Anl-Hep-Pr-09-15 Efi-09-08 A Heavy Higgs and a Light Sneutrino NLSP in the MSSM with Enhanced SU(2) D-terms

Anibal D. Medina , Nausheen R. Shah 
and Carlos E. M. Wagner 

Department of Physics, University of California, One Shields Ave. Davis, CA 95616 , USA
Enrico Fermi Institute  and Kavli Institute for Cosmological Physics ,
University of Chicago, , 5640 S. Ellis Ave., Chicago, IL 60637, USA

HEP Division, Argonne National Laboratory, 9700 Cass Ave., Argonne, IL 60439, USA 
June 14, 2021

The Minimal Supersymmetric extension of the Standard Model provides a solution to the hierarchy problem and leads to the presence of a light Higgs. A Higgs boson with mass above the present experimental bound may only be obtained for relatively heavy third generation squarks, requiring a precise, somewhat unnatural balance between different contributions to the effective Higgs mass parameter. It was recently noticed that somewhat heavier Higgs bosons, which are naturally beyond the LEP bound, may be obtained by enhanced weak D-terms. Such contributions appear in models with an enhanced electroweak gauge symmetry, provided the supersymmetry breaking masses associated with the scalars responsible for the breakdown of the enhanced gauge symmetry group to the Standard Model one, are larger than the enhanced symmetry breaking scale. In this article we emphasize that the enhanced D-terms will not only raise the Higgs boson mass but also affect the spectrum of the non-standard Higgs bosons, sleptons and squarks, which therefore provide a natural contribution to the parameter, compensating for the negative one coming from the heavy Higgs boson. The sleptons and non-standard Higgs bosons of these models, in particular, may act in a way similar to the so-called inert Higgs doublet. The phenomenological properties of these models are emphasized and possible cosmological implications as well as collider signatures are described.

1 Introduction

The Minimal Supersymmetric Standard Model (MSSM) provides an elegant solution to the hierarchy problem of the Standard Model (SM) and in the presence of R-parity, naturally includes a good dark matter candidate. The MSSM also leads to the presence of a Higgs boson, with SM-like properties, which is naturally light, with a tree-level mass smaller than the -gauge boson mass [1, 2]. Therefore, the current experimental bound on a SM-like Higgs boson from the LEP experiment,  GeV, demands relatively large radiative corrections induced by the third generation squarks [3],[4]. Such large corrections may only be obtained by large squark masses which lead at the same time to large negative radiative corrections to the soft supersymmetry breaking Higgs mass parameter. Hence, proper electroweak symmetry breaking (EWSB) may only be obtained by fine-tuning the negative soft supersymmetry breaking and positive term contributions to the effective Higgs mass parameter.

The situation may be improved if the electroweak SM gauge group proceeds from a larger gauge structure which is spontaneously broken to the SM group at energies of a few TeV. If the supersymmetry breaking parameter of the scalars, which are associated with the breakdown of the extended gauge symmetry, is much larger than the order parameter of the gauge symmetry breakdown, the D-term of the low energy weak interactions may be enhanced. This, in turn, leads to larger values of the tree-level SM-like Higgs boson mass and reduces fine tuning [5],[6],[7].

A natural implementation of these ideas may be realized by extending the weak gauge group to the group , where the two Higgs doublets of the MSSM as well as the third generation particles are charged under one of the two groups, , while the first and second generation particles are charged under  [8]. The symmetry is eventually broken to the diagonal group that may be identified with the one associated with the SM weak interactions. Such an extension of the MSSM is anomaly free and can lead to an understanding of the hierarchy of the third generation and the lighter generation masses. For relatively large values of the gauge coupling one can get SM-like Higgs boson masses up to 300 GeV.

Such large Higgs boson masses tend to be in conflict with precision electroweak observables [9]. The model described above, provides extra contributions to these observables. On one side, there are non-universal contributions to the third generation quark and lepton couplings to the weak gauge bosons, which are induced by the mixing of the heavy gauge bosons with the SM ones. Such contributions may be minimized for large values of the vacuum expectation value (vev) of the scalars that provide the breakdown of the extended symmetry (see, for example, Ref. [10]). However, the presence of a heavy Higgs still leads to a relatively large negative contribution to the -parameter, leading to further tension with the precision electroweak observables.

In this work we emphasize that the same D-term contributions that lead to an enhancement of the Higgs mass also lead to a splitting of the left-handed super-partners of the third generation squarks and sleptons as well as the non-standard Higgs bosons. We show that the mass splitting of these doublets is naturally of the size necessary to compensate the large negative Higgs contribution, restoring agreement of the model with precision electroweak data, similar to the inert Higgs doublet models [12]. The modification of the spectrum leads to novel phenomenological properties with respect to the MSSM. It is the aim of this article to discuss these properties as well as the associated supersymmetry breaking mechanism that may be consistent with such a spectrum.

The article is organized as follows. In section 2 we review the model. In section 3 we describe the Higgs and sparticle spectrum and discuss the contributions to the -parameter. In section 4 we describe a possible realization of supersymmetry breaking that leads to a spectrum of third generation left-handed sparticles much lighter than the first and second generation ones and discuss the collider physics associated with this model. In section 5 we comment on the possible cosmological constraints. In section 6 we describe a different possibility, in which the non-standard Higgs bosons become light, while the left-handed squarks and sleptons remain heavy. We reserve section 7 for our conclusions.

2 Review of the Model

A simple way to implement the possibility of an enhanced electroweak D-term is through the enlarged weak gauge group . The two MSSM Higgs bosons and the third generation left-handed doublet super-fields are charged under but singlets under , while the lighter generations left-handed doublets are singlets under but charged under . A bidoublet, , is introduced which acquires a vev, , breaking the product group to the diagonal one, , which is identified with the SM weak group. The effective weak gauge coupling is therefore given by


where and are the and gauge couplings, respectively. For values of the weak coupling is approximately equal to . Following Ref [5], the breakdown of the enhanced gauge symmetry is governed by the superpotential


where is a gauge singlet. This leads to a potential of the form


where , is a soft supersymmetry breaking mass term and, for simplicity, we have considered all parameters to be real. There is also a contribution coming from the D-terms of the and gauge groups to the potential,


where are the generators of and, for completeness, we have added the extra third generation lepton and quark scalars, which were omitted in the analysis of Ref. [5].

For values of , the field acquires a vev along the D-flat direction, , with . Assuming that , with the vev of the SM Higgs boson, one can integrate out the heavy degrees of freedom and find the result for the enhanced D-terms




Therefore, ignoring mixing with the non-standard CP-even Higgs boson, the SM-like Higgs mass is enhanced to a value


which is the main result of Ref. [5]. For completeness, we added the possible contribution of a superpotential term


with a singlet superfield. In our analysis we shall assume that the D-terms give the dominant contribution to the tree-level Higgs mass. The term , however, may have important phenomenological implications as have been observed in several works, including Refs. [6, 11]. In our phenomenological analysis, we will consider the simple case in which .

Assuming that the value of is of the order of a few TeV, as required to minimize the non-oblique corrections to precision electroweak observables, the authors of Ref. [5] showed that the presence of the enhanced D-terms can naturally raise the Higgs mass up to values of about 250 GeV, and for large values of the coupling at the symmetry breaking scale, , values as large as 300 GeV may be obtained.

3 Sparticle Spectrum and Phenomenological Implications

An important aspect of this model that was omitted from Ref. [5] is that the presence of the D-terms will also induce additional splitting in the Higgs, squark and slepton masses. In order to understand this point, one can write the low energy D-term contributions to the effective potential in the following way


where are the doublets with non-trivial transformations under and is the antisymmetric Pauli matrix. To obtain the spectrum one should concentrate on interactions of the different particles with the Higgs fields. The first term in Eq. (9) leads to a positive contribution, to the mass of the third generation squarks and sleptons, where , and are the vevs. The second term in is the sum of the squares of the invariant combinations that couple to the corresponding quark and lepton singlets in the superpotential Yukawa terms. Therefore, it leads to negative contributions, , to the squark and slepton doublet component that couples via the Yukawa interaction with the Higgs , with .

The sparticles also receives -term contributions associated with the superpotential


In particular, the third generation squarks receive supersymmetric contributions proportional to their super-partner masses, which become particularly important in the case of the top squarks. The combination of the F-term and D-term contributions lead to the following splitting between the third generation left-handed squark and slepton mass parameters,




where  GeV is the SM Higgs boson vev and is the enhanced D-term contribution to the tree-level Higgs mass and we have ignored all SM quark and lepton masses apart from the top quark mass. For moderate to large values of , , which we will assume from now on, .

The case of the non-standard Higgs bosons should be treated separately. The charged Higgs and CP-odd states are defined as orthogonal to the corresponding charged and neutral Goldstone boson states, namely


where and are the charged Higgs and CP-odd components of the Higgs field doublets (), and for we redefine which carries the same hypercharge as .

Similar to the MSSM case, the neutral CP-odd mass is given by


where and , where and are the soft supersymmetry breaking square mass parameters. The resultant mass splitting is given by


3.1 Contributions to the -Parameter

The additional splitting described in the previous section between the masses of the Higgs bosons, sleptons and squarks can have important phenomenological implications. For instance, contrary to naive expectations, for large values of the D-term contribution to the Higgs mass, the left-handed sbottom becomes heavier than the left-handed stops. The exact stop and sbottom spectrum depends, however, on the mixing with the right-handed third generation squarks. In this section, to simplify the discussion, we will assume those mixings to be small, something that is natural for non-degenerate squarks, moderate values of and non-extreme values of .

The splitting between the upper and lower components of the left-handed doublets control their contribution to the parameter. For an doublet, with up and down mass eigenvalues and , the contribution to the -parameter is given by


where is the sine of the standard weak mixing angle .

If the ratio of the heavier doublet mass eigenstate to the lighter one is smaller than about 3, the contribution to the parameter may be approximated by [12]


where is the number of colors, and are the differences between the masses and the squared masses of the heavier and lighter components of the doublet. These contributions should be added to the ones associated with the heavy SM-like Higgs boson,


where is a Higgs mass reference value. As mentioned above, the up and down sfermion mass eigenstates are admixtures of doublet and singlet components. In the case of non-negligible mixing, the expression for , given by Eq. (18), needs to be reformulated. This turns out to be specially important for third generation sfermions. In the case of an doublet, taking into account mixing angles, the general expression for takes the form,


where and are the mixing angles for the up and down component of the doublet respectively, and are the mass eigenvalues. In the case when all masses are of the same order or we have zero mixing, the approximation used in Eq. (18) may be applied.

 Values of

Figure 1: Values of necessary to provide a good fit to electroweak precision data, for two values of the Higgs mass: GeV and GeV.

We present in Fig. 1 the necessary values of new physics contributions to the and parameters, to get agreement with precision electroweak observables at the 1  level. The values used here 111We are thankful to Jens Erler for providing us with the fit used to generate these values. include the recent measurements of  GeV and  GeV, and are consistent with the ones obtained in Ref. [9]. The precise values of and , however, depend on the observables used in the fit (see for example Ref. [13]). From now on, we will use the values displayed in Fig. 1 as our reference values.

The scalars give only a small contribution to the -parameter, hence the ellipses provide us with information about the values of . As can be seen from Fig. 1, for Higgs boson masses in the range  GeV, the necessary value of to provide a good fit to the precision electroweak observables is


where is the extra contribution to the parameter necessary to provide a good fit to the precision electroweak data with a Higgs of mass .

Before considering the implications for the sparticles and Higgs masses one should stress that the enhanced D-term contribution is obtained from a small deviation of the scalar from the singlet -direction. The triplet vev leads therefore to a contribution to the parameter


where is the triplet mass. For values of and the triplet mass necessary to significantly enhance the tree-level Higgs mass, these contributions prove to be too small to compensate for the negative Higgs mass contributions to the -parameter for GeV. Furthermore, it is clear from the numbers presented in Eq. (21) and Fig. 1, that for SM-like Higgs masses smaller than 150 GeV, the need for new physics contributions to the precision measurements, and therefore the constraints on the sparticle spectrum, become weaker. From now on, we will hence concentrate on the region  GeV, although somewhat smaller Higgs masses are still consistent with the presence of enhanced weak D-terms.

If sufficiently light, the third generation squark and sleptons, as well as the non-standard Higgs bosons can lead to large contributions to the parameter. The squark contribution is enhanced by a color factor, but is suppressed by the cancellation between the D-term and F-term contributions to the left-handed sbottom-stop splitting. Moreover, in the simplest soft supersymmetry breaking schemes, the squarks become much heavier than the sleptons and, from Eq. (18) their contributions to the -parameter are further suppressed. We shall first assume that the non-standard Higgs boson mass is a few times larger than the third generation left-handed slepton masses, something that is realized, for instance, in the simple scenario to be discussed in the following section. This means that the non-standard Higgs bosons will lead to small contributions to the -parameter compared to the slepton one.

Considering that only the sleptons contribute to the parameter, the requirement of restoring agreement with precision electroweak observables defines the allowed range of slepton masses. Using the values obtained in Fig. 1 for a Higgs mass of 150 GeV, ignoring mixing in the squark and slepton sectors and assuming that the Higgs mass receives two-loop contributions from third generation squarks with masses of about  TeV, this leads, for the lower (upper) required values of the new physics contribution to the parameter, to sneutrino and stau masses:


For a Higgs mass of 300 GeV, instead, we get a relatively heavier spectrum


The sleptons should then acquire masses of the order of a few hundred GeV, with a relatively large mass splitting, which grows for larger Higgs masses and is in the range of a few tens of GeV to more than a 100 GeV. The results are shown in Figs. 2, 3 and 4. In Fig. 3 we have also drawn a straight line with slope of . Sneutrinos below the line are potential candidates for Higgs decays.

 Range of preferred values of the stau mass [GeV] as a function of the Higgs mass [GeV].

Figure 2: Range of preferred values of the stau mass [GeV] as a function of the Higgs mass [GeV].

 Range of preferred values of the tau-sneutrino mass
[GeV] as a function of the Higgs mass [GeV]. Sneutrinos below the
black line have masses less than

Figure 3: Range of preferred values of the tau-sneutrino mass [GeV] as a function of the Higgs mass [GeV]. Sneutrinos below the black line have masses less than and therefore are potential candidates for Higgs decays.

 Range of preferred values of the stau–sneutrino mass difference [GeV] as a function of the Higgs mass [GeV].


Furthermore, there exists a lower bound on the sneutrino mass, GeV, coming from the invisible decay width of the gauge boson measured at LEP[13]. This bound, as shown in Fig. 3, is almost automatically fulfilled for sneutrino masses in the range selected by precision electroweak measurements for  GeV included in the plots.

4 Phenomenological Properties

4.1 Higgs Boson Searches

One of the most important differences of this model with the standard implementation of the MSSM is the Higgs mass range, which has an important impact on its searches. For the mass range 150 GeV  300 GeV that we are considering in this article, the most important SM-like Higgs boson search channels will be its decays into charged and neutral gauge bosons, namely


These searches will become very efficient in the first years of the LHC run [14], and therefore we expect these kind of models to be probed with the first few fb  of LHC running. Moreover, if the Higgs mass is below 190 GeV, then even the Tevatron will be able to probe these models in the coming years [15]. Indeed, the Tevatron has already excluded the existence of a SM-like Higgs boson with mass between 160 and 170 GeV at the 95% confidence level, and is expected to probe the whole range of masses,  GeV, by the end of next year.

The Higgs boson searches would change if there would be new, supersymmetric decays of the Higgs bosons. If we assume that the lightest superpartner of the SM particles is the light tau-sneutrino discussed in the last section, there is only a small region of parameters where these decays would be open, and only for masses below 190 GeV, that coincides with the range to be explored by the Tevatron collider. As can be seen from Fig. 3, for larger values of the Higgs mass, the tau-sneutrino is sufficiently heavy as to avoid any Higgs decay into light supersymmetric particles.

For Higgs boson masses below 190 GeV the sneutrinos may be light enough to allow on-shell decays of the Higgs into two sneutrinos. Moreover, the coupling of third generation sneutrinos to the Higgs boson is enhanced with respect to the one in the MSSM, due to the enhanced D-term contribution and is given by


Due to this enhanced coupling, the Higgs boson may have a significant decay branching ratio into light sneutrinos, therefore avoiding the Tevatron bounds. More quantitatively, assuming masses above the 2  threshold, the decay width for decays into two vector bosons is given by


where is the Fermi constant, is the charge of the massive gauge boson, , and is its mass. For the decay into sneutrinos, instead, the result is


For instance, for a Higgs mass  GeV and a sneutrino mass of about 70 GeV, the branching ratio of the Higgs into a pair of gauge bosons is reduced to less than half of its SM value, avoiding the current Tevatron bound. Somewhat smaller or larger values of the sneutrino masses, within the range consistent with precision measurements and smaller than a half of the Higgs mass, lead to more or less restrictive Tevatron bounds on this model, respectively.

4.2 Supersymmetric Particle Spectrum

In this section, we will work in the moderate limit, which for universal scalar masses, tend to lead to heavy non-standard Higgs bosons and is therefore close to the so-called decoupling limit in the Higgs sector. In the foregoing discussion we assumed that the mixing of left-handed and right-handed third generation sleptons is small. Wether the lightest stau is mostly left-handed or right-handed depends on the supersymmetry breaking mechanism. We will assume that is mostly left-handed while is mostly right-handed, and present a mechanism that realizes this possibility below.

The tree-level third generation Yukawa couplings are given by


As is well known, and can become comparable to in the large regime. As previously mentioned, we are interested in the moderate limit and therefore only the top quark Yukawa will be of importance. In the examples found later in the text, we take the reference value of .

We shall assume that Yukawa couplings for the first and second generation quarks and leptons are generated by adding a massive Higgs-like pair of doublets which transform under , as was suggested in [5], and work with this minimal spectrum. With this minimal spectrum, the function coefficients are given by


where and correspond to the and gauge groups, while and correspond to the hypercharge and strong interactions, respectively. The above values should be compared to the MSSM case:


This will generally upset unification of couplings [16]. Let us stress, however, that for the chosen low energy values of these couplings, the coupling becomes close to and at scales of about the standard grand unification scale, GeV.

The modified function coefficients also have consequences for the soft supersymmetry breaking parameters. For instance, assuming a common value for the gaugino mass, , at the messenger scale, the running of the Bino mass is modified, making the lightest neutralino lighter than in the MSSM for the same value of . Regarding the third generation masses, if we assume a common gaugino mass, they will be pushed to large values driven by the strong gaugino effects. Therefore, for the third generation sleptons to remain light, we need a mechanism of SUSY breaking that keeps the third generation soft scalar masses small at low energies while the strong coupling runs to large values.

We can accomplish this with a model where SUSY breaking is transmitted to the visible sector via only the gauginos. The gauge sector then does not contribute to the running of soft third generation masses. For simplicity, the input parameters for the model are: ; a universal gaugino mass for the , and gauginos; a universal scalar mass for all squarks and sleptons; soft-supersymmetry breaking parameters and for the two Higgs bosons which interact under ; and we assume positive sign() and at the messenger scale which is of the order of . The gaugino remains massless, but acquires a mass of order , together with the gauge bosons, after the breakdown of .

Lets take a look at the one-loop renormalization group equations (RGE) for the left- and right-handed soft stau masses at energy scales larger than the gauge symmetry breaking scale ,


where is given by,


In Eqs.(32) and (33) we have neglected the terms proportional to the -Yukawa coupling, which remain small unless is very large and, as stressed above, we have assumed that our symmetry breaking scheme is blind. Furthermore we take and since we have chosen a universal scalar mass at high energy, this implies that vanishes and does not run with energy. Therefore, given that the charges for left-handed sleptons are smaller than the charges of the right-handed sleptons, this naturally leads to the left-handed stau soft masses being smaller than the right-handed ones, as can be seen from Eqs.(32) and (33). This is in contrast to what happens in the MSSM [17, 18, 19], where the non-universal requirement is necessary to obtain smaller left-handed masses for the third generation sleptons. In the case of soft gaugino masses, their one-loop RGE take the form,


where, as stressed above, up to the breaking scale for the , , and gauge groups, and after the breakdown of , we get the standard MSSM result, .

The solution of the RG equations show that the soft supersymmetry breaking parameters and are approximately given by


while the low energy Bino and Wino masses are given by


The requirement of getting the appropriate stau and tau-sneutrino masses for a given value of the Higgs mass and defines the allowed parameter space in the plane. In particular, looking at Eq.(18) and (36), we notice that for a fixed Higgs mass and in the absence of stau mixing there is an ellipsoidal area in the plane where our spectrum fits electroweak precision data at a 68 % confidence level. In Fig. 5 we plot this correlation for several Higgs masses neglecting the stau mixing. For large values of , there is a lower bound of GeV coming from the LEP bound on chargino masses [20]. We see that the preferred region of parameter space is relatively thin and moves to higher soft masses as the Higgs mass increases, roughly maintaining its thickness. The red (medium light gray), blue (dark gray) and purple (medium dark gray) regions in the figure have the additional constraint of a NLSP, whereas in the green (light gray) region . The blue and purple regions instead, have the constraint that the bino is heavier than the stau, . Finally, in the blue region the stau dominant decay mode is into an on-shell and a tau-sneutrino; this does not happen in the purple region, where it decays off-shell to and a tau-sneutrino and also into an off-shell Bino and a lepton. We can see from the figure that, as expected, the region where is the NLSP becomes more prominent for smaller values of . Furthermore, for larger values of the Higgs mass, the mass difference between the stau and the tau-sneutrino is sufficiently large to allow on-shell decays into a sneutrino and a charged gauge boson in most of the parameter space.

Correlation of Correlation of Correlation of Correlation of
Figure 5: Correlation of and for different Higgs masses and . Red represents the region where is the NLSP and , blue and purple are the regions where is the NLSP and and staus decay predominantly to on shell Ws and tau sneutrinos (blue region) or to off-shell Ws and sneutrinos or off-shell binos and taus (purple region). Green is the region where is the NLSP.

We will assume in this work, as is natural if the messenger scale is somewhat smaller than the GUT scale, that the LSP is the gravitino and, as can be seen in Fig. 5 appropriate boundary conditions at high energy can be chosen such that the NLSP is the lightest tau sneutrino, . This should be compared with, for instance, the standard low scale gaugino mediated scenario, in which the right-handed staus are naturally the NLSP [21, 22, 23].

Due to our mechanism of SUSY breaking and the new big D-term contributions to third generation sleptons, there is a lower bound on the soft scalar universal mass coming from the requirement of the sneutrino to be in the right mass range to lead to agreement with precision electroweak observables. This can be seen in Fig. 5, where for example, for a Higgs mass  GeV, GeV for GeV to fulfill this requirement.

In the case of a universal gaugino mass, , at high energy, we naturally obtain that the lightest neutralino, , is mostly bino-like, while the second lightest neutralino, , is mostly wino-like. This implies that right-handed squarks mostly decay to . From Fig. 5, depending on the initial masses, and , we see that we can have either or for a small scalar mass and a moderate gaugino mass , once we take into account the D-term corrections. We also expect the left-handed first and second family squarks and sleptons to be heavier than the lightest neutralino since their masses run with and couplings respectively. With these considerations in mind, for a light sneutrino NLSP, we infer the following possible mass spectra:


which are realized in Tables 1, 2 and 3.

In order to calculate the particle spectrum at low energies for some sample points at high energies and to calculate the main decays we used SDECAY [24]. SDECAY works mainly within the MSSM and thus we had to slightly modify the RGE used in the program to make it suitable for our model. From the RG running we expect modifications to the spectrum at high energies. Furthermore SDECAY only calculates two body decays of sparticles. To understand the behavior at low energies, let us write the tree level stau mass matrix, taking into account the non-zero trilinear terms and the left-right mixing,


where and are the third generation left- and right-handed slepton soft breaking masses respectively, and . We can see that the mass eigenstates will have an admixture of left- and right-handed components, mainly due to the mixing caused by the term in Eq.(40). However, for , due to the smallness of the mass, we expect this admixture to be small. Similarly, the tau sneutrino modified mass is given by,


where .

Furthermore, minimizing the tree level Higgs potential we find the following expression for ,


where , and likewise the tree-level Higgs masses are given by,


Observe that for , the above expressions reduce to the well known MSSM ones.

4.3 Collider Signatures

The particle spectrum and the most important branching ratios for some sample points are presented in Tables 12 and 3. Table 1 presents a case of sneutrinos which are light enough to allow the decay of a Higgs into two on-shell tau-sneutrinos. Similar to the example discussed in the previous section, the Higgs decay branching ratio into a pair of ’s is reduced to a value that is less than half of the SM result, therefore avoiding the current Tevatron bounds.

As can be seen from Table 2 and 3, two body decays, , tend to be kinematically allowed and thus may be an important decay modes for the light staus. Therefore, we expect relatively hard leptons andor jets plus missing energy to be the an important signature from decays. This is very different from regular gaugino mediated SUSY breaking scenarios in the MSSM where the lightest stau tends to decay into ’s and gravitinos, and the heaviest stau, since the mass difference, is small, tends to decay into an on-shell and a Bino. Indeed, the small sneutrino-stau mass difference allows only 3-body decays, which through an off-shell , leads to soft fermions: plus missing energy [18].

Sparticle Mass[GeV] Dominant decay modes
1146 (18),  (36),  (23) ,  (23)
1047, 1050 (32) ,   (64)
1010,1007 (99)
804 (34) ,  (27) ,  (14)
644 (54) ,  (17)
644 (28) ,  (26) ,  (18)
630 (57) ,  (25)
385 (48) ,  (41)
385 (50) ,  (38)
346 (100)
337 (100)
209 (100)
218 (72) ,  (27)
178 (83) ,  (17)
Table 1: Spectrum and branching ratios for GeV, , , GeV, and GeV. Since the first and second generations are almost degenerate, we only give results for the first and third sfermion generations.
Sparticle Mass[GeV] Dominant decay modes
1564 (16.2),  (31.4),  (20) ,  (24)
1428, 1429 (32) ,   ( 64)
1374,1368 (99)
1112 (19) ,  (25) ,  (17) ,  (23)
864 (56) ,  (19)
864 (28) ,  (28) ,  (20)
852 (56) ,  (26)
551 (47) ,  (39)
551 (49) ,  (37)
486 (100)
480 (100)
300 (100)
303 (72) ,  (28)
249 (90) ,  (10)
217 (100)
Sparticle Mass[GeV] Dominant decay modes
829 (42),  (16) ,  (42)