeV. In this paper we have discussed the possible implications of such an assumed signal within the MSSM, where we have investigated both the possibilities that the assumed signal is associated with the light CP-even Higgs boson of the MSSM, h, and the (slightly more exotic) possibility that the assumed signal in fact corresponds to the heavier CP-even Higgs boson H.
Investigating the interpretation M h = 125 ± 1 GeV first, we have demonstrated that there is a significant parameter space of the MSSM compatible with the interpretation that the assumed signal corresponds to the lighter CP-even MSSM Higgs boson. While it would not be appropriate to assign any physical significance to point densities in MSSM parameter space, our scans nevertheless do not seem to indicate a strong case for going from the MSSM to non-minimal SUSY models even though the reported excess is not very far away from the upper bound on the lightest Higgs mass in the MSSM. It should be noted that the question to what extent the scenarios discussed in this paper can be realized in constrained GUT-based models of SUSY breaking is of a very different nature. We do not pursue this any further here, besides mentioning that it has already been shown to be rather difficult to get to such high M h values in models such as the CMSSM, mGMSB, mAMSB, or NUHM1 [25].
We performed two kinds of complementary investigations of the implications of an assumed Higgs signal at M h = 125 ± 1 GeV. Setting the parameters that enter via the (in general) numerically large higher-order corrections in the MSSM Higgs sector to their values in the m max h benchmark scenario, which maximizes the upward shift in M h as compared to the tree-level value, we have obtained conservative lower limits on the parameters governing the M h prediction at tree level, M A and tan β. We have found that an assumed signal of M h = 125±1 GeV (when including conservatively estimated intrinsic theoretical uncertainties from unknown higher orders, and taking into account the most important parametric uncertainties arising from the experimental error on the top-quark mass) yields the lower bounds M A > 133 GeV and tan β > 3.2 (for M SUSY = 1 TeV). The bound on M A translates directly into a lower limit M H ± > 155 GeV, which restricts the kinematic window for MSSM charged Higgs production in the decay of top quarks.
Choosing values for M A and tan β in the decoupling region, in a second step we have investigated the constraints on the scalar top and bottom sector of the MSSM from an assumed signal at M h = 125 ± 1 GeV. In particular, we have found that a lightest stop mass as light as mt 1 ∼ 100 GeV is still compatible with the assumed Higgs signal. The bound on mt 1 raises to mt 1 > ∼ 250 GeV if one restricts to the negative sign of the stop mixing parameter X t ≡ A t − µ/ tan β, which in general yields better compatibility with the constraints from BR(b → sγ).
As an alternative possibility, we have investigated in how far it is possible to associate the assumed Higgs signal with the heavier CP-even Higgs boson H. Performing a scan over M A , tan β, M SUSY and X t we have found an allowed area at low M A and moderate tan β. A SM-like rate for production and decay of the heavier CP-even Higgs in the relevant search channels at the LHC is possible for large values of µ and large mixing in the stop sector. It is interesting to note that in the scenario where the assumed Higgs signal is interpreted in terms of the heavier CP-even Higgs boson H the mass of the lighter Higgs, M h , always comes out to be below the SM LEP limit of 114.4 GeV (with reduced couplings to gauge bosons so that the limits from the LEP searches for non-SM like Higgs bosons are respected). The fact that scenarios like this are in principle viable should serve as a strong motivation for extending the LHC Higgs searches, most notably in the γγ final states, also to the mass region below 100 GeV.
Needless to say, an MSSM interpretation of the observed excess would of course gain additional momentum if the searches for the scalar quarks of the third generation and the direct searches for the colour-neutral SUSY states, which so far have resulted in only very weak limits, would soon give rise to a tantalising excess (or more than one) as well.