Abstract
We perform a parameter scan of the phenomenological Minimal Supersymmetric Standard Model (pMSSM) with eight parameters taking into account the experimental Higgs boson results from Run I of the LHC and further lowenergy observables. We investigate various MSSM interpretations of the Higgs signal at . First, we consider the case where the light even Higgs boson of the MSSM is identified with the discovered Higgs boson. In this case it can impersonate the SM Higgslike signal either in the decoupling limit, or in the limit of alignment without decoupling. In the latter case, the other states in the Higgs sector can also be light, offering good prospects for upcoming LHC searches and for searches at future colliders. Second, we demonstrate that the heavy even Higgs boson is still a viable candidate to explain the Higgs signal — albeit only in a highly constrained parameter region, that will be probed by LHC searches for the odd Higgs boson and the charged Higgs boson in the near future. As a guidance for such searches we provide new benchmark scenarios that can be employed to maximize the sensitivity of the experimental analysis to this interpretation.
BONNTH201606, DESY 16151, IFTUAM/CSIC16068, NIKHEF 2016033, SCIPP 16/10
The Light and Heavy Higgs Interpretation of the MSSM
Philip Bechtle, Howard E. Haber, Sven Heinemeyer, Oscar Stål,
[.5em]
Tim Stefaniak, Georg Weiglein and Lisa Zeune^{*}^{*}*Electronic addresses:
bechtle@physik.unibonn.de,
haber@scipp.ucsc.edu,
Sven.Heinemeyer@cern.ch,
tistefan@ucsc.edu,
Georg.Weiglein@desy.de,
lisa.zeune@nikhef.nl
[0.4cm] Physikalisches Institut der Universität Bonn, Nußallee 12, D53115 Bonn, Germany
[0.1cm] Santa Cruz Institute for Particle Physics (SCIPP) and Department of Physics
University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95060, USA
[0.1cm] Campus of International Excellence UAM+CSIC, Cantoblanco, E–28049 Madrid, Spain
[0.1cm] Instituto de Física Teórica, (UAM/CSIC), Universidad Autónoma de Madrid,
Cantoblanco, E28049 Madrid, Spain
[0.1cm] Instituto de Física de Cantabria (CSICUC), E39005 Santander, Spain
[0.1cm] The Oskar Klein Centre, Department of Physics, Stockholm University,
SE106 91 Stockholm, Sweden (former address)
[0.1cm] Deutsches ElektronenSynchrotron DESY, Notkestraße 85, D22607 Hamburg, Germany
[0.1cm] Nikhef, Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands
1 Introduction
The discovery of a Higgslike scalar boson in Run I of the Large Hadron Collider (LHC) [1, 2] marks a milestone in the exploration of electroweak symmetry breaking (EWSB). Within experimental and theoretical uncertainties, the properties of the new particle are compatible with the Higgs boson of the Standard Model (SM) [3]. However, a variety of other interpretations of the Higgs signal are possible, corresponding to very different underlying physics. Here, a prime candidate for the observed scalar boson is a even Higgs boson of the Minimal Supersymmetric Standard Model (MSSM) [4, 5, 6], as it possesses SM Higgslike properties over a significant part of the model parameter space with only small deviations from the SM in the Higgs production and decay rates [7].
One of the main tasks of the LHC Run II will be to determine whether the observed scalar boson forms part of the Higgs sector of an extended model. In contrast to the SM, two Higgs doublets are needed in the MSSM to give mass to up and downtype fermions. The extended Higgs sector entails the existence of five scalar bosons, namely a light and heavy even Higgs bosons, and , a odd Higgs boson, , and a pair of charged Higgs bosons, . Mixing between the neutral even and odd states are possible in the violating case [8, 9, 10, 11, 12, 13], which we will not considered here. At lowest order, the Higgs sector of the MSSM can be fully specified in terms of the and boson masses, and , the odd Higgs boson mass, , and , the ratio of the two neutral Higgs vacuum expectation values. However, higherorder corrections are crucial for a precise prediction of the MSSM Higgs boson properties and introduce dependences on other model parameters, see e.g. Refs. [14, 15, 16] for reviews.
Many fits for the Higgs rates in various models and within the effective field theory approach have been performed over the last years, see e.g. Ref. [17, 18]. Focusing on the MSSM, recent fits have shown that the interpretation of the observed scalar as the light even MSSM Higgs boson (“light Higgs case”) is a viable possibility, providing a very good description of all data [19, 20, 21, 22, 23, 24]; see also Refs. [25, 26, 27] for global fits including also astrophysical data. In the lightHiggs case, decoupling of the heavy Higgs bosons () [28, 29, 30, 31] naturally explains the SMlike couplings of the light MSSM Higgs boson [7]. Another interesting possibility to explain the SMlike behavior of without decoupling in the MSSM—the socalled limit of alignment without decoupling—has been outlined in Refs. [32, 33], relying on an (accidental) cancellation of treelevel and loop contributions in the even Higgs boson mass matrix. This led to the definition of a specific benchmark scenario [33], which has since been ruled out in the interesting low region via searches [23].
Alternatively, it was demonstrated that the heavy even Higgs boson can also be identified with the observed signal [7, 34, 35, 36, 37, 19] (“heavy Higgs case”).^{1}^{1}1Such a situation is more common in extensions of the MSSM. In particular, in the NMSSM it occurs generically if the singletlike even state is lighter than the doubletlike Higgs bosons, see e.g. Refs. [38, 39, 40, 41, 42]. In this scenario all five MSSM Higgs bosons are relatively light, and in particular the lightest even Higgs boson has a mass (substantially) smaller than with suppressed couplings to gauge bosons. This led to the development of the low benchmark scenario [43]. This particular scenario has meanwhile been ruled out by ATLAS and CMS searches for a light charged Higgs boson [44, 45]. However the heavy Higgs interpretation in the MSSM remains viable, as we will discuss in this paper.
The questions arise, whether, and if so by how much, the MSSM can improve the theoretical description of the experimental data compared to the SM, and which parts of the MSSM parameter space are favored. In a previous analysis [19] we analyzed these questions within the MSSM. We performed a scan over the seven most relevant parameters for MSSM Higgs boson phenomenology, taking into account the data up to July 2012, which showed in particular some enhancement in the measured rate for . We found that both the light and the heavy Higgs case provided a good fit to the data. In particular, the MSSM light Higgs case gave a better fit than the SM when the data in the channel and lowenergy data was included.
The situation has changed in several respects with the release of additional Higgs data by the ATLAS and CMS Collaborations [46]. In particular, the final data obtained in the LHC Run I does not show a significant enhancement over the SM prediction in the channel anymore, and the heavy Higgs case is much more restricted due to light charged Higgs boson searches. The main aim of the present paper is to study the MSSM Higgs sector in full detail taking into account the current experimental data and in particular the final LHC Run I results, and to propose paths towards a complete exploration of the heavy Higgs case at the LHC in the ongoing Run II. We incorporate the available measurements of the Higgs boson mass and signal strengths, as well as measurements of the relevant lowenergy observables. Furthermore we take into account all relevant constraints from direct Higgs and supersymmetric (SUSY) particle searches. We investigate whether the MSSM can still provide a good theoretical description of the current experimental data, and which parts of the parameter space of the MSSM are favored. Within the light Higgs case we analyze the situation with very large (decoupling), as well as for small/moderate (alignment without decoupling). We also investigate the feasibility of the heavy Higgs case and define new benchmark scenarios in which this possibility is realized, in agreement with all current Higgs constraints.
The paper is organized as follows. We employ the phenomenological MSSM with 8 parameters (pMSSM 8), which is introduced in detail in Sect. 2. In this section, we also expand upon the theoretical background of the two possible limits that lead to alignment in the even Higgs sector, i.e. when one of the even neutral MSSM Higgs bosons behaves like the SM Higgs boson. In particular, we outline how leading twoloop effects on the conditions for alignment can be assessed and present a brief quantitative discussion of these effects.^{2}^{2}2More details will be presented in a separate publication [47]. The parameter scan with sampling points, the techniques to achieve good coverage, as well as the considered experimental observables and constraints are described in Sect. 3. In Sect. 4 we present our results for the bestfit points and the preferred parameter regions for the light Higgs and the heavy Higgs interpretation. The effects of the Higgs mass and Higgs rates measurements, precision observables, and direct Higgs and SUSY searches are discussed, and the phenomenology of the other MSSM Higgs states is outlined. In particular, in Sect. 4.4 we propose new benchmark scenarios for the study of the heavy Higgs case, which can be probed at the LHC Run II. We conclude in Sect. 5. In Appendix A, we discuss the extent of the tuning associated with the regions of the MSSM parameter space that exhibit approximate Higgs alignment without decoupling. Finally in Appendix B, we provide tables listing the signal strength measurements from ATLAS, CMS and the Tevatron (DØ and CDF) that are included in our analysis.
2 Theoretical Background
2.1 The MSSM Higgs sector
In this section we briefly review the most important features of the MSSM Higgs sector and motivate the choice of the eight free pMSSM parameters in our scan. We provide a detailed description of the relevant MSSM parameter sectors and our notations, which remain unchanged compared to [19].
In the supersymmetric extension of the SM, an even number of Higgs multiplets consisting of pairs of Higgs doublets with opposite hypercharge is required to avoid anomalies due to the supersymmetric Higgsino partners. Consequently the MSSM employs two Higgs doublets, denoted by and , with hypercharges and , respectively. After minimizing the scalar potential, the neutral components of and acquire vacuum expectation values (vevs), and . Without loss of generality, we assume that the vevs are real and nonnegative (this can be achieved by appropriately rephasing the Higgs doublet fields). The vevs are normalized such that
(1) 
In addition, we define
(2) 
Without loss of generality, we may assume that (i.e., is nonnegative). This can always be achieved by a rephasing of one of the two Higgs doublet fields.
The twodoublet Higgs sector gives rise to five physical Higgs states. The mass eigenstates correspond to the neutral Higgs bosons , (with ) and , and the charged Higgs pair . Neglecting possible violating contributions of the softsupersymmetrybreaking terms (which can modify the neutral Higgs properties at the loop level), and are the light and heavy even Higgs bosons, and is odd.
At lowest order, the MSSM Higgs sector is fully described by and two MSSM parameters, often chosen as the odd Higgs boson mass, , and . In the MSSM at the treelevel the mass of the light even Higgs boson does not exceed . However, higher order corrections to the Higgs masses are known to be sizable and must be included, in order to be consistent with the observed Higgs signal at [3]. Particularly important are the one and twoloop contributions from top quarks and their scalar top (“stop”) partners. In order to shift the mass of up to , large radiative corrections are necessary, which require a large splitting in the stop sector and/or heavy stops. For large values of , the sbottom contributions to the radiative corrections also become sizable. The stop (sbottom) sector is governed by the soft SUSYbreaking mass parameter and ( and ), where SU(2) gauge invariance requires , the trilinear coupling () and the Higgsino mass parameter .
To achieve a good sampling of the full MSSM parameter space with points, we restrict ourselves to the eight MSSM parameters
(3) 
most relevant for phenomenology of the Higgs sector (the scan ranges will be given in Sect. 3.1), under the assumption that the third generation squark and slepton parameters are universal. That is, we take , and . Note that the soft SUSYbreaking mass parameter in the stau sector, , can significantly impact the Higgs decays as light staus can modify the loopinduced diphoton decay. is therefore taken as an independent parameter in our scans. Even though the other slepton and gaugino parameters are generally of less importance for the Higgs phenomenology, we scan over the SU(2) gaugino mass parameter as well as over the mass parameter of the first two generation sleptons, , (assumed to be equal) as these parameters are important for the lowenergy observables included in our analysis. The remaining MSSM parameters are fixed,
(4)  
(5) 
We choose relatively high values for the squark and gluino mass parameters, which have a minor impact on the Higgs sector, in order to be in agreement with the limits from direct SUSY searches. Finally, the U(1) gaugino mass parameter, , is fixed via the GUT relation
(6) 
with and . For more details on the definition of the MSSM parameters, we refer to [19].
2.2 The Higgs alignment limit
In light of the Higgs data, which indicates that the properties of the observed Higgs boson are SMlike, we seek to explore the region of the MSSM parameter space that yields a SMlike Higgs boson. In general, a SMlike Higgs boson arises if one of the neutral Higgs mass eigenstates is approximately aligned with the direction of the Higgs vev in field space. Thus, the limit of a SM Higgs boson is called the alignment limit.
To analyze the alignment limit, it is convenient to define
(7) 
where and , and there is an implicit sum over the repeated SU(2) index . For consistency of the notation, we denote the corresponding neutral Higgs vevs by and . We now define the following linear combinations of Higgs doublet fields,
(8) 
such that and , which defines the socalled Higgs basis [48, 49, 50].^{3}^{3}3Since the treelevel MSSM Higgs sector is conserving, the Higgs basis is defined up to an overall sign ambiguity, where . However, since we have adopted the convention in which is nonnegative [cf. the comment below Eq. (2)], the overall sign of the Higgs basis field is now fixed. It is straightforward to express the scalar Higgs potential in terms of the Higgs basis fields and ,
(9) 
where the most important terms of the scalar potential are highlighted above. The quartic couplings , and are linear combinations of the quartic couplings that appear in the MSSM Higgs potential expressed in terms of and . In particular, at treelevel,
(10) 
where and are the SU(2) and U(1) gauge couplings, respectively, and . Hence, the are parameters.
One can then evaluate the squaredmass matrix of the neutral even Higgs bosons, with respect to the neutral Higgs states, ,
(11) 
If were a Higgs mass eigenstate, then its treelevel couplings to SM particles would be precisely those of the SM Higgs boson. This would correspond to the exact alignment limit. To achieve a SMlike neutral Higgs state, it is sufficient for one of the neutral Higgs mass eigenstates to be approximately given by . In light of the form of the squaredmass matrix given in Eq. (11), we see that a SMlike neutral Higgs boson can arise in two different ways:

. This is the socalled decoupling limit, where is SMlike and .

. In this case is SMlike if and is SMlike if .
In particular, the even mass eigenstates are:
(12) 
where and are defined in terms of the mixing angle that diagonalizes the even Higgs squaredmass matrix when expressed in the original basis of scalar fields, . Since the SMlike Higgs must be approximately , it follows that is SMlike if [51] and is SMlike if [52]. The case of a SMlike necessarily corresponds to alignment without decoupling.
In the case of exact alignment without decoupling, , the treelevel couplings of the SMlike Higgs boson are precisely those of the Higgs boson of the Standard Model. Nevertheless, deviations from SM Higgs boson properties can arise due to two possible effects. First, there might exist new particles that enter in loops and modify the loopinduced Higgs couplings to , and . For example, if is the SMlike Higgs boson, then the charged Higgs boson mass is not significantly larger than the observed Higgs mass, in which case the charged Higgs loop can shift the oneloop induced couplings of the observed Higgs boson to and [52]. Similarly, SUSY particles can give a contribution at the looplevel to other, at the treelevel SMlike, couplings. Second, there might exist new particles with mass less that half the Higgs mass, allowing for new decay modes of the SMlike Higgs boson. An example of this possibility arises if is the SMlike Higgs boson and , in which case the decay mode is allowed. Indeed, in the exact alignment limit where , the treelevel coupling in the MSSM is given by [53]
(13) 
The possibility of alignment without decoupling has been analyzed in detail in Refs. [31, 54, 32, 55, 33, 56, 51, 52] (see also the “phobic” benchmark scenario in Ref. [57]). It was pointed out that exact alignment via can only happen through an accidental cancellation of the treelevel terms with contributions arising at the oneloop level (or higher). In this case the Higgs alignment is independent of , and . This has two phenomenological consequences. First, the remaining Higgs states can be light, which would imply good prospects for LHC searches. Second, either the light or the heavy neutral Higgs mass eigenstate can be aligned with the SM Higgs vev and thus be interpreted as the SMlike Higgs boson observed at .
The leading oneloop contributions to , and proportional to , where
(14) 
is the top quark Yukawa coupling, have been obtained in Ref. [33] in the limit (using results from Ref. [58]):
(15)  
(16)  
(17) 
where , denotes the SUSY mass scale, given by the geometric mean of the light and heavy stop masses, and
(18) 
In Eqs. (15)–(18), we have assumed for simplicity that and (as well as the gaugino mass parameters that contribute subdominantly at oneloop to the ) are real parameters. That is, we are neglecting CPviolating effects that can enter the MSSM Higgs sector via radiative corrections.
The approximate expression for given in Eq. (17) depends only on the unknown parameters , , and . Exact alignment arises when . Note that trivially occurs when or (corresponding to the vanishing of either or ). But, this choice of parameters is not relevant for phenomenology as it leads to a massless quark or quark, respectively, at treelevel. Henceforth, we assume that is nonzero and finite. In our convention, is positive with .
We can simplify the analysis of the condition by solving Eq. (15) for and inserting this result back into Eq. (17). The resulting expression for now depends on , , and the ratios,
(19) 
Using Eq. (18) to rewrite the final expression in terms of and , we obtain,
(20) 
Setting , we can identify with the mass of the observed (SMlike) Higgs boson (which may be either or depending on whether is close to 1 or 0, respectively). We can then numerically solve for for given values of and . The values of the real positive solutions of obtained by using the oneloop approximate formula given in Eq. (20) are illustrated by the contour plots shown in the three left panels of Fig. 1, where each panel corresponds to a different solution of . Note that at every point in the plane, the value of has been adjusted according to Eq. (15) such that the squaredmass of the SMlike Higgs boson in the alignment limit is given by . Taking the three left panels together, one can immediately discern the regions of zero, one, two and three positive solutions of Eq. (20), and their corresponding values. A more detailed discussion of these solutions will be presented in a separate paper [47].
It is instructive to obtain an approximate analytic expression for the value of the largest real positive solution. Assuming the following approximate alignment condition, first written in Ref. [33], is obtained,
(21) 
where denotes the (oneloop) mass of the SMlike Higgs boson obtained from Eq. (15), which could be either the light or heavy even Higgs boson. It is clear from Eq. (21) that a positive solution exists if either and , or if , and is sufficiently large such that the numerator of Eq. (21) is negative. Keeping in mind that Eq. (21) was derived under the assumption that , one easily verifies that the largest of the three roots of Eq. (20) shown in Fig. 1 always satisfies the stated conditions above. Another consequence of Eq. (21) is that by increasing the value of (in the region where ), it is possible to lower the value at which alignment occurs.
If , then Eq. (21) is no longer a good approximation. Returning to Eq. (20), we set and again assume that . We can then solve approximately for ,
(22) 
For example, in the parameter regime where and , we obtain .
The question of whether the light or the heavy even Higgs boson possesses SMlike Higgs couplings in the alignment without decoupling regime depends on the relative size of and . Combining Eqs. (16) and (17), it follows that in the limit of exact alignment where , we identify as the squared mass of the observed SMlike Higgs boson and
(23) 
We define a critical value of ,
(24) 
where and is given by Eq. (23). Furthermore, since the squaredmass of the nonSMlike even Higgs boson in the exact alignment limit, , must be positive, it then follows that the minimum value possible for the squaredmass of the odd Higgs boson is
(25) 
That is, if is sufficiently large and negative, then the minimal allowed value of is nonzero and positive.
We focus again on the parameter region in the ) plane, and compute from Eq. (23) using the value of obtained from setting in Eq. (20). This allows us to determine the value of for each point in the ) plane. The interpretation of is as follows. If , then can be identified as the SMlike Higgs boson with GeV. If , then can be identified as the SMlike Higgs boson with GeV. The corresponding contours of are exhibited in the three left panels of Fig. 2, which are in onetoone correspondence with the three left panels of Fig. 1.
As previously noted, the analysis above was based on approximate oneloop formulae given in Eqs. (15)–(17), where only the leading terms proportional to are included. In the exact alignment limit, we identify given by Eq. (15) as the squaredmass of the observed SMlike Higgs boson. However, it is well known that Eq. (15) overestimates the value of the radiatively corrected Higgs mass. Remarkably, one can obtain a significantly more accurate result simply by including the leading twoloop radiative corrections proportional to .
In Ref. [59], it was shown that the dominant part of these twoloop corrections can be obtained from the corresponding oneloop formulae with the following very simple two step prescription. First, we replace
(26) 
where GeV is the top quark mass [60], and the running top quark mass in the oneloop approximation is given by
(27) 
In our numerical analysis, we take . Second, when multiplies that threshold corrections due to stop mixing (i.e., the oneloop terms proportional to and ), then we make the replacement,
(28) 
where
(29) 
Note that the running topquark mass evaluated at includes a threshold correction proportional to that enters at the scale of supersymmetry breaking. Here, we only keep the leading contribution to the threshold correction under the assumption that (a more precise formula can be found in Appendix B of Ref. [59]). The above two step prescription can now be applied to Eqs. (15)–(17), which yields a more accurate expression for the radiatively corrected Higgs mass and the condition for exact alignment without decoupling. Details of this analysis will be presented in a forthcoming work [47].
The end results are summarized below. We have derived analogous expressions to Eqs. (20) and (23) that incorporate the leading twoloop effects at . It is convenient to introduce the following notation,
(30) 
where is the top quark mass, and
(31) 
Then, the twoloop corrected condition for the exact alignment limit corresponding to is given by,
(32) 
which supersedes Eq. (20), and the correction to Eq. (23) is given by,
(33) 
One can now define twoloop improved versions of and [cf. Eqs. (24) and (25)].
In the right panels of Figs. 1 and 2, we plot the twoloop improved versions of the corresponding oneloop results shown in the left panels. There are a few notable changes, which we now discuss. First, in our scan of the plane, we have observed numerically that there is a new solution to the alignment condition [cf. Eq. (32)] that is unrelated to the solutions found in the oneloop analysis. However, this solution always corresponds to a value of , which lies outside our region of interest. Henceforth, we simply discard this possibility. What remains are solutions that can be identified as the twoloop corrected versions of the oneloop results obtained above. The right panels of Fig. 1 exhibit the remaining real positive solutions of Eq. (32).
We can now see the effects of including the leading corrections. The regions where positive solutions to Eq. (32) exist shown in the right panels of Fig. 1 have shrunk somewhat as compared to the corresponding positive solutions to Eq. (20) shown in the left panels of Fig. 1. For example, only one positive solution for exists for large and in the twoloop approximation, whereas three positive solutions exist in the oneloop approximation. Using the values of found in the right panels of Fig. 1, one can now produce the corresponding twoloop corrected plots shown in the right panels of Fig. 2. The qualitative features of the oneloop and twoloop results are similar, after taking note of the slightly smaller regions in which positive solutions for exist in the twoloop approximation.
One new feature of the twoloop approximation not yet emphasized is that we must now carefully define the input parameters and . In the above formulae and plots we interpret these parameters as parameters. However, it is often more convenient to reexpress these parameters in terms of onshell parameters. In Ref. [59], the following expression was obtained for the onshell squark mixing parameter in terms of the squark mixing parameter , where only the leading corrections are kept,
(34) 
Since the onshell and versions of are equal at this level of approximation, we also have
(35) 
A more detailed examination of the above results, when expressed in terms of the onshell parameters, will be treated in Ref. [47].
The approximations employed in the section capture some of the most important radiative corrections relevant for analyzing the alignment limit of the MSSM. However, it is important to appreciate what has been left out. First, higherorder corrections beyond are known to be relevant (see, e.g., Ref. [61]). In particular the corrections are in magnitude roughly 20% of the corrections, and enter with a different sign, thus leading to potentially nonnegligible corrections to the approximate twoloop results obtained above. On more general grounds, the analysis of this section ultimately corresponds to a renormalization of , which governs the treelevel couplings of the Higgs boson and its departure from the alignment limit. However, radiative corrections also contribute other effects that modify Higgs production cross sections and branching ratios. It is wellknown that for , the effective lowenergy theory below the scale is a general two Higgs doublet model with the most general Higgsfermion Yukawa couplings. These include the socalled wrongHiggs couplings of the MSSM [62, 63], which ultimately are responsible for the and corrections that can significantly modify the coupling of the Higgs boson to bottom quarks and tau leptons.^{4}^{4}4For a review of these effects and a guide to the original literature, see Ref. [64]. The implication of these couplings will be briefly reviewed in Sect. 2.3. In addition, integrating out heavy SUSY particles at the scale can generate higher dimensional operators that can also modify Higgs production cross sections and branching ratios [65]. None of these effects are accounted for in the analysis presented in this section.
2.3 Implications of the wrongHiggs couplings
At treelevel, the Higgsfermion Yukawa couplings follow the TypeII pattern [66, 53] of the twoHiggs doublet model (2HDM), in which the hypercharge Higgs doublet field couples exclusively to righthanded downtype fermions and the hypercharge Higgs doublet field couples exclusively to righthanded uptype fermions. When radiative corrections are included, the socalled wrongHiggs Yukawa couplings are induced by supersymmetrybreaking effects, in which couples to righthanded uptype fermions and couples to righthanded downtype fermions. We shall denote by a generic scale that characterizes the size of supersymmetric mass parameters. In the limit where , , the radiativelycorrected Higgsquark Yukawa couplings can be summarized by an effective Lagrangian,^{5}^{5}5For simplicity, we ignore the couplings to first and second generation fermions. We also neglect weak isospin breaking effects that distinguish between the coupling of neutral and charged Higgs scalars.
(36) 
which yields a modification of the treelevel relations between , and , as follows [67, 68, 69, 70, 71, 72, 73, 74, 64]:
(37)  
(38) 
The dominant contributions to are enhanced, with . Moreover, in light of our assumption that , , it follows that is suppressed, whereas does not decouple. This nondecoupling can be explained by the fact that arises from the radiativelygenerated wrongHiggs couplings. Below the scale , the effective low energy theory is the 2HDM which contains the most general set of Higgsfermion Yukawa couplings allowed by gauge invariance, and is no longer restricted to be of TypeII [62]. Similarly, is suppressed, whereas does not decouple. However, is not enhanced and thus yields only small corrections to the Higgs boson couplings to fermions in the parameter regime of interest (i.e., where ).
In the parameter regime where , [67, 68, 69, 73, 75],
(39) 
where is the gluino mass, and are the bottom and top squark masses, respectively, and smaller electroweak corrections have been ignored. The loop integral is given by
(40) 
Note that
(41) 
and . Thus, in the limit in which all supersymmetric parameters appearing in Eq. (39) are all very large, of , we see that does not decouple, as previously advertised.
From Eq. (36) we can obtain the couplings of the physical Higgs bosons to third generation fermions. The resulting interaction Lagrangian is of the form,
(42) 
Expressions for the Higgs couplings to the third generation quarks can be found in Ref. [64]. In particular, the charged Higgs coupling to the third generation quarks is noteworthy. It is convenient to write the approximate oneloop corrected coupling in the following form,
(43) 
where .
One of the important constraints on the MSSM Higgs sector is derived from the decay rate for due to the presence of one loop diagrams involving a charged Higgs boson. At large , it is important to incorporate SUSY corrections to the charged Higgs couplings to quarks^{6}^{6}6By including the radiative corrections via Eq. (43), we are effectively incorporating the leading twoloop contributions to the decay matrix element for induced by SUSY vertex corrections. in the computation of [76]. Including the radiatively corrected and couplings using Eq. (43), suitably generalized to include intergenerational quark mixing, and taking ,
(44) 
after comparing the result obtained from the contribution of the charged Higgs loop in the MSSM, including the leading SUSY radiative corrections to the charged Higgsfermion couplings, to the corresponding results of the 2HDM with TypeII Yukawa couplings. In Eq. (44), is given by Eq. (39) and is given by [76]
(45) 
where is the mass of the SUSY partner of the lefthanded strange quark, is the – mixing angle [77], and is defined in Eq. (40). Once again, the nondecoupling behavior of is evident in the limit in which all supersymmetric parameters appearing in Eq. (45) are of . As previously emphasized, the nondecoupling properties and arise due to the wrongHiggs Yukawa couplings, and are responsible for the significance of the deviation from TypeII behavior of the twoHiggs doublet sector of the MSSM.
3 Parameter sampling, Observables and Constraints
3.1 Sampling of the parameter space
We sample the pMSSM 8 parameter space with uniformly distributed random values in the eight input parameters. Scans are performed separately for the light Higgs and heavy Higgs interpretation of the observed Higgs signal (see below for details) over the parameter ranges given in Table 1. Besides the scan parameters listed in Table 1, the remaining MSSM parameters are chosen as described in Sect. 2.1.
Light Higgs case  Heavy Higgs case  

Parameter  Minimum  Maximum  Minimum  Maximum 
[GeV]  90  1000  90  200 
1  60  1  20  
[GeV]  200  5000  200  1500 
[GeV]  200  1000  200  1000 
[GeV]  200  1000  200  1000 
[GeV]  5000  
[GeV]  
[GeV]  200  500  200  500 
In both cases, we start with