Dark matter particles captured in the Sun would annihilate producing a neutrino flux that could be detected at the Earth. In some channels, however, the neutrino flux lies in the MeV range and is thus undetectable at IceCube, namely when the dark matter particles annihilate into $e^+e^-$, $μ^+μ^-$ or light quarks. On the other hand, the same interaction that mediates the annihilations into light fermions also leads, via higher order effects, to the production of weak gauge bosons (and in the case of quarks also gluons) that generate a high energy neutrino flux potentially observable at IceCube. We consider in this paper tree level annihilations into a fermion-antifermion pair with the associated emission of one gauge boson and one loop annihilations into two gauge bosons, and we calculate the limits on the scattering cross section of dark matter particles with protons in scenarios where the dark matter particle couples to electrons, muons or light quarks from the non-observation of an excess of neutrino events in the direction of the Sun. We find that the limits on the spin-dependent scattering cross section are, for some scenarios, stronger than the limits from direct detection experiments.
Dark matter particles in the galactic halo can scatter off particles in celestial bodies such as stars or planets, lose energy and become gravitationally trapped. In this process, an accumulation of dark matter in the center of celestial bodies is expected, for example, at the center of the Earth. If dark matter self-annihilates into Standard Model particles, the end products of these annihilations include neutrinos. The IceCube Neutrino Observatory at the geographic South Pole can detect the resulting flux of neutrinos originating from dark matter annihilation in the center of the Earth. A se…
We present a model-independent interpretation of searches for dark matter annihilation in the Sun using an effective field theory approach. We identify a set of effective operators contributing to spin-dependent scattering of dark matter with protons in the non-relativistic limit and explore simple new physics models which would give rise to such operators. Using the limits on the spin-dependent scattering cross-section set by the IceCube collaboration in their search for dark matter annihilation in the Sun, we derive limits on effective couplings and corresponding masses of mediating particle…
The deployment of DeepCore array significantly lowers IceCube's energy threshold to about 10 GeV and enhances the sensitivity of detecting neutrinos from annihilations and decays of light dark matter. To match this experimental development, we calculate the track event rate in DeepCore array due to neutrino flux produced by annihilations and decays of galactic dark matter. We also calculate the background event rate due to atmospheric neutrino flux for evaluating the sensitivity of DeepCore array to galactic dark matter signatures. Unlike previous approaches, which set the energy threshold for…
It is assumed that heavy dark matter particles (HDMs) with a mass of O(TeV) are captured by the Sun. HDMs can decay to relativistic light dark matter particles (LDMs), which could be measured by km$^3$ neutrino telescopes (like the IceCube detector). The numbers and fluxes of expected LDMs and neutrinos were evaluated at IceCube with the $Z^{\prime}$ portal dark matter model. Based on the assumption that no events are observed at IceCube in 6 years, the corresponding upper limits on LDM fluxes were calculated at 90\% C. L.. These results indicated that LDMs could be directly detected in the O(…
Excesses on positron and electron fluxes measured by ATIC, and the PAMELA and Fermi--LAT telescopes can be explained by dark matter annihilation in our Galaxy. However, this requires large boosts on the dark matter annihilation rate. There are many possible enhancement mechanisms, such as the Sommerfeld effect or the existence of dark matter clumps in our halo. If enhancements on the dark matter annihilation cross section are taking place, the dark matter annihilation in the core of the Earth should also be enhanced. Here we use recent results from the IceCube 40-string configuration to probe …
We explore the possibility of distinguishing neutrino mass hierarchies through the neutrino signal from dark matter annihilation at neutrino telescopes. We consider a simple extension of the standard model where the neutrino masses and mixing angles are obtained via the type-II seesaw mechanism as an explicit example. We show that future extensions of IceCube neutrino telescope may detect the neutrino signal from DM annihilation at the Galactic Center and inside the Sun, and differentiate between the normal and inverted mass hierarchies, in this model.
It is assumed that heavy dark matter particles $ϕ$ with O(TeV) mass captured by the Sun may decay to relativistic light milli-charged particles (MCPs). These MCPs could be measured by the IceCube detector. The massless hidden photon model was taken for MCPs to interact with nuclei, so that the numbers and fluxes of expected MCPs and neutrinos may be evaluated at IceCube. Based on the assumption that no events are observed at IceCube in 6 years, the corresponding upper limits on MCP fluxes were calculated at 90\% C. L.. These results indicated that MCPs could be directly detected in the seconda…
We study in detail the ability of the nominal configuration of the IceCube neutrino telescope (with 80 strings) to probe the parameter space of the Constrained MSSM (CMSSM) favoured by current collider and cosmological data. Adopting conservative assumptions about the galactic halo model and the expected experiment performance, we find that IceCube has a probability between 2% and 12% of achieving a 5sigma detection of dark matter annihilation in the Sun, depending on the choice of priors for the scalar and gaugino masses and on the astrophysical assumptions. We identify the most important ann…
In models with one universal extra dimension (UED), the first Kaluza-Klein excitations of the hypercharge gauge boson, B^(1), and the neutral component of isospin gauge boson, W^3(1), are each viable dark matter candidates. In either case, such particles are predicted to accumulate in the core of the Sun, where they annihilate to generate a potentially observable flux of high energy neutrinos. In this article, we calculate the flux of neutrinos produced in this model and determine the constraints that can be placed on the UED parameter space from current IceCube data. For the case of B^(1) dar…
We study the capture, annihilation and evaporation of dark matter (DM) inside the Sun. It has been shown that the DM self-interaction can increase the DM number inside the Sun. We demonstrate that this enhancement becomes more significant in the regime of small DM mass, given a fixed DM self-interaction cross section. This leads to the enhancement of neutrino flux from DM annihilation. On the other hand, for DM mass as low as a few GeVs, not only the DM-nuclei scatterings can cause the DM evaporation, DM self-interaction also provides non-negligible contributions to this effect. Consequently, …
The 79-string IceCube search for dark matter in the Sun public data is used to test Secluded Dark Matter models. No significant excess over background is observed and constraints on the parameters of the models are derived. Moreover, the search is also used to constrain the dark photon model in the region of the parameter space with dark photon masses between 0.22 and $\sim$ 1 GeV and a kinetic mixing parameter $\varepsilon \sim 10^{-9}$, which remains unconstrained. These are the first constraints of dark photons from neutrino telescopes. It is expected that neutrino telescopes will be effici…
Dark matter decaying or annihilating into mu+mu- or tau+tau- has been proposed as an explanation for the e+e- anomalies reported by PAMELA and Fermi. Recent analyses show that IceCube, supplemented by DeepCore, will be able to significantly constrain the parameter space of decays to mu+mu-, and rule out decays to tau+tau- and annihilations to mu+mu- in less than five years of running. These analyses rely on measuring track-like events in IceCube+DeepCore from down-going nu_mu. In this paper we show that by instead measuring cascade events, which are induced by all neutrino flavors, IceCube+Dee…
We study the sensitivity of IceCube/DeepCore detector to dark matter annihilations in the Earth core. We focus on annihilation modes $χχ\to ν\barν, \, τ^+ τ^-, \, b \bar{b}$, and $W^+W^-$. Both track and cascade events are considered in our analysis. By fixing the dark matter annihilation cross section $\langle σ\upsilon\rangle$ at some nominal values, we study the sensitivity of IceCube/DeepCore detector to dark matter spin-independent cross section $σ_p^{\rm SI}$ for $m_χ$ ranging from few tens of GeV to 10 TeV. This sensitivity is compared with the existing IceCube 79-string constraint on t…
If light sterile neutrinos exist and mix with the active neutrino flavors, this mixing will affect the propagation of high-energy neutrinos from dark matter annihilation in the Sun. In particular, new Mikheyev-Smirnov-Wolfenstein resonances can occur, leading to almost complete conversion of some active neutrino flavors into sterile states. We demonstrate how this can weaken IceCube limits on neutrino capture and annihilation in the Sun and how potential future conflicts between IceCube constraints and direct detection or collider data might be resolved by invoking sterile neutrinos. We also p…
Recent results from PAMELA and ATIC hint that O(TeV) dark matter (DM) is annihilating, in our galactic neighborhood, predominantly to leptons. The annihilation rate is much larger now than during freeze-out, one possible explanation of this is a low-velocity enhancement of the annihilation cross section. In a model independent fashion, we show that in this case the rate of neutrino emission from the Earth, due to DM annihilation, may be greatly enhanced while the rate from the Sun is unaltered. There is potential for IceCube to see these earthborn neutrinos while the same parameter space will …
Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of Chicago（芝加哥大学）；Kavli Institute for Cosmological Physics, University of Chicago（芝加哥大学卡弗里宇宙物理学研究所）
After scattering off nuclei in the Sun, dark matter particles can be gravitationally captured by the Sun, accumulate in the Sun's core and annihilate into Standard Model particles. Neutrinos originating from these annihilations can be detected by the IceCube Neutrino Observatory, located at the South Pole. Due to the non-observation of these neutrinos, constraints on the standard spin-dependent and spin-independent dark matter-nucleon scattering cross sections have been placed. Based on these constraints, we present upper limits on the coupling constants of the non-relativistic effective theor…
Weakly Interacting Massive Particles (WIMPs) are well-motivated candidates for Dark Matter (DM). WIMP models often include self-annihilation into Standard Model particles such as neutrinos which could potentially be detected by the IceCube Neutrino Observatory. Various searches for a dark matter induced signal have been performed with the existing IceCube detector. However, since there is so far no evidence for WIMPs at TeV scales, more attention is brought to DM candidates at GeV masses, for which the IceCube detector is not sensitive due to its energy threshold. The IceCube collaboration is …
We investigate neutralino dark matter in the framework of NMSSM performing a scan over its parameter space and calculating neutralino capture and annihilation rates in the Sun. We discuss the prospects of searches for neutralino dark matter in neutrino experiments depending on neutralino content and its main annihilation channel. We recalculate the upper limits on neutralino-proton elastic cross sections directly from neutrino telescopes upper bounds on annihilation rates in the Sun. This procedure has advantages as compared with corresponding recalcalations from the limits on muon flux, namel…
We consider a simplified model for Majorana fermion dark matter and explore constraints from direct, indirect and LHC collider searches. The dark matter is assumed to couple to the Standard Model through a vector mediator with axial-vector interactions. We provide detailed analyses of LHC mono-jet searches and IceCube limits on dark matter annihilation in the Sun. In particular, we develop a method for calculating limits on simplified WIMP dark matter models from public IceCube data, which are only available for a limited number of Standard Model final states. We demonstrate that LHC and IceCu…
We provide ingredients and recipes for computing neutrino signals of TeV-scale Dark Matter annihilations in the Sun. For each annihilation channel and DM mass we present the energy spectra of neutrinos at production, including: state-of-the-art energy losses of primary particles in solar matter, secondary neutrinos, electroweak radiation. We then present the spectra after propagation to the Earth, including (vacuum and matter) flavor oscillations and interactions in solar matter. We also provide a numerical computation of the capture rate of DM particles in the Sun. These results are available…
In this paper we discuss two mechanisms by which high energy electrons resulting from dark matter annihilations in or near the Sun can arrive at the Earth. Specifically, electrons can escape the sun if DM annihilates into long-lived states, or if dark matter scatters inelastically, which would leave a halo of dark matter outside of the sun. Such a localized source of electrons may affect the spectra observed by experiments with narrower fields of view oriented towards the sun, such as ATIC, differently from those with larger fields of view such as Fermi. We suggest a simple test of these possi…
We discuss the event rate in DeepCore array due to neutrino flux produced by annihilations and decays of galactic dark matter. This event rate is calculated with a 10 GeV threshold energy, which is smaller than the threshold energy taken in previous works. Taking into account the background event rate due to the atmospheric neutrino flux, we evaluate the sensitivity of DeepCore array for probing dark matter annihilation cross section and decay time. The sensitivity studies include the annihilation modes $χχ\to b\bar{b}, \ τ^+ τ^-$, \ $μ^+μ^-$, and $ν\barν$, and decay modes $χ\to b\bar{b}, \ τ^…
Weakly interacting massive particles (WIMPs) can be gravitationally captured by the Sun and trapped in its core. The annihilation of those WIMPs into Standard Model particles produces a spectrum of neutrinos whose energy distribution is related to the dark matter mass. In this work, we present the theoretical framework for relating an observed neutrino flux to the WIMP-nucleon cross section and summarize a previous solar WIMP search carried out by IceCube. We then outline an ongoing updated solar WIMP search, focusing on improvements over the previous search.
We investigate the prospects to observe a high energy neutrino signal from dark matter annihilations in the Sun in scenarios where the dark matter is a Majorana fermion that couples to a quark and a colored scalar via a Yukawa coupling. In this minimal scenario, the dark matter capture and annihilation in the Sun can be studied in a single framework. We find that, for small and moderate mass splitting between the dark matter and the colored scalar, the two-to-three annihilation $q \bar q g$ plays a central role in the calculation of the number of captured dark matter particles. On the other ha…
In this Letter we focus our attention on the IceCube events in the energy range between 60 and 100 TeV, which show an order 2-sigma excess with respect to a power-law with spectral index 2. We analyze the possible origin of such an excess by comparing the distribution of the arrival directions of IceCube events with the angular distributions of simply distributed astrophysical galactic/extragalactic sources, as well as with the expected flux coming from DM interactions (decay and annihilation) for different DM profiles. The statistical analysis performed seems to disfavor the correlation with …
Dark matter (DM) scattering and its subsequent capture in the Sun can boost the local relic density, leading to an enhanced neutrino flux from DM annihilations that is in principle detectable at neutrino telescopes. We calculate the event rates expected for a radiative seesaw model containing both scalar triplet and singlet-doublet fermion DM candidates. In the case of scalar DM, the absence of a spin dependent scattering on nuclei results in a low capture rate in the Sun, which is reflected in an event rate of less than one per year in the current IceCube configuration with 86 strings. For si…
We consider two classes of supersymmetric flipped SU(5) models with gravity mediated supersymmetry breaking such that the thermal neutralino relic abundance provides the observed dark matter density in the universe. We estimate the muon flux induced by neutrinos that arise from neutralino annihilations in the Sun and discuss prospects for detecting this flux in the IceCube/Deep Core experiment. We also provide comparisons with the corresponding fluxes in the constrained minimal supersymmetric standard model and non-universal Higgs models. Regions in the parameter space that can be explored by …
We describe several components in the diffuse flux of high energy neutrinos reaching the Earth and discuss whether they could explain IceCube's observations. Then we focus on TeV neutrinos from the Sun. We show that this solar neutrino flux is correlated with the cosmic-ray shadow of the Sun measured by HAWC, and we find that it is much larger than the flux of atmospheric neutrinos. Stars like our Sun provide neutrinos with a very steep spectrum and no associated gammas. We argue that this is the type of contribution that could solve the main puzzle presented by the high energy IceCube data.
With the augmentation of IceCube by DeepCore, the prospect for detecting dark matter annihilation in the Sun is much improved. To complement this experimental development, we provide a thorough template analysis of the particle physics issues that are necessary to precisely interpret the data. Our study is about nitty-gritty and is intended as a framework for detailed work on a variety of dark matter candidates. To accurately predict the source neutrino spectrum, we account for spin correlations of the final state particles and the helicity-dependence of their decays, and absorption effects at…
We investigate the prospects for indirect detection of fermion WIMPless dark matter at the neutrino telescopes IceCube and DeepCore. The dark matter annihilating in the Sun is a hidden sector Majorana fermion that couples through Yukawa couplings to a connector particle and a visible sector particle, and it exhibits only spin-dependent scattering with nuclei via couplings to first generation quarks. We consider cases where the annihilation products are taus, staus, or sneutrinos of the three generations. To evaluate the muon fluxes incident at the detector, we propagate the neutrino spectra th…
We consider a new technique for neutrino energy and topology reconstruction at DUNE. In particular, we show that when the direction of the incoming neutrino is known, one can use the measured directions of the outgoing leptonic and hadronic particles to reconstruct poorly-measured quantities, such as the hadronic cascade energy. We show that this alternative technique yields an energy resolution which is comparable to current reconstruction methods which sum measured energies. As a proof of concept we apply this new reconstruction method to a search for dark matter annihilation in the Sun. We …
Galaxy clusters are one of the most promising candidate sites for dark matter annihilation. We focus on dark matter with mass in the range 10 GeV - 100 TeV annihilating to muon pairs, neutrino pairs, top pairs, or two neutrino pairs, and forecast the expected sensitivity to the annihilation cross section into these channels by observing galaxy clusters at IceCube/KM3NeT. Optimistically, the presence of dark matter substructures in galaxy clusters is predicted to enhance the signal by 2-3 orders of magnitude over the contribution from the smooth component of the dark matter distribution. Optimi…
Dark matter (DM) annihilations in the Galaxy may produce high energy neutrinos, which can be detected by the neutrino telescopes, for example IceCube, ANTARES and Super-Kamiokande. The neutrinos can also arise from hadronic interaction between cosmic ray and atmosphere around the Earth, known as atmospheric neutrino. Current measurements on neutrino flux is consistent with theoretical prediction of atmospheric neutrino within the uncertainties. In this paper, by requiring that the DM annihilation neutrino flux is less than the current measurements, we obtain an upper bound on the cross section…
If dark matter particles self-interact, their capture by astrophysical objects should be enhanced. As a consequence, the rate by which they annihilate at the center of the object will increase. If their self scattering is strong, it can be observed indirectly through an enhancement of the flux of their annihilation products. Here we investigate the effect of self-interaction on the neutrino flux produced by annihilating dark matter in the center of the Sun. We consider annihilation into two channels: $W^+W^-$ (or $τ^+τ^-$ for a dark matter mass below the $W$ mass) and $b\overline{b}$. We estim…
We present an interpretation of searches for Dark Matter in a simplified model approach. Considering Majorana fermion Dark Matter and a neutral vector mediator with axial-vector interactions we explore mono-jet searches at the LHC and searches for neutrinos from Dark Matter annihilation in the Sun at IceCube and place new limits on model parameter space. Further, we compare the simplified model with its effective field theory approximation and discuss the validity of the latter one.
We investigate the prospects for indirect detection of right-handed sneutrino dark matter at the IceCube neutrino telescope in a $U(1)_{B-L}$ extension of the MSSM. The capture and annihilation of sneutrinos inside the Sun reach equilibrium, and the flux of produced neutrinos is governed by the sneutrino-proton elastic scattering cross section, which has an upper bound of $8 \times 10^{-9}$ pb from the $Z^{\prime}$ mass limits in the $B-L$ model. Despite the absence of any spin-dependent contribution, the muon event rates predicted by this model can be detected at IceCube since sneutrinos main…
We consider the capture of dark matter in the Sun by inelastic scattering against nuclei as in the inelastic dark matter scenario. We show that, assuming a WIMP-nucleon cross-section of σ_n = 10^{-40}\cm^2 the resulting capture rate and density are sufficiently high so that current bounds on the muon neutrino flux from the Sun rule out any appreciable annihilation branching ratio of WIMPs into W^+W^-, Z^0Z^0, τ^+τ^-, t\bar{t} and neutrinos. Slightly weaker bounds are also available for annihilations into b\bar{b} and c\bar{c}. Annihilations into lighter particles that may produce neutrinos, su…
We argue that the detection of neutrino signature from the Earth's core can effectively probe the coupling of heavy dark matter ($m_χ>10^{4}$ GeV) to nucleons. We first note that direct searches for dark matter (DM) in such a mass range provide much less stringent constraint than the constraint provided by such searches for $m_χ\sim 100$ GeV. Furthermore the energies of neutrinos arising from DM annihilation inside the Sun cannot exceed a few TeVs at the Sun surface due to the attenuation effect. Therefore the sensitivity to the heavy DM coupling is lost. Finally, the detection of neutrino sig…
A monochromatic line in the cosmic neutrino spectrum would be a smoking gun signature of dark matter. It is intriguing that the IceCube experiment has recently reported two PeV neutrino events with energies that may be equal up to experimental uncertainties, and which have a probability of being a background fluctuation estimated to be less than a percent. Here we explore prospects for these events to be the first indication of a monochromatic line signal from dark matter. While measurable annihilation signatures would seem to be impossible at such energies, we discuss the dark matter quantum …
The flux of neutrino-induced muons at the surface of the Earth is calculated from injection of neutralino annihilation products in the core of the Sun and the Earth. An improved treatment of neutrino propagation through the Sun is performed and the results are presented in an easy-to-use parameterization. For an explicit supersymmetric model, an observable neutralino annihilation signal is demonstrated.
The nonrelativistic annihilation of Majorana dark matter in the Sun to a pair of light fermions is chirality-suppressed. Annihilation to 3-body final states $\ell^+f^-V$, where $V=W,Z,γ$, and $\ell$ and $f$ are light fermions (that may be the same), becomes dominant since bremsstrahlung relaxes the chirality suppression. We evaluate the neutrino spectra at the source, including spin and helicity dependent effects, and assess the detectability of each significant bremsstrahlung channel at IceCube/DeepCore. We also show how to combine the sensitivities to the dark matter-nucleon scattering cross…
We present a new dataset analysis of the neutrino experiment at the Baksan Underground Scintillator Telescope with muon energy threshold about 1 GeV for the longest exposure time toward the Sun. In search for a signal from self-annihilations of dark matter particles in the center of the Sun we use an updated sample of upward through-going muons for 24.12 years of live time. No observable excess has been found in measured muons relative to expected background from neutrinos of atmospheric origin. We present an improved data analysis procedure and describe it in detail. We set the 90\% C.L. new …
We investigate the prospects for indirect detection of right-handed sneutrino dark matter at the IceCube neutrino telescope in a $U(1)_{B-L}$ extension of the MSSM. The capture and annihilation of sneutrinos inside the Sun reach equilibrium, and the flux of produced neutrinos is governed by the sneutrino-proton elastic scattering cross section, which has an upper bound of $8 \times 10^{-9}$ pb from the $Z^{\prime}$ mass limits in the $B-L$ model. Despite the absence of any spin-dependent contribution, the muon event rates predicted by this model can be detected at IceCube since sneutrinos main…
We calculate the annihilation rate of weakly interacting massive particles (WIMPs) in the Sun as a function of their mass and elastic scattering cross section. One byproduct of the annihilation, muon neutrinos, may be observed by the next generation of neutrino telescopes. Previous estimates of the annihilation rate assumed that any WIMPs from the Galactic dark halo that are captured in the Sun by elastic scattering off solar nuclei quickly reach thermal equilibrium in the Sun. We show that the optical depth of the Sun to WIMPs and the gravitational forces from planets both serve to decrease t…
The non-observation of neutrinos by the IceCube at the Glashow resonance energy of 6.3 PeV has been a long standing unresolved issue. In this paper we propose a t-channel neutrino absorption by the C$ν$B, which causes a cutoff at 4.5 PeV neutrino energy, to explain the IceCube observations. We present a neutrinophilic 2HDM where the neutrino masses are generated by a low scale seesaw mechanism. A $\mathcal{O}$(10) MeV scalar mediates the interactions between left and right handed neutrinos and generates the t-channel diagram used for explaining the absence of Glashow resonance. The same scalar…
We present a method to derive conservative upper limits on the coupling constants of the effective theory of dark matter-nucleon interactions, taking into account the interference among operators. The method can be applied in any basis, and can be easily particularized to any UV complete model. To illustrate our method, we use the IceCube constraints on an exotic neutrino flux from dark matter annihilations in the Sun to derive conservative upper limits on the dark matter-nucleon coupling constants of the effective theory, as well as to derive conservative upper limits on the dark matter-proto…
The observation of GeV neutrinos coming from the Sun would be an unmistakable signal of dark matter. Current neutrino detectors have so far failed to detect such a signal, however, and bounds from direct and indirect dark matter searches may significantly restrict the possibility of observing it in future experiments such as Hyper-Kamiokande or IceCube-Gen2. In this work, we assess in the light of current data and of expected experimental sensitivities, the prospects for the detection of a neutrino signal from dark matter annihilations in the Sun. To be as general as possible, equilibrium betw…
We propose an interpretation of the two neutrino initiated cascade events with PeV energies observed by IceCube: Ultra-high energy cosmic ray protons (or Fe nuclei) scatter on CMB photons through the Delta-resonance (the Berezinsky-Zatsepin process) yielding charged pions and neutrons. The neutron decays give electron-antineutrinos which undergo neutrino oscillations to populate all antineutrino flavors, but the electron-antineutrino flux remains dominant. At 6.3 PeV electron-antineutrino energy their annihilation on electrons in the IceCube detector is enhanced by the Glashow resonance (the W…
Dark matter annihilations in the Sun to neutrino-antineutrino pairs have striking signatures in neutrino detectors such as IceCube and KM3. We make a model independent study of the signals after propagation of the neutrinos from the center of the Sun to the Earth. A large spin-dependent DM capture cross section in the Sun make the discovery prospects robust.
We consider the upward-going muon flux due to the WIMP annihilations in the cores of the sun and the earth, including the upper bound on the branching ratio for $B_s \to μ^+ μ^-$ decay. We find that the constraint from $B_s \to μ^+ μ^-$ is very strong in most parameter space, and exclude the supergravity parameter space regions where the expected upward-going muon fluxes are within the expected reach of AMANDA II.
