Direct and indirect detection of higgsino-like WIMPs: concluding the story of electroweak naturalness
aa r X i v : . [ h e p - ph ] M a r Direct and indirect detection of higgsino-like WIMPs:concluding the story of electroweak naturalness
Howard Baer ∗ , Vernon Barger † and Dan Mickelson ‡ Dept. of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA Dept. of Physics, University of Wisconsin, Madison, WI 53706, USA
Abstract
Supersymmetric models which fulfill the conditions of electroweak naturalness generallycontain light higgsinos with mass not too far from m h ≃
125 GeV, while other sparticlescan be much heavier. In R -parity conserving models, the lightest neutralino is thena higgsino-like WIMP (albeit with non-negligible gaugino components), with thermalrelic density well below measured values. This leaves room for axions to function asco-dark matter particles. The local WIMP abundance is then expected to be belowstandard estimates, and direct and indirect detection rates must be accordingly rescaled.We calculate rescaled direct and indirect higgsino-like WIMP detection rates in SUSYmodels that fulfill the electroweak naturalness condition. In spite of the rescaling, we findthat ton-scale noble liquid detectors can probe the entire higgsino-like WIMP parameterspace, so that these experiments should either discover WIMPs or exclude the conceptof electroweak naturalness in R -parity conserving natural SUSY models. Prospects forspin-dependent or indirect detection are more limited due in part to the rescaling effect. ∗ Email: [email protected] † Email: [email protected] ‡ Email: [email protected]
Introduction
The recent discovery of a Higgs-like resonance by Atlas and CMS collaborations[1, 2] at m h ≃
125 GeV seemingly adds another supporting pillar to the theory of weak scale supersymmetry,since in the Minimal Supersymmetric Standard Model (MSSM)[3] we expect m h ≃ − Q ≃ × GeV within the MSSM, 2. the large value of the top quark mass isprecisely what is needed to drive electroweak symmetry breaking via radiative corrections and 3.SUSY is replete with several possible cold dark matter (CDM) candidates (neutralino/WIMP,gravitino, axino) in the form of the lightest SUSY particle (LSP).Since a variety of SUSY model parameters enter into the scalar potential of the theory, andthus contribute to the
W, Z and Higgs masses, it is widely expected that superpartners shouldexist at or around the weak scale. This mantra has been repeated in numerous talks and papersover the past decades, so we refer to it here as the story of SUSY electroweak naturalness .Indeed, the concept of naturalness may dictate to some degree when it is time to give up onweak scale supersymmetry should no signal be ultimately found[5].While the existence of a Higgs-like scalar at ∼
125 GeV is a boon for SUSY models, on thecontrary, no signal for superpartners has yet emerged at LHC. In models such as the popularmSUGRA/CMSSM[6], the Atlas and CMS collaborations[7, 8] now require m ˜ g > ∼ . m ˜ q ∼ m ˜ g and m ˜ g > ∼ m ˜ q ≫ m ˜ g . Already this fact has led some astute physicists togive up on weak scale SUSY[9], or to at least concede that weak scale SUSY is finetuned. Thus,the recent LHC limits on sparticle masses seemingly exacerbate what is known as the LittleHierarchy Problem (LHP): why is there such a disparity between the sparticle mass scale andthe electroweak scale?Before jumping to conclusions, it pays to scrutinize electroweak naturalness more closely.We can be more precise if we re-phrase the LHP in the following terms: how is it that the Z -boson mass can exist at just 91.2 GeV while gluino and squark masses are at, or even wellbeyond, the TeV scale? The answer proposed in Ref’s [10, 11, 12] is that all the individual weak scale contributions feeding mass into m Z should be not too far from m Z . The value of m Z in the MSSM is given by m Z m H d + Σ dd ) − ( m H u + Σ uu ) tan β (tan β − − µ ≃ − m H u − µ , (1)where the latter approximate equality obtains for ratio-of-Higgs vevs tan β ≡ v u /v d > ∼ uu and Σ dd terms represent the sum of various radiative corrections[12]. To bequantitative, a finetuning measure∆ EW = max i (cid:12)(cid:12)(cid:12) C i / ( m Z / (cid:12)(cid:12)(cid:12) (2)may be defined, where C i represents any of the terms on the right-hand-side of Eq. 1 ( e.g. C H u ≡ − m H u tan β/ (tan β −
1) and C µ ≡ − µ ). The finetuning measure ∆ EW enjoys several We thank Yuri Gershtein for making this point m , m / , A , tan β, µ, m A , (3)scans have found that values of ∆ EW as low as ∼
10 (corresponding to ∆ − EW ∼
10% electroweakfinetuning) could be found[10, 12]. To achieve low ∆ EW , one needs a ) | µ | ∼ m Z ∼ − b ) m H u ∼ (1 − m so that m H u is driven radiatively (via the large top-quark Yukawacoupling) to small but negative values at the weak scale and c ) moderate values of m / ∼ . − A ∼ . m are required. The large A -terms yield large mixing in the top-squark sector which simultaneously softens the radiativecorrections Σ uu (˜ t ) and Σ uu (˜ t ), while lifting the value of m h into the 125 GeV range[10]. Whilethe NUHM2 model admits values of ∆ EW even below 10, the mSUGRA/CMSSM model isconsiderably more tuned, where a minimum ∆ EW ∼
100 has been found, although typically∆ EW for mSUGRA is more like 10 − . Models with low ∆ EW < ∼
30 have been dubbed radiative natural SUSY (RNS) since the low electroweak finetuning is radiatively driven.The sparticle spectra found for RNS models with ∆
EW < ∼
30 is characterized by: • light higgsino-like f W ± and e Z , with masses ∼ −
300 GeV, • gluinos with mass m ˜ g ∼ − • top squarks with m ˜ t ∼ − m ˜ t ∼ − • first/second generation squarks and sleptons with masses m ˜ q, ˜ ℓ ∼ − m ˜ q, ˜ ℓ rangecan be pushed up to 20-30 TeV if non-universality of generations with m (1 , > m (3)is allowed.The RNS model with the above spectra yields branching fractions BF ( b → sγ ) and BF ( B s → µ + µ − ) in accord with measured values, unlike many models with lighter top squarks[14].As far as testability goes, RNS models should yield observable signals from gluino pairproduction at LHC14 with ∼
300 fb − for m ˜ g < ∼ . pp → f W ± e Z → W ± W ± + E T gives a reach in terms of m ˜ g of m ˜ g ∼ . m ˜ g can range up to ∼ ∼ −
300 GeV. A linear e + e − collider operating at √ s > ∼ | µ | can definitivelydiscover/exclude RNS models, e.g. √ s ∼ . EW < ∼ Direct and indirect higgsino detection
In this paper, we generate RNS models from the Isasugra spectrum generator[17] using thesame NUHM2 parameter space scan as utilized in Ref. [12]. We will require that the modelgenerated from each parameter set obeys the LEP2 bound that m e W > . EW <
50 (100) corresponding to better than 2% (1%) electroweak finetuning.We calculate the “standard thermal neutralino abundance” Ω std e Z h using the IsaReD[18] relicdensity subroutine. We will accept only models with Ω std e Z h < .
12 for reasons to be madeclear shortly. The relic abundance from RNS models is shown in Fig. 1. The red crosses have∆ EW <
50 whilst blue dots have ∆ EW < std e Z h ∼ .
004 for m e Z ∼
100 GeV to Ω std e Z h ∼ .
02 for m e Z ∼
300 GeV, i.e. there is typically a standard underabundance of higgsino dark matter compared to measurementfrom WMAP9[19] by a factor ranging from 3-25. There is some spread in these values aboveand below the main band from cases where µ is quite large and m / is small so that onehas instead a mixed higgsino-bino LSP state. The bulk of points above the band are alreadyexcluded as we shall see. Thus, the mainly higgsinolike neutralino by itself does not make agood CDM candidate. Additional new physics is needed to match the measured dark matterdensity.One compelling way to address the dark matter deficiency is by invoking the Peccei-Quinn-Weinberg-Wilczek solution to the strong CP problem[20] via introduction of a PQ symmetryand concommitant axions . Since we are working in SUSY models, the axion will be accompaniedby R -parity-even spin-0 saxions s and R -parity-odd spin- axinos ˜ a [21]. In gravity-mediationmodels (as assumed here), the saxion and axino are expected to have masses m s ∼ m ˜ a ∼ m / ∼ −
20 TeV[22], the same mass scale as matter scalars m in the theory. In this case,the dark matter would consist of both axions and higgsinos acting as co-dark matter particles.The relic abundance of mixed axion-neutralino CDM has been addressed in Ref’s [23, 24,25, 26]. In [26], it was found that SUSY models with a standard overabundance of dark matterare still excluded in the PQMSSM by a combination of dark matter overabundance constraints,BBN constraints and dark radiation constraints. However, SUSY models with a standardunderabundance of neutralinos are still allowed over large ranges of PQMSSM parameters. Formodels with a standard underabundance, then thermal production and decay of axinos in theearly universe augments the neutralino abundance, sometimes by too much, other times notenough: the former case would be excluded whilst in the latter case, the remaining abundanceis made up of relic axions produced through the usual vacuum misalignment mechanism. Inaddition, for large values of PQ breaking scale f a ∼ − GeV, then saxions can beproduced at large rates via coherent oscillations. The saxions can augment the neutralinoabundance by decaying to SUSY particles ( e.g. s → ˜ g ˜ g ), or they can dilute all relics if theydecay after freezeout into SM particles. Saxions may also decay into axion pairs s → aa leadingto production of dark radiation[27]. From the PQMSSM scans in Ref. [26], it is found thatin the case where s → aa branching fraction is at all substantial, then entropy dilution is The standard thermal abundance refers to the neutralino density derived from assuming neutralinos inthermal equilibrium at high temperature followed by freeze-out due to the Universe’s expansion. −3 −2 −1 Ω h m(higgsino) (GeV) ∆ EW <100 ∆ EW <50 Ω h =0.11 Figure 1: Plot of standard thermal neutralino abundance Ω std e Z h versus m ( higgsino ) from ascan over NUHM2 parameter space with ∆ EW <
50 (red crosses) and ∆ EW <
100 (blue dots).Green points are excluded by current direct/indirect WIMP search experiments. We also showthe central value of Ω
CDM h from WMAP9. 4 lways accompanied by a violation of either BBN or dark radiation constraints (parametrizedby ∆ N eff > ∼ . N eff is the effective number of additional neutrinos beyond the SMvalue). Thus, the scans over PQMSSM parameter space in Ref. [26] find that the standardunderabundance can be augmented by any factor leading to Ω std e Z h < Ω e Z h < .
11, but notdiminished without violating BBN or DR constraints. Models with too much CDM production,or models which violate BBN or dark radiation constraints would be excluded. The upshot isthat in RNS models, for any particular parameter set, we expect the relic higgsino abundance tolie somewhere between the standard value Ω std e Z h (which would correspond to axion domination)up to the measured value 0 .
11, in which case CDM would be higgsino-dominated. The questionthen arises: what are the prospects for direct/indirect detection of relic higgsinos in WIMPdetection experiments?In Fig. 2, we show the spin-independent higgsino-proton scattering rate in pb as calculatedusing IsaReS[28]. The result is rescaled by a factor ξ = Ω std e Z h / .
11 to account for the fact thatthe local relic abundance might be far less than the usually assumed value ρ local ≃ . ,as suggested long ago by Bottino et al. [29] (the remainder would be composed of axions). Thehiggsino-like WIMP in our case scatters from quarks and gluons mainly via h exchange. The e Z − e Z − h coupling involves a product of both higgsino and gaugino components. In thecase of RNS models, the e Z is mainly higgsino-like, but since m / is bounded from above bynaturalness, the e Z contains enough gaugino component that the coupling is never small: inthe notation of Ref. [3] L ∋ − X h e Z e Z h (4)where X h = − (cid:16) v (1)2 sin α − v (1)1 cos α (cid:17) (cid:16) gv (1)3 − g ′ v (1)4 (cid:17) , (5)and where v (1)1 and v (1)2 are the higgsino components and v (1)3 and v (1)4 are the gaugino compo-nents of the lightest neutralino, α is the Higgs mixing angle and g and g ′ are SU (2) L and U (1) Y gauge couplings. Thus, for SUSY models with low ∆ EW < ∼ − ξ .From the Figure, we see that the current reach from 225 live-days of Xe-100 running[30]already bites into a significant spread of parameter points. The excluded points are coloredgreen. The projected reach of the LUX 300 kg detector[31] is also shown by the black-dashedcontour, which should explore roughly half the allowed RNS points. The reach of SuperCDMS150 kg detector[32] is shown as the purple-dashed contour. The projected reach of Xe-1-ton,a ton scale liquid Xenon detector, is also shown[33]. Our main result is this: the projectedXe-1-ton detector, or other comparable noble liquid detectors, can make a complete explorationof the RNS parameter space. Since deployment of the Xe-1-ton detector is imminent, it seemsdirect WIMP search experiments may either verify or exclude RNS models in the near future,thus bringing the story of electroweak naturalness to a conclusion!While the above result is indeed compelling, it is not a theorem, and is subject to severalreasonable assumptions. These include the assumption of R -parity conservation with a higgsino-like co-DM particle, along with the assumption of non-negligible s → aa decay rate. If the s → aa decay rate is somehow forbidden or highly suppressed, then s → gg (gluons) may bedominant, in which case substantial entropy dilution can still occur[24, 25].5
00 150 200 250 300 35010 −48 −47 −46 −45 −44 −43 −42 −41 ξ σ S I ( ˜ Z p )( c m ) m(higgsino) (GeV) ∆ EW <100 ∆ EW <50Xe−100LUX300SuperCDMS150kgXe−1Ton Figure 2: Plot of rescaled higgsino-like WIMP spin-independent direct detection rate ξσ SI ( e Z p )versus m ( higgsino ) from a scan over NUHM2 parameter space with ∆ EW <
50 (red crosses)and ∆ EW <
100 (blue dots). Green points are excluded by current direct/indirect WIMPsearch experiments. We also show the current reach from Xe -100 experiment, and projectedreaches of LUX, SuperCDMS 150 kg and Xe -1 ton.6
00 150 200 250 300 35010 −43 −42 −41 −40 −39 −38 −37 m(higgsino) (GeV) ξ σ S D ( ˜ Z p )( c m ) ∆ EW <100 ∆ EW <50COUPP Figure 3: Plot of rescaled spin-dependent higgsino-like WIMP detection rate ξσ SD ( e Z p ) versus m ( higgsino ) from a scan over NUHM2 parameter space with ∆ EW <
50 (red crosses) and∆ EW <
100 (blue dots). Green points are excluded by current direct/indirect WIMP searchexperiments. We also show current reach from the COUPP detector.An alternative method for rescuing theories with an underabundance of WIMPs is to hy-pothesize the existence of some scalar field (such as a modulus field from string theory) whichcan be produced via coherent oscillations, and which can engage in late decays injecting ei-ther more WIMPs (thus increasing the WIMP abundance) or entropy (thus decreasing theabundance[34]). The resulting abundance just depends on two parameters: the scalar fielddecay temperature and the branching fraction into SUSY particles[35, 36, 37, 38]. In our case,with a higgsino-like WIMP underabundance, the decaying scalar field would increase the hig-gsino abundance to its measured value, and the rescaling factor ξ = 1. For this possibility, theresults of Ref. [12] would apply.In Fig. 3, we show the rescaled spin-dependent higgsino-proton scattering cross section ξσ SD ( e Z p ). Here we show recent limits from the COUPP[39] detector. Current limits are stillabout an order of magnitude away from reaching the predicted rates from RNS models.To compare against the current reach of IceCube[40], we show in Fig. 4 the value of σ SD ( e Z p ), with no rescaling factor. Here, the IceCube rates should not be rescaled since theIceCube detection depends on whether the Sun has equilibrated its core abundance betweencapture rate and annihilation rate[41]. Typically for the Sun, equilibration is reached for almost7
00 150 200 250 300 35010 −43 −42 −41 −40 −39 −38 −37 m(higgsino) (GeV) σ S D ( ˜ Z p )( c m ) ∆ EW <100 ∆ EW <50ICECUBE Figure 4: Plot of (non-rescaled) spin-dependent higgsino-like WIMP detection rate σ SD ( e Z p )versus m ( higgsino ) from a scan over NUHM2 parameter space with ∆ EW <
50 (red crosses)and ∆ EW <
100 (blue dots). Green points are excluded by current direct/indirect WIMPsearch experiments. We also show current reach from IceCube.all of SUSY parameter space[42]. The IceCube limits have entered the RNS parameter spaceand excluded the largest values of σ SD ( e Z p ).In Fig. 5, we show the rescaled thermally-averaged neutralino annihilation cross sectiontimes relative velocity in the limit as v → ξ h σv i| v → . This quantity enters into the rateexpected from WIMP halo annihilations into γ , e + , ¯ p or ¯ d . The rescaling appears as ξ sincelimits depend on the square of the local WIMP abundance[43]. Anomalies in the positron and γ spectra have been reported, although the former may be attributed to pulsars[44], while thelatter 130 GeV gamma line may be instrumental. Soon to be released results from AMS-02should clarify the situation. On the plot, we show the limit derived from the Fermi LAT gammaray observatory[45] for WIMP annihilations into W W . These limits have not yet reached theRNS parameter space due in part to the squared rescaling factor.8 −30 −29 −28 −27 −26 −25 −24 −23 m(higgsino) (GeV) ξ < σ v > ( c m / s ) ∆ EW <100 ∆ EW <50FERMI Figure 5: Plot of rescaled ξ h σv i| v → versus m ( higgsino ) from a scan over NUHM2 parameterspace with ∆ EW <
50 (red crosses) and ∆ EW <
100 (blue dots). Green points are excludedby current direct/indirect WIMP search experiments. We also show current reach from FermiLAT, Ref. [45]. 9
Conclusions:
In conclusion, we have found that SUSY models can elude the Little Hierarchy Problem inthe guise of radiative natural SUSY models which feature a mainly higgsino-like neutralinothat may act as a co-dark-matter particle along with the axion. While LHC can explore aportion of RNS parameter space, an ILC can probe it entirely, although such a machine maybe well over a decade in the future. However, current WIMP direct detection experimentsare biting into the meat of RNS parameter space, even if we take into account rescaling ofthe local abundance due to the fact that higgsinos may make up only a portion of the darkmatter. LUX and ultimately SuperCDMS will probe further. The soon-to-be-deployed Xe-1-ton noble liquid detector should be able to completely explore the entire RNS parameterspace (as shown in Fig. 2), thus either discovering a higgsino-like WIMP or rejecting the storyof SUSY electroweak naturalness. Complementary signals from spin-dependent and indirectWIMP detection channels are less likely since these are usually suppressed by the reduced localWIMP density which is expected from models of mixed dark matter.
Acknowledgments
We thank K. J. Bae, Y. Gershtein, P. Huang, A. Lessa, A. Mustafayev and X. Tata for dis-cussions. This work was supported in part by the US Department of Energy, Office of HighEnergy Physics.
References [1] G. Aad et al. [ATLAS Collaboration],
Phys. Lett.
B 716 (2012) 1.[2] S. Chatrchyan et al. [CMS Collaboration],
Phys. Lett.
B 716 (2012) 30.[3] H. Baer and X. Tata,
Weak Scale Supersymmetry: From Superfields to Scattering Events , (Cam-bridge University Press, 2006).[4] M. S. Carena and H. E. Haber,
Prog. Part. Nucl. Phys. (2003) 63 [hep-ph/0208209].[5] For a recent review, see e.g. J. L. Feng, arXiv:1302.6587 [hep-ph].[6] A. Chamseddine, R. Arnowitt and P. Nath,
Phys. Rev. Lett. (1982) 970; R. Barbieri, S. Ferraraand C. Savoy, Phys. Lett.
B 119 (1982) 343; N. Ohta,
Prog. Theor. Phys. (1983) 542; L. Hall,J. Lykken and S. Weinberg, Phys. Rev.
D 27 (1983) 2359; for a recent review, see R. Arnowitt,A. H. Chamseddine and P. Nath, Int. J. Mod. Phys. A (2012) 1230028.[7] G. Aad et al. (ATLAS collaboration), Phys. Lett.
B 710 (2012) 67.[8] S. Chatrchyan et al. (CMS collaboration),
Phys. Rev. Lett. (2011) 221804.[9] See e.g.
M. Shifman, Mod. Phys. Lett. A (2012) 1230043.[10] H. Baer, V. Barger, P. Huang, A. Mustafayev and X. Tata, Phys. Rev. Lett. (2012) 161802.
11] H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, arXiv:1210.3019.[12] H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev and X. Tata, arXiv:1212.2655 [hep-ph].[13] J. Ellis, K. Olive and Y. Santoso,
Phys. Lett.
B 539 (2002) 107; J. Ellis, T. Falk, K. Olive andY. Santoso,
Nucl. Phys.
B 652 (2003) 259; H. Baer, A. Mustafayev, S. Profumo, A. Belyaev andX. Tata,
J. High Energy Phys. (2005) 065.[14] H. Baer, V. Barger, P. Huang and X. Tata,
J. High Energy Phys. (2012) 109.[15] H. Baer, V. Barger, A. Lessa and X. Tata,
Phys. Rev.
D 86 (2012) 117701.[16] H. Baer, V. Barger, P. Huang, D. Mickelson, A. Mustafayev, W. Sreethawong and X. Tata,arXiv:1302.5816 [hep-ph].[17] H. Baer, C. H. Chen, R. Munroe, F. Paige and X. Tata,
Phys. Rev.
D 51 (1995) 1046; H. Baer,J. Ferrandis, S. Kraml and W. Porod,
Phys. Rev.
D 73 (2006) 015010.[18] IsaReD, see H. Baer, C. Balazs and A. Belyaev,
J. High Energy Phys. (2002) 042.[19] G. Hinshaw, D. Larson, E. Komatsu, D. N. Spergel, C. L. Bennett, J. Dunkley, M. R. Nolta andM. Halpern et al. , arXiv:1212.5226 .[20] R. Peccei and H. Quinn,
Phys. Rev. Lett. (1977) 1440 and Phys. Rev.
D 16 (1977) 1791; S.Weinberg,
Phys. Rev. Lett. (1978) 223; F. Wilczek, Phys. Rev. Lett. (1978) 279.[21] H. P. Nilles and S. Raby, Nucl. Phys. B (1982) 102; J. E. Kim, Phys. Lett. B (1984)378; J. E. Kim and H. P. Nilles, Phys. Lett. B (1984) 150; for a review, see e.g. F. D. Steffen,Eur. Phys. J. C (2009) 557.[22] P. Moxhay and K. Yamamoto, Phys. Lett.
B 151 (1985) 363; E. Chun and A. Lukas,
Phys. Lett.
B 357 (1995) 43; J. E. Kim, M.-S. Seo, Nucl.Phys.
B864 (2012) 296 ; C. Cheung, G. Elor andL. J. Hall, Phys. Rev. D (2012) 015008.[23] K-Y. Choi, J. E. Kim, H. M. Lee and O. Seto, Phys. Rev.
D 77 (2008) 123501.[24] H. Baer, A. Lessa, S. Rajagopalan and W. Sreethawong, JCAP (2011) 031.[25] H. Baer, A. Lessa and W. Sreethawong, JCAP (2012) 036.[26] K. J. Bae, H. Baer and A. Lessa, arXiv:1301.7428 [hep-ph].[27] See e.g.
V. Barger, J. P. Kneller, H. -S. Lee, D. Marfatia and G. Steigman, Phys. Lett. B (2003) 8; K. Ichikawa, M. Kawasaki, K. Nakayama, M. Senami and F. Takahashi, JCAP (2007) 008; J. Hasenkamp, Phys. Lett. B (2012) 121; J. Hasenkamp and J. Kersten,arXiv:1212.4160; D. Hooper, F. Queiroz and N. Gnedin,
Phys. Rev.
D 85 (2012) 063513; E. DiValentino, S. Galli, M. Lattanzi, A. Melchiorri, P. Natoli, L. Pagano and N. Said, arXiv:1301.7343[astro-ph.CO]; M. Cicoli, J. P. Conlon and F. Quevedo, arXiv:1208.3562 [hep-ph]; P. Graf andF. D. Steffen, arXiv:1208.2951 and arXiv:1302.2143 [hep-ph].[28] H. Baer, C. Balazs, A. Belyaev and J. O’Farrill, JCAP (2003) 007.
29] A. Bottino, F. Donato, N. Fornengo and S. Scopel, Phys. Rev. D (2001) 125003.[30] E. Aprile et al. [XENON100 Collaboration], Phys. Rev. Lett. (2012) 181301.[31] D. S. Akerib et al. [LUX Collaboration], Nuclear Inst. Methods in Physics Research A704 (2013)111-126 [arXiv:1211.3788 [physics.ins-det]].[32] P. L. Brink et al. [CDMS-II Collaboration], eConf C (2004) 2529 [astro-ph/0503583].[33] E. Aprile [XENON1T Collaboration], arXiv:1206.6288.[34] T. Moroi and L. Randall,
Nucl. Phys.
B 570 (2000) 455.[35] G. Gelmini and P. Gondolo,
Phys. Rev.
D 74 (2006) 023510; G. Gelmini, P. Gondolo, A. Sol-datenko and C. Yaguna,
Phys. Rev.
D 74 (2006) 083514.[36] M. Endo and F. Takahashi, Phys. Rev. D (2006) 063502.[37] B. Acharya, G. Kane, S. Watson and P. Kumar, Phys. Rev.
D 80 (2009) 083529.[38] R. Allahverdi, B. Dutta and K. Sinha, Phys. Rev. D (2012) 095016; R. Allahverdi, B. Duttaand K. Sinha, arXiv:1212.6948 [hep-ph].[39] E. Behnke et al. [COUPP Collaboration], Phys. Rev. D (2012) 052001.[40] R. Abbasi et al. (IceCube collaboration), Phys. Rev.
D 85 (2012) 042002.[41] G. Jungman, M. Kamionkowski and K. Griest, Phys. Rept. (1996) 195.[42] V. Niro, A. Bottino, N. Fornengo and S. Scopel, Phys. Rev. D (2009) 095019.[43] A. Bottino, F. Donato, N. Fornengo and P. Salati, Phys. Rev. D (2005) 083518.[44] V. Barger, Y. Gao, W. Y. Keung, D. Marfatia and G. Shaughnessy, Phys. Lett. B (2009)283 ; S. Profumo, Central Eur. J. Phys. (2011) 1.[45] M. Ackermann et al. (Fermi Collaboration), Phys. Rev. Lett. (2011) 241302; A. Geringer-Sameth and S. M. Koushiappas,
Phys. Rev. Lett. (2011) 241303.(2011) 241303.