Natural Dark Matter in SUSY GUTs with Non-universal Gaugino Masses
aa r X i v : . [ h e p - ph ] M a y November 3, 2018
Natural Dark Matter in SUSY GUTs with Non-universalGaugino Masses
S. F. King a, , J. P. Roberts b, and D. P. Roy c,d, a School of Physics and Astronomy, University of Southampton b Institute of Theoretical Physics, Warsaw University,00-681 Warsaw, Poland c Homi Bhabha Centre for Science Education,Tata Institute of Fundamental Research,Mumbai 400088, India d Instituto de Fisica Corpuscular, CSIC-U.de Valencia, Correos,E-46071 Valencia, Spain
Abstract
We consider neutralino dark matter within the framework of SUSY GUTswith non-universal gaugino masses. In particular we focus on the case of SU (5) with a SUSY breaking F-term in the 1, 24, 75 and 200 dimensionalrepresentations. We discuss the 24 case in some detail, and show that thebulk dark matter region cannot be accessed. We then go on to consider theadmixture of the singlet SUSY breaking F-term with one of the 24, 75 or200 dimensional F-terms, and show that in these cases it becomes possibleto access the bulk regions corresponding to low fine-tuned dark matter. Ourresults are presented in the ( M , M ) plane for fixed M and so are usefulfor considering general GUT models, as well as more general non-universalgaugino models. E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
Introduction
Supersymmetry (SUSY) at the TeV scale remains an attractive possibility for newphysics beyond the Standard Model. SUSY helps in the unification of couplingsin Grand Unified Theories (GUTs), and provides a resolution of some aspects ofthe hierarchy problem. In addition the lightest SUSY particle (LSP) may be aneutralino consisting of a linear combination of Bino, Wino and neutral Higgsinos,providing a consistent WIMP dark matter candidate [1]. For example the minimalsupersymmetric standard model (MSSM) with conserved R-parity provides suchan LSP with a mass of order the electroweak scale. Although general argumentssuggest that such a particle should provide a good dark matter candidate [2], thesuccessful regions of parameter space allowed by WMAP and collider constraintsare now tightly restricted [3]-[18].Such a restricted parameter space has lead to recent claims that supersymmetrymust be fine-tuned to fit the observed dark matter relic density [19]. This isa serious concern for supersymmetry, especially as much of the motivation forsupersymmetry arises from fine-tuning arguments in the form of its solution to thehierarchy problem. In previous work [20]-[22] we quantitatively studied the fine-tuning cost of the primary dark matter regions within the MSSM. It was found thatthe majority of dark matter regions did indeed require some degree of fine-tuning,and that this fine-tuning could be directly related to the mechanism responsible forthe annihilation of SUSY matter in the early universe that defined each region. Theone region that exhibited no fine-tuning at all was the ‘bulk region’ in which thedominant annihilation mechanism is via t-channel slepton exchange. This regioncan be accessed in models in which the gauginos have non-universal soft masses atthe GUT scale [4].These results motivate a more careful study of models that give rise to non-universalgaugino masses. In our previous work such a region was accessed by allowing all thegaugino masses to vary independently. Such an approach is very unconstrained.We would expect the gaugino masses to arise from a deeper theory such as stringconstructions, as studied in [21], [22] or in GUT models [23]-[25]. Both approachesgenerally impose specific relations between the gaugino masses at the GUT scale.In this paper we shall discuss non-universal gaugino masses in a more general waythan previously, allowing for different relative signs of gaugino masses, focusing on SU (5) GUTs as an example, although it is clear that similar effects can be achievedin other GUTs such as SO (10) or Pati-Salam. We shall show how the bulk regionmay be readily accessed in such models providing that the SUSY breaking sectorarises from a combination of an SU (5) singlet 1, together with an admixture ofone of the 24, 75 or 200 representations of SU (5). We will also show that in allcases the fine-tuning required to access such a region remains small.1he rest of the paper is set out as follows. First we review our methodologyin section 2. In section 3 we review the structure of gaugino non-universality in SU (5). In section 4 we consider the specific case where all of the gaugino massesarise from a 24 of SU (5). In section 5 we generalise this to the case where themasses arise from an admixture of the singlet representation and one of the 24, 75or 200. In section 6 we present our conclusions. The GUT structure of the theory is a structure that is imposed on the soft SUSYbreaking masses at the GUT scale, m GUT ≈ × GeV. To study the low energyphenomenology of such a model we need to run the mass spectrum down to theelectroweak scale. To do this we use the RGE code
SoftSusy [26]. This interfaceswith the MSSM package within micrOMEGAs [27]. We use this to calculate the darkmatter relic density Ω
CDM h , as well as BR ( b → sγ ) and δa µ . Not all choices of parameters are equal. After running the mass spectrum of themodel point from the GUT scale to the electroweak scale we perform a number ofchecks. A point is ruled out if it:1. doesn’t provide radiative electroweak symmetry breaking (REWSB).2. violates mass bounds on particles from the Tevatron and LEP2.3. results in a lightest supersymmetric particle (LSP) that is not the lightestneutralino.In the remaining parameter space we plot regions that fit BR ( b → sγ ) and δa µ at1 σ and 2 σ . δa µ Present measurements of the value of the anomalous magnetic moment of the muon a µ deviate from the theoretical calculation of the SM value . Taking the current There is a long running debate as to whether the calculation of the hadronic vacuum po-larisation in the Standard Model should be done with the e + e − data, or the τ . The weight of a µ ) exp − ( a µ ) SM = δa µ = (2 . ± . × − (2.1)which amounts to a 3.4 σ deviation from the Standard Model value. BR ( b → sγ )The variation of BR ( b → sγ ) from the value predicted by the Standard Modelis highly sensitive to SUSY contributions arising from charged Higgs-top loopsand chargino-stop loops. To date no deviation from the Standard Model has beendetected. We take the current world average from [29] of the BELLE [30], CLEO[31] and BaBar [32] experiments: BR ( b → sγ ) = (3 . ± . × − (2.2) Ω CDM h Evidence from the CMB and rotation curves of galaxies both point to a largeamount of cold non-baryonic dark matter in the universe. The present measure-ments [33] place the dark matter density at:Ω
CDM h = 0 . ± .
008 (2.3)For any point that lies within the 2 σ allowed region we calculate the fine-tuningand plot the resulting colour-coded point. As in [20] we follow Ellis and Olive [34] in quantifying the fine-tuning price offitting dark matter with the measure:∆ Ω a = (cid:12)(cid:12)(cid:12)(cid:12) ∂ ln (Ω CDM h ) ∂ ln ( a ) (cid:12)(cid:12)(cid:12)(cid:12) (2.4)where we take the total fine-tuning of a point to be equal to the largest individualtuning, ∆ = max(∆ a ). evidence indicates the e + e − data is more reliable and we use this in our work. Gaugino Non-universality in SU (5) In the non-universal SU (5) model [16], in addition to the singlet F-term SUSYbreaking, the gauge kinetic function can also depend on a non-singlet chiral super-field Φ, whose auxiliary F -component acquires a large vacuum expectation value(vev). In general the gaugino masses come from the following dimension five termin the Lagrangian: L = < F Φ > ij M P lanck λ i λ j (3.5)where λ , , are the U (1), SU (2) and SU (3) gaugino fields i.e. the bino ˜ B , the wino˜ W and the gluino ˜ g respectively. Since the gauginos belong to the adjoint repre-sentation of SU (5), Φ and F Φ can belong to any of the irreducible representationsappearing in their symmetric product, i.e.(24 × symm = 1 + 24 + 75 + 200 (3.6)The minimal supergravity (mSUGRA) model assumes Φ to be a singlet, whichimplies equal gaugino masses at the GUT scale. On the other hand if Φ belongsto one of the non-singlet representations of SU (5), then these gaugino masses areunequal but related to one another via the representation invariants. Thus thethree gaugino masses at the GUT scale in a given representation n are determinedin terms of a single SUSY breaking mass parameter m / by M , , = C n , , m / (3.7)where C , , = (1 , , C , , = ( − , − , C , , = ( − , ,
1) and C , , =(10 , , M i ’s for each n are listed in Table 1. Of course in n M M M − / − /
275 1 3 − n of the chiral superfield Φ.general the gauge kinetic function can involve several chiral superfields belongingto different representations of SU (5) which gives us the freedom to vary mass ra-tios continuously. In this, more general, case we can parameterise the GUT scalegaugino masses as: M , , = C n , , m n / (3.8)4here m n / is the soft gaugino mass arising from the F -term vev in the represen-tation n .These non-universal gaugino mass models are known to be consistent with theobserved universality of the gauge couplings at the GUT scale [23]-[25], [35] α = α = α = α ( ≃ /
25) (3.9)Since the gaugino masses evolve like the gauge couplings at one loop level of therenormalisation group equations (RGE), the three gaugino masses at the elec-troweak scale are proportional to the corresponding gauge couplings, i.e. M EW = ( α /α G ) M ≃ (25 / C n m n / M EW = ( α /α G ) M ≃ (25 / C n m n / M EW = ( α /α G ) M ≃ (25 / C n m n / (3.10)For simplicity we shall assume a universal SUSY breaking scalar mass m at theGUT scale. Then the corresponding scalar masses at the EW scale are given bythe renormalisation group evolution formulae [36]. We have previously seen [20] that a ratio M : M : M = 0 . M to be largewe can avoid a light Higgs while allowing M to be light enough to give a light binoneutralino and light sleptons. This enhances neutralino decay via light t-channelslepton exchange and gives access to the bulk region.From Table 1 we observe that only the 24 model predicts a mass ratio M < M .Therefore we shall explore the 24 model first. For the 24 model we have the inputparameters: a ∈ (cid:8) m , m / , A , tan β, sign( µ ) (cid:9) . where the masses are all set as in the CMSSM except for the gaugino masses whichhave the form: M = − . m / M = − . m / M = m / With this gaugino mass structure, the bino mass in the 24 for a given m / is halfof the bino mass in the CMSSM for the same m / . The bino mass also affects the5unning of the slepton masses such that lower M corresponds to a lower sleptonmass. Therefore the 24 will have lower mass sleptons than the CMSSM for a givenvalue of m and m / . Light sleptons enhance the annihilation of neutralinos viat-channel slepton exchange (giving rise to a WMAP region known as the bulkregion). Therefore we expect the bulk region to appear at larger m / than in theCMSSM and thus circumvent the Higgs mass bound.Figure 1: The parameter space for the CMSSM (top-left), the 24 model with sign( µ ) +ve(top-right) and with sign( µ ) − ve (bottom). Low m is ruled out as the ˜ τ becomes theLSP(light green). Low m / is ruled out as m h < τ − ˜ χ coannihilation strip which showscomparable degrees of tuning in all plots. To study this effect, we look at the ( m , m / ) plane in both the CMSSM and the24 in Fig. 1. The CMSSM is shown in the top-left panel, the 24 with µ positive inthe top-right panel and the 24 with µ negative is shown in the bottom-left panel.6n the CMSSM scan we can see that low m is ruled out as the stau becomeslighter than the neutralino. Low m / is ruled out as m h < σ for δa µ (green short and long dashed lines respectively) are plottedin the remaining parameter space, showing that the current measurement of δa µ favours low m and m / . Finally the region that satisfies WMAP is plotted as amulticoloured strip that runs alongside the light green region ruled out by a stauLSP. This WMAP strip is mostly red. This colour coding refers to a log measureof the fine-tuning and can be read off via the log-scale on the right hand side. Thetuning of the ˜ τ coannihilation strip agrees with our previous findings.In the second and third panels of Fig. 1 we once again display the ( m , m / )plane but this time using the 24 model’s soft gaugino masses with µ positive andnegative respectively. In both cases, low m is ruled out by a stau LSP and low m / is ruled out by a light Higgs.The δa µ and BR ( b → sγ ) values are significantly different in the 24 model thanin the CMSSM. Firstly neither 24 plot has a region that agrees with the currentmeasured value of δa µ (they both give δa µ ± O (10 − )). Secondly BR ( b → sγ )becomes an important constraint. For µ +ve, the model agrees with the measuredvalue of BR ( b → sγ ) at 1 σ for large m / ( >
700 GeV) and agrees at 2 σ for low m / . With µ − ve, only the parameter space at m >
700 GeV fits BR ( b → sγ )at 2 σ . Lower m exceeds this limit.Now consider the change in the dark matter strip. We expected to be able toaccess the bulk region in this model as we would have a lighter bino neutralinoand lighter sleptons in the 24 model than in the CMSSM. This should move thebulk region to larger values of m / and out from under the region ruled out bythe LEP2 bound on the lightest Higgs boson.Contrary to our naive expectations, though the bulk region has moved to larger m / in the 24 model, it remains ruled out. This is because the gaugino massrelations in the 24 also result in a lighter Higgs mass than the CMSSM, for thesame m , m / . The only difference between the CMSSM and the 24 model is themagnitude and sign of the M and M gaugino masses. Therefore the Higgs massmust be sensitive either to the sign difference between M , and M or the largervalue of M .First consider the effect of the relative sign between M , and M . In most RGEsthe gaugino masses appear squared, however the trilinear RGEs have the form: dA t dt = 18 π (cid:20) | Y t | A t + | Y b | A b + (cid:18) g M + 3 g M + 1315 g M (cid:19)(cid:21) (4.11)If all M i are positive, then the gauginos provide a large positive contribution tothe RGE and so help to push the trilinear negative through the running. This inturn affects the running of the Higgs mass. In the 24 case, the sign of M , are7 q − − − − − − − − − − A t ( G e V ) CMSSM M : M : M = 1 : 1 : 1GUT-24 model M : M : M = − . − . Figure 2:
Here we show the running of A t from the GUT scale value of A t = 0 to theweak scale for the point m = 100GeV, m / = 350GeV, tan β = 10, A = 0. Therunning for the CMSSM is shown in blue, the running for the 24 model is shown in red. opposite to that of M and so they reduce the contribution from the Gauginosand thus reduce the magnitude of the running, resulting in a small trilinear atthe electroweak scale. Now we note that the contribution of M , are suppressedrelative to that of M by a factor of g i , but this is partially compensated by thefact that | M | > | M | at the GUT scale. Therefore both the sign and magnitude of M (GUT) are responsible for a substantial change in the running of the trilinears.This is shown in Fig. 2.The change in the trilinear affects the running of m H u via the RGE: dm H u dt = 18 π (cid:20) | Y t | (cid:0) m Q + m U + m H u + | A t | (cid:1) − (cid:18) g | M | + 35 g | M | (cid:19)(cid:21) (4.12)A smaller top trilinear results in a smaller running of the Higgs mass and a lighterHiggs. Therefore, as the 24 model results in a smaller value of A t at all energiesbelow the GUT scale, it gives a smaller mass for the lightest Higgs than for the samemodel point in the CMSSM. This means that the LEP mass bounds for the lightestHiggs are more restrictive in the 24 model than in the CMSSM. Unfortunately, thisresults in the LEP Higgs bound ruling out the bulk region for all interesting regions8f parameter space of the 24 model. SU (5) Sectors
We have seen that neither the CMSSM, corresponding to a singlet SUSY breakingsector, nor the 24 model is capable of accessing the bulk region of neutralinoparameter space. Equally, as the 75 and 200 models have | M | > | M | , thesesectors are even worse. In this section we therefore consider the next simplestpossibility, namely that of two different SUSY breaking SU (5) representationsacting together. Indeed, once one has accepted the existence of a single 24, 75or 200 dimensional SUSY breaking sector, it seems perfectly natural to allow thestandard singlet SUSY breaking sector at the same time. In practice it may bedifficult to avoid this scenario.Therefore we shall focus on the three simplest scenarios. We take the cases of aSUSY breaking sector consisting of:A (1 + 24)B (1 + 75)C (1 + 200)If we were to extend our model to allow three or four SU (5) representations con-tributing to SUSY breaking at once, we would be able to produce any pattern ofnon-universal gaugino masses. By constraining our model to two sectors we providerestrictions on the choice of gaugino masses which makes access to the bulk regionnon-trivial, and provides insight into what ingredients are required to achieve it.Mass A (1 + 24) B (1 + 75) C (1 + 200) M m / − . m / m / − m / m / + 10 m / M m / − . m / m / + 3 m / m / + 2 m / M m / + m / m / + m / m / + m / Table 2: The gaugino mass relations for the different (1 + n ) SUSY breakingscenarios.Within these models, we have different gaugino mass relations, shown in Table. 2.By varying the soft gaugino masses m ,n / , we describe three planes in the M , , parameter space.Our aim is to access the bulk region. In [20] we found that the bulk region canbe accessed in a model with non-universal gaugino masses for m = 50 −
80 GeV.9igure 3:
The ( M , M ) plane with non-universal gaugino masses defined at the GUTscale. We take m = 70 GeV, A = 0 and tan β = 10 throughout vary M : (a) M =300 GeV, (b) M = 400 GeV, (c) M = 500 GeV, (d) M = 600 GeV. For fixed M , theallowed parameter space for each GUT mixture plotted as a line the ( M , M ) parameterspace. The WMAP allowed regions correspond to the elliptical regions in each quadrant,and are partially obscured by disallowed regions in panels (a) and (b). The BR ( b → sγ )and δa µ regions are displayed as in Fig. 1 and discussed in the text. Therefore we fix m = 70 GeV, A = 0 and tan β = 10. In Figs. 3(a)-(d) we plotthe ( M , M ) plane for increasing values of M , from 300 −
600 GeV. As M and10 can in general be either positive or negative in (1 + n ) scenarios, we allow M and M to take positive and negative values. For a given M , the gaugino massrelation of Table 2 constrain each of the (1 + n ) scenarios to a line in the ( M , M )plane. We plot these lines for each case.As each model has the singlet representation as a limit when m n / →
0, all thelines converge at a point. At this point the model is precisely that of the CMSSM,and as such is ruled out for almost all M by a ˜ τ LSP or the LEP bound onthe lightest Higgs. The other end of each line corresponds to the opposite limit m / = 0 , m n / = M .We also plot the BR ( b → sγ ) and δa µ constraints. The only region that doesn’t fit BR ( b → sγ ) within 2 σ is panel (a) at large M . The values of δa µ are insensitive to M . In the quadrant with M and M +ve we have the largest SUSY contributionto δa µ , enabling the model to fit δa µ at 1 σ . In the quadrant with M +ve, M -ve,the model can fit δa µ at 2 σ . For negative M we get a negative SUSY contribution, δa µ . If we were to plot the parameter space with µ negative, δa µ would have theopposite sign and the model would fit the observed value of δa µ for negative M .Finally, we plot the dark matter regions with colours corresponding to their fine-tuning calculated with respect to the general non-universal gaugino model withparameters: a ∈ { m , M , M , M , A , tan β } . This allows us to easily pickout the bulk region as it is ‘supernatural’ with ∆ Ω < n ) representationprovides access to the bulk region. We take these points and calculate the darkmatter fine-tuning with respect to the (1 + n ) model in question.First consider the 1 + 24 model. In Figs. 3(a), (b) the model does not access thebulk region. This fits with our results of section 4 as low m / is ruled out by alight Higgs in the 24 scenario. In Figs. 3(c), (d), we can access the bulk region witha mixture that is primarily 24. We show the corresponding fine-tuning for bothpoints in Table 3. Note that for both points m / > m / , so the gaugino massesarise predominantly from the 24.Next consider the 1 + 75 model. This model lies along the blue short dashed line.The 75 limit is not shown. This is because in the pure 75 scenario M = − M .Therefore the 75 limit lies outside the range plotted for all M that we consider.In such a limit, as studied in [14], [16], the lightest neutralino is predominantlyhiggsino. As discussed earlier we cannot access the bulk region in such a limit.This limit lies off the plots and we do not consider it further here.In the 75, M is negative. This results in two scenarios in which M < M . For asmall m / , the negative contribution results in a small, positive, M . For a slightlylarger m / , we get a small, negative M . This is shown in the plots and is thereason that the 1 + 75 accesses the bulk region twice for most values of M , once11arameter A1 A2value ∆ Ω value ∆ Ω m
70 1.43 70 0.96 m / m / A β
10 0.37 10 0.21Max 1.43 0.96 M -200 0.19 -150 0.59 M -666.7 0.21 -650 0.38 M
500 0.075 600 0.0088Table 3:
The fine-tuning for points A1 and A2 that lie within the bulk region for the(1 + 24) model. For both points m / > m / , so the gaugino masses arise predominantlyfrom the 24. In the lower section of the table we give the corresponding GUT scale M i foreach point. As the tunings plotted in Fig. 3 are calculated with respect to the parameterset a ∈ { m , M , M , M , A , tan β } , we give the relevant tunings with respect to theindividual M i for comparison. for each sign of M . We study the 7 resulting points in the bulk regions in Table 4.Note that for all points m / < m / , so the gaugino masses arise predominantlyfrom the singlet.Finally consider the case of the 1 + 200 model. The lines corresponding to thismodel are plotted in red with long dashes. As in the 1 + 75 case, in the 200 limitthe lightest neutralino is higgsino and we cannot access the bulk region. This limitlies off the plots and we do not consider it further here.As the 200 has all gaugino masses positive, and large M , we cannot access thebulk region in the 200 limit. However by combining with the singlet we can get | M | < | M | by taking a small, negative m / . This allows such a model to accessthe bulk region for positive and negative small M . We study the resulting 6 pointsin the bulk region in Table 5.In all points | m / | < | m / | so the gaugino massesarise predominantly from the 1.The hierarchy of the weak scale SUSY spectrum is fairly stable for all the pointsshown in Fig 3. Table 6 lists the neutralino, chargino and sfermion masses alongwith M , M and the Higgsino mass parameter µ for the point B5 as an example.In contrast to the CMSSM the bino is lighter than the wino by a factor of 6.Correspondingly the right and left slepton masses are split by a large factor. Thesmall value of m also ensures that the right handed sleptons are considerablylighter than the wino. Hence a large fraction of wino decay is predicted to proceedvia ˜ τ , resulting in one or more tau leptons in the final state in addition to the12arameter B1 B2 B3 B4value ∆ Ω value ∆ Ω value ∆ Ω value ∆ Ω m
70 0.91 70 1.18 70 0.86 70 1.0 m /
217 0.78 300 0.64 363 1.4 387 1.1 m / A β
10 0.13 10 0.29 10 0.14 10 0.32Max 1.4 0.91 1.4 1.5 M -200 0.66 -200 0.38 180 0.67 -180 0.51 M
467 0.086 600 0.032 473 0.096 727 0.075 M
300 0.13 400 0.071 400 0.061 500 0.047Parameter B5 B6 B7value ∆ Ω value ∆ Ω value ∆ Ω m
70 0.75 70 0.95 70 0.84 m /
450 1.8 475 1.7 530 2.0 m /
50 0.99 125 2.4 70 1.2 A β
10 0.15 10 0.32 10 0.22Max 1.8 2.4 2.0 M
200 0.80 -150 0.55 180 0.64 M
600 0.038 850 0.082 740 0.031 M
500 0.014 600 0.16 600 0.12Table 4:
The fine-tuning for points B1-7 that lie within the bulk region for the (1 + 75)model. For all points m / < m / , so the gaugino masses arise predominantly from thesinglet. In the lower section of the table we give the corresponding GUT scale M i foreach point. As the tunings plotted in Fig. 3 are calculated with respect to the parameterset a ∈ { m , M , M , M , A , tan β } , we give the relevant tunings with respect to theindividual M i for comparison. missing- E T . Though the light selectron and smuon have negligible left-handedcomponents, and so cannot take part in the wino decay, the heavier selectron andsmuon are still lighter than the wino in all points we consider. A wino decay viaa left-handed selectron/smuon would give a distinctive signal in the form of hardelectron(s)/muon(s) in addition to the missing- E T . Thus one expects a distinctiveSUSY signal from squark/gluino cascade decays at LHC containing hard isolatedleptons in addition to the missing- E T and jets.13arameter C1 C2 C3value ∆ Ω value ∆ Ω value ∆ Ω m
70 1.6 70 0.89 70 1.1 m /
467 0.11 424 1.7 576 1.4 m / -66.7 0.40 -24.4 0.93 -75.6 2.2 A β
10 0.79 10 0.25 10 0.54Max 1.6 1.7 2.2 M -200 0.19 180 0.67 -180 0.56 M
333 0.83 376 0.31 424 0.59 M
400 0.75 400 0.22 500 0.39Parameter C4 C5 C6value ∆ Ω value ∆ Ω value ∆ Ω m
70 0.78 70 0.97 70 0.86 m /
533 2.3 683 2.3 647 2.5 m / -33.3 1.3 -83.3 3.1 -46.7 1.7 A β
10 0.23 10 0.43 10 0.25Max 2.3 3.1 2.5 M
200 0.80 -150 0.59 180 0.63 M
467 0.25 517 0.49 553 0.22 M
500 0.13 600 0.20 600 0.047Table 5:
The fine-tuning for points C1-6 that lie within the bulk region for the (1 + 200)model. For all points | m / | < | m / | , so the gaugino masses arise predominantly fromthe 1. We also give the corresponding GUT scale M i for each point. As the tunings inFig. 3 are calculated with respect to the parameters a ∈ { m , M , M , M , A , tan β } ,we give the tunings with respect to M i for comparison. In previous work we found that a model with non-universal gaugino masses couldaccess the bulk region in which t-channel slepton exchange alone could account forthe observed dark matter relic density. The bulk region is an attractive prospectas it allows SUSY to account for the observed dark matter relic density withoutany appreciable fine-tuning. However, a model with entirely free gaugino massesis very unconstrained. Such non-universality must arise from a deeper structureand such structures should impose restrictions on the precise form of the gauginomasses at the GUT scale.In this paper we have considered neutralino dark matter within the framework of14article Mass (GeV)˜ χ (bino) 78.1˜ χ (wino) 457˜ χ (higgsino) 614˜ χ (higgsino) 636˜ χ +1 (wino) 461˜ χ +2 (higgsino) 635 M EW M EW M EW µ g τ τ e R , ˜ µ R e L , ˜ µ L t t b b q , ,R ∼ q , ,L ∼ The SUSY mass spectrum of point B5 from Fig. 3. This spectrum is charac-teristic of all bulk region points we have studied. We display the hierarchy and flavourof the neutralino and chargino sectors. We also display the values of the neutralino massparameters for completeness. For the squarks we take a typical squark mass rather thanlist the full squark spectrum. The exceptions are the 3rd family squarks that we listseparately. Finally, the sneutrinos are degenerate with ˜ e, ˜ µ L . SU (5) GUT model where the gaugino masses arise from different irreduciblerepresentations of the symmetric product of the adjoint representations. In partic-ular we focused on the case of SU (5) with a SUSY breaking F-term in the 1, 24, 75and 200 dimensional representations. We discussed the 24 case in some detail, andshowed that the bulk dark matter region cannot be accessed in this case. In generalif we just take the simplest case in which the gaugino masses arise from only onerepresentation, we find that as far as achieving the bulk region is concerned, thereis no advantage over the CMSSM. This is in part due to the surprising result thatthe sign and magnitude of M with respect to M has an important effect on thelightest Higgs mass through its effect on the top trilinear.We then went on to consider the case of the singlet SUSY breaking F-term com-bined with an admixture of one of the 24, 75 or 200 dimensional F-terms. Sucha scenario is natural once we allow the higher dimensional representations in ourtheory. In all these cases we showed that it becomes possible to access the bulkregions corresponding to low fine-tuned dark matter. In addition, the degree offine-tuning required to access the bulk region remains small in the GUT models.Therefore we conclude that such models can access the bulk region and naturallyaccount for the observed dark matter relic density.Finally we note that the results in Fig. 3 are presented in the ( M , M ) plane forfixed M and so are useful for considering general GUT models, as well as moregeneral non-universal gaugino models. The hierarchy of weak scale SUSY spectrumis fairly stable for all the points shown in Fig. 3. Both the right and left sleptons arelighter than the wino, implying a large leptonic BR of wino decay. This promisesa distinctive SUSY signal from squark/gluino cascade decays at LHC in the formof hard isolated leptons in addition to the missing- E T and jets. Acknowledgements
SFK would like to thank the Warsaw group for its hospitality and support underthe contract MTKD-CT-2005-029466. The work of JPR was funded under theFP6 Marie Curie contract MTKD-CT-2005-029466. The work of DPR is partlysupported by MEC grants FPA2005-01269, SAB2005-0131.
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