Abstract
We study a specific SUGRA model with nonuniversal gaugino masses
as an alternative to the minimal SUGRA model in the context of
supersymmetric dark matter.
The lightest supersymmetric particle
in this model comes out to be a Higgsino dominated
instead of a bino dominated lightest neutralino.
The thermal relic density of this Higgsino dark matter is somewhat lower than
the cosmologically favoured range, which means it may be only a subdominant
component of the cold dark matter. Nonetheless, it predicts favourable
rates of indirect detection, which can be seen in squarekm size neutrino
telescopes.
PACS: 13.40.Em, 04.65.+e, 14.60.Ef, 14.80.Ly
TIFR/TH/0310
Higgsino Dark Matter in a SUGRA Model with Nonuniversal Gaugino Masses
Utpal Chattopadhyay and D.P. Roy Department of Theoretical Physics, Indian Association for the Cultivation of Science, Raja S.C. Mullick Road, Kolkata 700032, India
Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
1 Introduction
The lightest supersymmetric particle (LSP) in the standard Rparity conserving supersymmetric model is the leading particle physics candidate for the dark matter (DM) of the universe [1]. The most popular supersymmetry (SUSY) breaking model is the minimal supergravity (SUGRA) model having universal scalar, gaugino masses and trilinear couplings at the GUT scale. Over most of the parameter space of this model the LSP is dominantly a bino () which does not couple to W or Zboson. Hence they can only pairannihilate via the exchange of superparticles like squarks or sleptons, . The experimental limits on these particle masses, and [2], imply a rather slow rate of pair annihilation. Consequently, the model predicts an overabundance of the DM relic density over most of the parameter space [3]. This has led to several recent works, extending the SUSY DM investigations to nonminimal SUGRA models [ReferencesReferences]. While many of them explore models with nonuniversal scalar masses, we shall concentrate here on nonuniversal gaugino mass models. In particular, we shall focus on a model leading generically to a Higgsinolike LSP. Because of its unsuppressed coupling to W and Z bosons the annihilation rates via schannel Zboson and tchannel Higgsino exchanges are large. Besides, there is a near degeneracy of the lighter neutralinos and lightest chargino masses in this case,
(1) 
where is the supersymmetric Higgsino mass parameter. This leads to large coannihilation cross sections [8]. Consequently, the Higgsino DM density falls below the cosmologically favoured range [9],
(2) 
where the lower limit corresponds to the galactic density of DM () from rotation curves. Thus the Higgsino DM can only be a subdominant component of the galactic DM density. However, its large coupling to Z implies a large rate of capture inside the Sun. Hence, the model predicts a sizable indirect detection rate of Higgsino DM via high energy neutrinos coming from their pair annihilation in the solar core. This is much larger than the minimal SUGRA model prediction and should be detectable at the future neutrino telescopes, as shown below.
2 NonUniversal Gaugino Mass Model
SUGRA model with nonuniversal gaugino masses at the GUT scale have been discussed in many earlier works [10, 11, 12]. We shall only quote the main results here, focusing on the SU(5) GUT. In this model the gauge kinetic function depends on a nonsinglet chiral superfield , whose auxiliary component acquires a large vacuum expectation value (vev). Then the gaugino masses come from the following dimension five term in the Lagrangian:
(3) 
where are the , and gaugino fields i.e. the bino , the wino and the gluino respectively. Since the gauginos belong to the adjoint representation of SU(5), and can belong to any of the irreducible representations appearing in their symmetric product, i.e.
(4) 
The minimal SUGRA model assumes to be a singlet, which implies equal gaugino masses at the GUT scale. On the other hand if belongs to one of the nonsinglet representations of , then these gaugino masses are unequal but related to one another via the representation invariants. Thus the three gaugino masses at the GUT scale in a given representation are determined in terms of a single SUSY breaking mass parameter by
(5) 
where , , and . The resulting ratios of ’s for each are listed in Table 1.
1  1  1  1 

24  1  
75  1  3  
200  1  2  10 
Of course in general the gauge kinetic function can involve several chiral superfields belonging to different representations of which gives us the freedom to vary mass ratios continuously. We shall explore such a possibility in a future work. But let us concentrate here on the representations 1, 24, 75 and 200 individually. While the singlet representation corresponds to universal gaugino masses, each of the nonsinglet representations corresponds to definite mass ratios and is therefore as predictive as the former.
These nonuniversal gaugino mass models are known to be consistent with the observed universality of the gauge couplings at the GUT scale [References–References]
(6) 
Since the gaugino masses evolve like the gauge couplings at one loop level of the renormalisation group equations (RGE), the three gaugino masses at the electroweak (EW) scale are proportional to the corresponding gauge couplings, i.e.
(7) 
For simplicity we shall assume a universal SUSY breaking scalar mass at the GUT scale. Then the corresponding scalar masses at the EW scale are given by the renormalisation group evolution formulae [14]. A very important SUSY breaking mass parameter at this scale is , as it appears in the EW symmetry breaking condition,
(8) 
where the last equality holds for the 5 region, which is favoured by the Higgs mass limit from LEP [2]. Expressing at the right hand side in terms of the GUT scale mass parameters at a representative value of gives [14, 15]
(9)  
neglecting the contribution from the trilinear coupling term at the GUT scale. Moreover, the coefficients vary rather mildly over the moderate region. Although we shall use exact numerical solutions to the twoloop RGE, two points are worth noting from this simple equation.
Firstly, eq.(9) gives a measure of finetuning from the required degree of cancellation between the dominant terms and to give the right EW scale . The LEP limit on the lightest chargino mass, [2] implies
(10) 
while eq.(9) implies
(11) 
Thus for the universal gaugino mass case of mSUGRA eqs.(7), (10) and (11) imply finetuning at least at the level of [16]. On the other hand one sees from these equations that the finetuning problem is significantly alleviated in the nonuniversal models with and 200, corresponding to and 2 respectively [17].
Secondly, the universal gaugino mass model corresponds to , which implies that the lighter chargino and neutralinos are dominantly gauginos with hierarchical masses i.e. and . There is however a narrow strip of very large region where the first term of eq.(9) pushes down towards the LEP limit as given in eq.(10). This is the so called focus point region [18], where the lighter chargino and neutralinos are mixed Higgsinogaugino states. But, over the bulk of the parameter space the LSP is dominantly a , which leads to an overabundance of the DM relic density, as discussed earlier. One expects from Table 1 a similar result for the model. In fact it predicts a larger hierarchy between the and masses, and . Consequently the LSP is completely dominated by and can be relatively light. The SUSY DM phenomenology for this case has been discussed recently in Ref. [6, 7, 19]. In contrast we see from eqs.(7), (11) and Table 1 that the model predict the opposite hierarchy , while the model has . Thus the lighter chargino and neutralino states are Higgsino dominated and roughly degenerate (eq.(1)) over the bulk of the parameter space for both and 200 models. This leads to a DM relic density somewhat below the cosmologically favoured range (eq.(2)). We should mention here that unlike the case of mSUGRA, there is no possibility of having stau coannihilations in the and the models. This is related to staus being significantly heavier than in these scenarios for all values of . This in fact originates from the gauge sector running of the slepton RGEs due to the specific gaugino mass nonuniversalities.
It is for the above reason that the Higgsino DM phenomenology of the nonuniversal SUGRA models, corresponding to and 200 have not been explored in detail so far. We feel that this is important for two reasons: (i) Even though the Higgsino may be a subdominant component of the galactic DM density, its large coupling to boson implies large rate of capture inside the Sun. Hence the model predicts a sizable indirect detection rate via high energy neutrinos coming from their pair annihilation inside the sun. Even after rescaling by the low DM density factor the indirect detection rate comes out to be larger than the minimal SUGRA predictions [20]. (ii) It is possible that the thermal relic density of the Higgsino DM is enhanced by either a modification of the freezeout temperature of the standard cosmological model due to a quintessence field as suggested in Ref.[21] or by nonthermal production mechanisms of the type suggested in Ref.[22]. In that case it can be the dominant component of the galactic DM density. Therefore we have computed the indirect and direct detection rates both with and without rescaling.
3 Higgsino Dark Matter in the n=200 SUGRA Model
We shall concentrate on the nonuniversal SUGRA model corresponding to because it can generate radiative electroweak symmetry breaking (EWSB) over a much wider range of parameters compared to the case, the latter being restricted to have small solutions only. Fig. 1 shows the allowed regions in the plane for 5, 10, 30 and 50. The area marked I at the top is disallowed because falls below the LEP limit (eq.10) and then becomes negative, signalling the absence of EWSB. The area marked II at the bottom is disallowed because the Higgs potential becomes unstable at the GUT scale. We have chosen since the branch is strongly disfavoured by the branching ratio, along with the muon anomalous magnetic moment () constraint. This figure shows that the constraint to be rather mild for . The lower limit from (not shown) is even milder.
We see from the contours of in Fig. 1 that one generally has GeV in the model as anticipated. It also shows the gaugino component of the LSP,
(12) 
where
(13) 
We see that the bulk of the allowed parameter space corresponds to , which means that the LSP is dominated by the Higgsino component to more that . Finally Fig. 1 shows the contours of neutralino relic density which was computed using the micrOMEGAs of Ref. [23]. It is seen to generally lie below the lower limit of the cosmologically desirable range of eq.(2) by a factor of 2 to 4. This is due to the rapid pair annihilation processes via schannel Zboson and tchannel Higgsino exchanges, as mentioned earlier. Besides, the near degeneracy of the lighter chargino and neutralino masses (eq.1) leads to large coannihilations. In view of the mass degeneracy it is important to include radiative corrections to the and masses in the Higgsino LSP scenario [24]. We have included this using the code of Manuel Drees. But, it does not enhance the neutralino relic density significantly. It should be noted here that the dominant gaugino component of the LSP (eq.13) comes from instead of , in view of the inverted mass hierarchy in this model. Since, the winos have very similar annihilation mechanisms like the Higgsinos there is no increase in the relic density in the mixed Higgsinogaugino region ().
4 Indirect Detection Rates
Since the Zboson couples only to the Higgsino component of neutralino, the coupling is proportional to [25]. Moreover, the spin dependent force from Zexchange is known to dominate the interaction rate with the solar matter, which is predominantly Hydrogen [1]. Hence the solar capture rate of the Higgsino DM is predicted to be enormously larger than the bino DM of the minimal SUGRA model. This implies in turn an enormously higher rate of pair annihilation, , since the capture and annihilation rates balance one another at equilibrium. The high energy neutrinos coming from W(Z) decay are expected to be detected at the large area neutrino telescopes like the IceCubes [26] and the ANTARES [27] via their charged current interaction (). The resulting muons constitute the so called indirect DM detection signal. Fig. 2 shows the indirect signal rate contours over the full parameter space which was computed by using DARKSUSY of Ref. [28]. The signal contours are shown both with and without rescaling by a factor [29]. The denominator corresponds to which is the galactic DM relic density assumed in this computation. Even with rescaling one expects muon flux of 5100 over practically the full parameter space of the model. In contrast the minimal SUGRA model predicts a over the entire parameter space, except for a very narrow strip at the boundary corresponding to a larger Higgsino content in the LSP [20]. The proposed large area neutrino telescopes like IceCube and ANTARES are expected to cover a detection area of 1. The irreducible background for these experiments, coming from the high energy neutrinos produced by the cosmic ray interaction with the solar corona is estimated to be [20]. Therefore these experiments can probe a signal of , as expected over practically the full parameter space of this nonuniversal SUGRA model. It may be mentioned here that in the presence of some enhancement mechanism for the Higgsino DM relic density [21, 22], it can become the dominant component of the cold dark matter. This will enhance the indirect detection rate further, as indicated by the contours without rescaling.
5 Direct Detection Rates
For the sake of completeness we have computed the elastic scattering crosssections in this model, which determine the signal rate in direct detection experiments. Both the spindependent and the spinindependent crosssections have been computed using the DARKSUSY code [28].
The spindependent cross section is known to be dominated by Zexchange. Therefore the spindependent crosssections are much larger here compared to the minimal SUGRA model. Fig. 3 gives scatter plots of spindependent cross section against the LSP mass, both with and without rescaling for 10 and 50. Even the rescaled crosssection is 12 orders of magnitude larger than the minimal SUGRA predictions [30]. Unfortunately, the direct detection experiments are not sensitive to the spindependent crosssection as they are based on heavy nuclei. For example the UKDMC detector is only sensitive to a spindependent cross section [30], which is much above any SUSY model prediction.
The spin independent (scalar) crosssection is dominated by Higgs exchanges. Since the Higgs couplings to a pair is proportional to the product of their Higgsino and gaugino components [25], they are suppressed for both Higgsino and gaugino dominated DM. Fig. 4 gives scatter plots of the scalar crosssection with and without rescaling for 10 and 50. The upper range of the scatterplots correspond to the mixed Higgsinogaugino region () of Fig. 1, as expected. The cross sections without the rescaling factors are moderately larger than the minimal SUGRA prediction [30]. But the rescaled crosssections are similar in size to the latter. Fig. 4 also shows that a significant part of the unrescaled crosssection lies above the discovery limits of the future CDMS [31] and GENIUS [32] experiments; but the rescaled crosssections generally lie below these limits except for the mixed Higgsinogaugino region. The DAMA [33] and present CDMS limits are also shown. In other words the upcoming experiments can detect the Higgsino DM if it is the dominant component of the galactic DM, but not if it is only a subdominant component of the latter.
6 Summary
We have investigated the dark matter phenomenology of a SUGRA model with nonuniversal gaugino masses. Its gauge kinetic function is a function of a nonsinglet chiral superfield, belonging to the 200plet representation of SU(5). It is as predictive as the minimal SUGRA model and has less finetuning problem than the latter. It predicts a dominantly Higgsino LSP over the practically entire parameter space. The resulting thermal relic density of the Higgsino dark matter lies moderately below the cosmologically favoured range of eq.(2). Thus the Higgsino can only be a subleading component of the cold dark matter in the standard cosmological scenario. On the other hand its unsuppressed coupling to the Zboson implies an enhanced rate of capture by the Sun. Consequently the predicted rate of indirect detection via high energy neutrinos coming from its pairannihilation inside the Sun is much larger than the minimal SUGRA even after rescaling by the low density factor. This signal can be detected by the proposed neutrino telescopes like IceCube and ANTARES over practically the full parameter space of the model. For the direct detections the predicted rate after rescaling is rougly similar to the minimal SUGRA prediction.
We thank Manuel Drees for discussion and for the use of his radiative correction code for chargino and neutralinos.
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