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Distinguishing among dark matter annihilation channels with neutrino telescopes

Rouzbeh Allahverdi1 and Katherine Richardson11 Department of Physics & Astronomy, University of New Mexico, Albuquerque, NM 87131, USA

We investigate the prospects for distinguishing dark matter annihilation channels using the neu-trino flux from gravitationally captured dark matter particles annihilating inside the sun. We showthat, even with experimental error in energy reconstruction taken into account, the spectrum of con-tained muon tracks may be used to discriminate neutrino final states from the gauge boson/chargedlepton final states and to determine their corresponding branching ratios. We also discuss the effectof ντ regeneration inside the sun as a novel method to distinguish the flavor of final state neutrinos.This effect as evidenced in the muon spectrum becomes important for dark matter masses above300 GeV. Distinguishing primary neutrinos and their flavor may be achieved using multi-year datafrom a detector with the same capability and effective volume as the IceCube/DeepCore array.

I. INTRODUCTION

Many lines of evidence support the existence of darkmatter (DM) in the universe, but its identity remains amajor problem at the interface of particle physics andcosmology. The weakly interacting massive particles(WIMPs) are promising DM candidates [1]. They can ex-plain the DM relic abundance, as precisely measured bycosmic microwave background (CMB) experiments [2],via thermal freeze-out of annihilation in the early uni-verse. Major experimental efforts seek to detect DMparticles via direct, indirect and collider searches. Theseexperiments provide complementary information on theproperties of DM such as its mass, elastic scattering crosssection with nucleons, annihilation cross section, and an-nihilation channels.Indirect searches investigate annihilation of DM to var-

ious final states (neutrinos, photons, charged particles)through astrophysical observations. Neutrinos providean especially interesting probe because they are least af-fected on their way from the production point to thedetection point. As a result, neutrino telescopes like Ice-Cube (IC) can trace a neutrino signal directly back to thesource. DM particles gravitationally captured inside thesun annihilate and produce such a signal. When equilib-rium between DM capture by the sun and DM annihi-lation inside the sun is established, the flux of producedneutrinos depends on the DM mass, scattering cross sec-tion off nucleons and the annihilation spectrum. TheDM mass and scattering cross section can be indepen-dently determined from other experiments. In particu-lar, the Large Hadron Collider (LHC) is on the verge ofdiscovering new physics, which will enable us to measurethe mass of the DM particle. Therefore, using the LHCmeasurements and the IC results in tandem, we hope toidentify the annihilation channels and their correspond-ing branching ratios.In this paper, we study the prospects for determin-

ing DM annihilation final states with IC. This model-independent study has two goals: 1) distinguishing sce-narios in which DM annihilates into neutrinos from sce-narios where DM annihilates into gauge bosons andcharged leptons, and 2) extracting information about fla-

vor composition of neutrino final states in the formercase.Gauge boson and charged fermion final states are the

dominant annihilation channels for the popular and ex-tensively studied neutralino DM in the minimal super-symmetric standard model (MSSM). On the other hand,annihilation to neutrinos can arise as the dominant chan-nel in extensions of the standard model (SM) in whichDM is related to the neutrino sector. Discriminating neu-trino final states from gauge boson and tau final stateswill therefore allow us to discern between the two largeclasses of DM models. In the case that DM mainly anni-hilates into neutrinos, it will be important to also knowthe flavor composition of the final state neutrinos. Thiswill shed further light on the specific aspects of the modelthat connect DM to neutrinos.We show that the contained muon tracks at neutrino

telescopes like IC may be used for both purposes. Thespectrum of contained muons can be used to determinethe branching ratios of neutrino final states versus gaugeboson and tau final states. We demonstrate this for sev-eral points in the parameter space within the reach ofthe one-year sensitivity limits of the IceCube/DeepCore(IC/DC) array, with the background from atmosphericneutrinos and the experimental error in energy recon-struction of the muons taken into account. In addition,the ντ regeneration due to charged current interactionsinside the sun may be used to extract information aboutthe flavor of final state neutrinos for DM masses above300 GeV. In particular, we see that the ντ final statecan be discriminated from the νµ and νe final states at asignificant level for DM masses as heavy as 800 GeV. Dis-tinguishing the neutrino final states and discriminatingthe flavor of neutrinos may be achieved with multi-yeardata from IC/DC.This paper is organized as follows. The DM signal in

neutrino telescopes is explained in section II. In sectionIII, we discuss the motivation for models where DM an-nihilates mainly into neutrinos. Section IV includes theanalysis distinguishing the neutrino final state from thegauge boson and tau final states. We investigate discrim-inating the neutrino flavor in the former case in sectionV. Finally, we conclude the paper in Section VI.

2

II. NEUTRINO TELESCOPES AS DARK

MATTER DETECTORS

A. The Sun as a Source of Dark Matter Neutrinos

DM annihilation in the sun produces a neutrino fluxthat can be probed by neutrino telescopes like IC. Thisneutrino flux is modeled by calculating the number ofgravitationally captured DM particles in the sun andthen considering the propagation and detection of theneutrinos produced in DM annihilation. The number ofcaptured DM particles as a function of time is governedby a differential equation that balances the capture ofparticles from elastic scattering on nucleons with the an-nihilation rate; see [3] for details. The total rate of anni-hilation in the sun is given by [4]

ΓA =C

2tanh2

(t

τeq

), (1)

where C is the capture rate of DM particles. The numberof particles captured will saturate at ΓA ≈ C/2 as longas the length of time for the process has exceeded theequilibration time, τeq ≡ (

√CA)−1.

With a nominal freeze-out annihilation rate of 3×10−26

cm3/s, DM readily achieves equilibrium within the life-time of the solar system, 4.5 Gyr, for spin-independentelastic scattering cross sections compatible with the lim-its set by the XENON100 experiment: σSI = few ×(10−9 − 10−8) pb for the mass range 100 GeV − 1TeV [5]. The spin-dependent cross section needed toreach equilibrium is larger by a factor of about 300 [3],which is well below the current experimental limit ofσSD ≤ 2.5× (10−4 − 10−3) pb for the 100 GeV − 1 TeVmass range [6].The difference between the equilibrium constraints on

σSI and σSD comes from the fact that σSI ∝ M4 whileσSD ∝ J(J+1); M and J are the mass and spin of targetnuclei inside the sun respectively. Heavy elements suchas iron account for only a thousandth of the sun’s massand suffer a two order of magnitude form-factor suppres-sion in capturing WIMP-scale DM masses [3]. On theother hand, hydrogen dominates the sun’s compositionand does not suffer a form factor suppression. Thus, theratio of the spin-independent contribution from iron tothe spin-dependent contribution from hydrogen is on theorder of (56)4/105 ∼ O(100). Since equilibrium is eas-ily achieved in the sun, the neutrino signal will dependsolely on C, or equivalently σSI and/or σSD.

1

Once neutrinos are produced from DM annihilation inthe sun, their spectra undergo a number of changes be-fore detection. Scattering via neutral current interactionsresults in neutrino energy loss, while charged current in-teractions result in absorption of neutrinos. These effects

1 The neutrino signal from DM annihilation in the earth is negli-gible assuming a standard DM velocity distribution in the halo.

are proportional to the energy of the neutrino and willtherefore have the greatest effect on the high energy partof the spectrum. Neutrinos are also affected by oscilla-tions on the way to the earth. Since the oscillation lengthis proportional to energy, Losc ∝ Eν , the effect is moreimportant for the low energy part of the spectrum.

B. Neutrino Background, Energy Reconstruction

and Thresholds

Neutrino telescopes access the neutrino signal fromDM annihilation by recording Cerenkov light from rel-ativistic charged particles in their volume. Muon neu-trinos produce muons via charged current interactions inthe detector. Cosmic ray showers create a muon back-ground that can be controlled by selecting for upward-going events since muons are stopped in the earth. Thislimits observation of a DM signal from the sun to halfthe year, when the sun is below the horizon. However,a portion of the detector may be used as a veto to ob-serve contained muon events with a conversion vertexof νµ to µ inside the instrumented volume. The vetoprocedure virtually eliminates the contribution to thebackground from through-going atmospheric muons byselecting for contained vertices. This increases the po-tential observation time to the full year when the sun isboth above and below the horizon. With through-goingmuons eliminated as a background, the most significantcontribution to the remaining background comes from at-mospheric neutrinos. The spectrum of the atmosphericneutrino background from cosmic rays is understood the-oretically to within 20% [7] and is measured above 100GeV to within 10% [8], but individual atmospheric neu-trino events cannot be distinguished from neutrinos fromDM annihilation.The DM neutrino signal can be further enhanced over

the background by allowing for an angular cut in the di-rection of the sun. The cut will be made on the muontrack, and not the incoming neutrino. A smaller angle be-tween the track and incident neutrino occurs for muonswith an energy closer to that of the neutrino.2 Thatis, the muon events that deflect little from the incom-ing neutrino path are the highest energy events. Whilethe smallest possible angular cut is desirable to eliminatebackground, more accommodating cuts on the angle be-tween the track and the sun provide information aboutlower energy events.Energy reconstruction of events can be approximated

in two regimes. Above 1 TeV, the light generatedby an event is proportional to the muon energy sinceBremsstrahlung radiation, nuclear interactions and pair

2 For an elastic collision, the dependence of the angle θνµ onthe muon energy Eµ angle is approximately given by θνµ <

∼

5.7◦ (100 GeV/Eµ)1/2.

3

production create charged particles each of which con-tribute to the Cerenkov radiation. Energy reconstructionin this regime will be logarithmic in energy with an errorof log10 σE ∼ 0.3 [9]. Meanwhile, below ∼ 300 GeV thelength of the track is proportional to the energy of theincident particle since the majority of energy loss in thisrange is governed by ionization. In this case reconstruc-tion will likely be more accurate for contained tracks,and reconstruction algorithms are currently in develop-ment [10]. Events between these regimes call for a morecomplicated reconstruction algorithm.Whereas the IC design is focused on event energies

above a TeV, IC/DC achieves an energy threshold aslow as 10 GeV. IC/DC consists of eight more densely in-strumented strings with high quantum-efficiency digitaloptical modules (DOMs). Surrounding IC strings vetothrough-going muons so IC/DC records muon-neutrinovertex events inside its volume. IC/DC increases the ICeffective volume at energies below 65 GeV and accountsfor the majority of events recorded below 100 GeV. Fur-ther infills of the IC array, such as PINGU, could extendthe energy threshold to a few GeV and further increasethe effective volume by a factor of two at 10 GeV [11].

III. PRIMARY NEUTRINOS FROM DARK

MATTER ANNIHILATION: THEORETICAL

MOTIVATION

DM particles can in principle annihilate into any ofthe SM particles. The annihilation rate to a final state isgiven by σannv = a+ bv2, where v is the relative velocityof annihilating particles. The two terms in this expres-sion represent the S-wave and P -wave contributions re-spectively. For DM annihilation inside the sun the ther-malized velocity is very low (v ∼ 10−4 for a 100 GeVDM particle). Therefore channels that proceed throughthe S-wave dominate annihilation (unless a is extremelysmall).For the popular and extensively studied neutralino DM

in the MSSM, annihilation is mainly into gauge bosonand charged fermion final states. For example, in thestau-neutralino coannihilation region of minimal super-gravity (mSUGRA) models [12], where DM is mostlyBino, annihilation in the S-wave of DM particles is typ-ically dominated by the tau final states. Taus producerelatively soft neutrinos via three-body decay. In the fo-cus point region of mSUGRA models [13], where DMparticles have a large Higgsino fraction, S-wave annihi-lation is predominantly into W bosons (and t-quarks ifkinematically allowed). W ’s produce neutrinos with aharder spectrum via two-body decay. As a result, an-nihilation of neutralino DM typically yields secondaryneutrinos from W and tau final states. The neutrino sig-nal that is produced inside the sun in this way has beenstudied in various cases [14]. Because of the existence ofcharged particles in the final state, annihilation of neu-tralino DM also results in a gamma-ray signal. This im-

plies that one can also obtain constraints by using datafrom the Fermi gamma-ray space telescope [15].Neutralino annihilation to primary neutrinos happens

via gauge interactions where neutrinos are producedthrough the Zνν vertex. It therefore produces a left-handed (LH) neutrino and a right-handed (RH) antineu-trino. Considering that the neutralino is a Majoranafermion, the S-wave contribution to such a final stateis extremely small due to the tiny masses of neutrinos.We note that the P -wave contribution to neutrino finalstates is also very small because of velocity suppression.In consequence, production of primary neutrinos with ahard spectrum from neutralino annihilation is highly sup-pressed.However, it is possible to enhance DM annihilation

into primary neutrinos by going beyond neutralino DM.If DM annihilation produces a νν pair, instead of a ννpair, it can proceed in the S-wave without any mass sup-pression. A detailed analysis of settings in which DMannihilation into neutrinos is enhanced has been givenin [16]. This can happen when DM is related to the neu-trino sector (for some specific models, see [17]).One particular model that can produce hard

monochromatic neutrinos is the B − L extension of theMSSM (B and L are baryon and lepton number respec-tively). A minimal extension of the SM gauge group,motivated by the nonzero neutrino masses, includes agauged U(1)B−L gauge symmetry [18]. Anomaly cancel-lation then implies the existence of three RH neutrinos

(N), the lightest superpartner of which (N) makes a vi-able DM candidate [19]. Thermal freeze-out of the sneu-trinos can yield the correct dark matter abundance if theB − L symmetry is broken around the TeV scale [20].The sneutrinos can annihilate in the S-wave to RH neu-trinos, which in turn decay to LH neutrinos and the SMHiggs. The energy of the resulting neutrinos will be closeto monochromatic as long as the difference between themasses of the RH sneutrino and RH neutrino is muchless than the RH sneutrino mass. The prospects for DMdetection for this model using IC is considered in [21].3

The neutrino signal is the main channel of indirectsearches for models with DM annihilation to primaryneutrinos. These models result in a highly suppressedgamma-ray signal, which escapes the bounds set byFermi [15]. It is worth pointing out that neutrinos fromDM annihilation in the galactic center provide comple-

3 This model has other interesting cosmological and phenomeno-logical implications. The Tevatron [23] and LEP [24] limits onthe Z′ mass bound the RH sneutrino-nucleon scattering crosssection to be σ < 7 × 10−9 pb, which is just below the boundfrom the XENON experiment [5]. Significant DM annihilation totaus is also possible [19] (also see [25]), which could provide anexplanation for the positron excess in the cosmic rays reportedby PAMELA [26]. In addition, this model can accommodate in-flation [27], provide a unified picture of inflation and dark mat-ter [20], and give rise to interesting predictions for neutrinolessdouble beta decay experiments [28].

4

mentary information to those from annihilation insidethe sun: the former constrains the DM annihilation crosssection [22], while the latter bounds the DM scatteringcross section off nucleons [6]. The signature of DM an-nihilation to neutrinos at the galactic center should bedistinctive with a hard cutoff (for example, see [29]).

IV. DISTINGUISHING NEUTRINO FINAL

STATE FROM W AND TAU FINAL STATES

MSSM neutralino annihilation predominantly pro-duces gauge bosons and charged fermions, each of whichin turn produce secondary neutrinos via two-body orthree-body decays. In this work, we adopt a model-independent approach and consider interesting neutrinospectra from DM annihilation to prompt ν’s, W ’s, andτ ’s.For charged fermions, we investigate only annihilation

to τ ’s for the following reasons. e’s and µ’s are stoppedimmediately in the sun, so µ decay will occur at low en-ergy and result in a very soft spectrum. When DM an-nihilation produces quarks, all quarks except the t-quarkhadronize before their subsequent decay. The t-quark de-cays to a W boson and a b-quark before hadronization,and the subsequent W decay produces a neutrino spec-trum comparable to that from the W final state. For theremaining hadronizing quarks, the lighter the quark thelonger it will take to decay, and hence the lower its energywill be. The b-quark produces neutrinos via three-bodydecay, which has a softer spectrum than that from τ . Allother quarks decay effectively at rest and have unmea-surable spectra at low energies that cannot compete withthe atmospheric background [3].With regard to gauge boson final states,W and Z spec-

tra are relatively similar; we consider only W final statesin our analysis. Finally, the Higgs boson final states alsoresult in a soft neutrino spectrum that is negligible com-pared to that from W and τ final states. The Higgsmainly decays to b-quarks, thus yielding a neutrino spec-trum similar to that from the b-quark final state.In the following, we therefore focus on secondary neu-

trinos from DM annihilation to W and τ final states vsprimary neutrinos and their corresponding spectra. Pre-vious investigations have shown that measuring the spec-trum can allow the reconstruction of the DM mass and itsannihilation branching ratios [30]. We perform an anal-ysis for reconstructing the DM elastic scattering crosssection and its annihilation channels, including experi-mental error in energy reconstruction and assuming thatits mass can be determined from other experiments (no-tably by the LHC).

A. Neutrino & Contained Muon Spectra

In this analysis, we consider the spectrum of containedmuon tracks so that the vertex at which νµ is converted

to a µ is within the detector volume. Hadronic and elec-tromagnetic cascade events in the ice also carry usefulinformation about low energy neutrinos and may showtau neutrino appearance from oscillations [31]. IC/DC isuniquely suited to measure these low energy events andrecently confirmed the observation of neutrino-inducedcascades [11]. For our purposes, since cascades are local-ized in the ice and thus suffer from an angular resolutionof about 60 degrees at 100 GeV, too much background isadmitted to perform a meaningful DM search with cas-cades [32].We use DarkSUSY to calculate the spectrum for any

given final state [33]. To the extent that the energy ofthe event may be well reconstructed in this range, wealso assume that the muon track itself is fully contained,ending inside the detector. We do not account for anyloss of events or poor energy reconstruction at the edgesof the fiducial volume.As an example, Fig. 1 depicts the theoretical prediction

for neutrino and muon spectra that result from the an-nihilation of 100 GeV DM particles in the sun to promptνµ’s, W ’s and τ ’s. The flux is given in events per km3

effective volume of the detector at earth per year. Only ahalf-year of data is taken for each calendar year, since weassume the neutrino telescope requires the sun to be be-low the horizon to observe the DM neutrino signal abovethe atmospheric muon background. For a DM mass of100 GeV the muons will be fully contained and accessi-ble in IC. The qualitative features of the neutrino andmuon spectra (such as peaks and kinematic cutoffs) arethe same for higher DM masses.The prompt neutrinos, Fig. 1a, result in a monochro-

matic peak at the DM mass in the neutrino spectrum.The contained muon spectrum is plotted along with theneutrino spectrum to emphasize the effect of the chargedcurrent conversion of neutrinos to muons. The conversiondemonstrates the weak scale reduction in events relativeto the incident neutrinos and is proportional to energy,so the peak from the neutrino annihilation channel iswell preserved. The spectra are largely insensitive to thechoice of neutrino oscillation parameters and annihilatingneutrino flavor. Here we depict θ13 = 10◦, normal masshierarchy and annihilation to νµ, but scenarios with in-verted mass hierarchy, 0 ≤ θ13 < 10◦ and other neutrinoflavors in the final state only slightly change the heightof the peak.4

The W bosons produce neutrinos via two-body decay,which are softer than the previous case. For a highlyboosted W (whose energy is equal to the DM mass), theenergy of secondary neutrinos is between M2

W /4MDM

and MDM/√2. This is the reason for the relatively sharp

kinematic edges in the neutrino spectrum in Fig. 1b. We

4 Recent results from T2K [34] and MINOS [35] experiments sug-gest nonzero θ13 at 2.5σ and 89% confidence respectively. Theresults are consistent with θ13 = 10◦.

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FIG. 1: Energy spectra of contained muon events (solid) andincident neutrinos (dashed) at the earth from a 100 GeV DMparticle for various annihilation channels. Relative to the sun1◦, 5◦ angular cuts have been placed on the signal and atmo-spheric background muons (thin black lines). The top plot forannihilation to neutrinos is for σSD = 10−41 cm2, while theother plots are for σSD = 10−40 cm2, all of which are belowthe current experimental bounds. Normal mass hierarchy andθ13 = 10◦ have been chosen here, but the spectra are largelyinsensitive to the oscillation parameters.

note that W ’s also decay to b-quarks, which in turn pro-duce tertiary neutrinos. This results in additional con-tributions to the neutrino spectrum lower than the kine-matic cutoff mentioned above. The muon spectrum has apeak at energies well below the DM mass resulting from

charged current interactions whose cross section is pro-portional to the neutrino energy.The τ ’s produce neutrinos via three-body decays,

which results in a much softer neutrino spectrum thatrises toward lower energies as seen in Fig. 1c. Thus thepeak of the resulting muon spectrum is located at a lowerenergy than that in Fig. 1b. However, there is no kine-matic cutoff in the neutrino spectrum in this case, andhence the muon spectrum extends smoothly to the DMmass.The important point is that there is a distinct sep-

aration in energy between the contained muon peak ofprompt neutrinos at the DMmass and theW and τ peaksat lower energies. This indicates that scenarios with DMannihilation to primary neutrinos can be distinguishedfrom those with DM annihilating to W bosons or τ ’s.Moreover, were a model to contain both a neutrino finalstate and a W or τ final state, the neutrino signal maybe used to determine the corresponding branching ratios.

B. Reconstruction of Annihilation Channels

The theoretical predictions shown in the previous sub-section are subject to experimental error. Individualmuon events from a particular annihilation channel can-not be tagged as such, nor can individual signal and back-ground events be distinguished. A more realistic pictureis shown in Fig. 2 for a 100 GeV DM particle, where twochannels along with background events have been addedtogether and subjected to a 5◦ angular cut. The branch-ing ratios are 90% to W bosons and 10% to neutrinoswith σSD = 10−40cm2. This is a factor of a few belowthe current bounds from IC [6] and just at the currentbounds of Super Kamiokande (SuperK) for annihilationto W ’s [37].5

Angular cuts on the muon tracks relative to the posi-tion of the sun lower the relevant atmospheric containedmuon background relative to the signal. Lower energyevents are preferentially scattered at higher angles rel-ative to the incoming neutrino; therefore, angular cutsdisproportionately remove low energy events. A 1◦ cutleaves the majority of the high energy muons from pri-mary neutrinos, which are clearly separated from a re-duced background. Meanwhile, a 5◦ cut admits morelower energy muons that are indicative of the pronouncedpeaks from W and τ final states. Different angular cutswill optimize the signal to background ratio for differ-ent annihilation channels. We have found a 5◦ cut tobe optimal, where the background does not overwhelmthe signal in the regime above 40 GeV and a significant

5 For a purely spin-independent cross section, the same result isobtained for σSI ≈ 3 × 10−43 cm2. However, such a large valueof σSI is already ruled out by direct detection experiments [5].For this reason we focus on the spin-dependent cross sections inthis analysis.

6

portion of the W peak remains. The contribution fromneutrinos is still easily distinguished in the peak cutoff.

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FIG. 2: Total contained muon spectrum from a 100 GeV DMparticle with σSD = 10−40 cm2 annihilating to W ’s (90%)and ν’s (10%) with the atmospheric background added. A5◦ cut has been placed on the events. Smeared spectra forenergy reconstruction errors of 10 GeV (dashed) and 40 GeV(dotted) are also shown.

The realistic energy reconstruction for a containedmuon spectrum at IC for these energies is not certain.Energy reconstruction for through-going TeV muons isapproximately σlog

10E = 0.3 [9]. Energy loss of the muon

is described by

dE

dx= a+ bE , (2)

where a quantifies muon loss via ionization, and b quan-tifies loss from pair productions, Brehmsstrahlung radi-ation and nuclear interactions. For ice at energies above1 TeV, enough Brehmsstrahlung and pair production oc-curs to ensure that the light deposited in the detector isproportional to the muon energy. However, for containedmuon events less than one kilometer in extent, the tracklength is proportional to the muon energy. Reconstruc-tion in this regime will be better than in the regime above1 TeV but will depend on the geometry of the detector.The energy resolution error of the IC detector for con-

tained muon events below 100 GeV should be linear withenergy, in that the track length is proportional to theenergy of the incoming muon. In Fig. 2, we recreate aGaussian energy reconstruction with an error, or width,equal to 10 or 40 GeV. This is equivalent to claiming thatthe track length can be known to within 50 − 200 m, aresolution that seems feasible for IC/DC to IC-like tele-scopes since IC/DC DOMs are spaced at 7 m verticallyand strings are 72 m apart while IC DOMs are spaced at17 m vertically and strings are 125 m apart.It is seen that the smoothing of the spectrum consider-

ably suppresses the distinct channel features, especiallyfor a 40 GeV error in energy reconstruction. Never-theless, it is still possible to reconstruct the total spin-dependent scattering cross section σSD and the branchingratio for annihilation to primary neutrinos BRν .

+

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FIG. 3: Contours of 2σ confidence for reconstructing spin-dependent cross section σSD and branching ratio to promptneutrinos BRν for a 100 GeV DM particle annihilating toν’s and W ’s. One year of data is used with energy recon-struction errors of 10 or 40 GeV (thick or thin contours).The region of interest is between the current SuperK upperbound (dashed) [37] and the future IC86 sensitivity bound(dotted) [22].

In Fig. 3 we show the 2σ confidence contours for a 100GeV DM particle annihilating to ν andW final states, us-ing one year of data and applying energy reconstructionerrors of 10 GeV and 40 GeV. These contours accountfor Poisson errors, the addition of background and a 40GeV energy cut; we have used the χ2 analysis in [36] toobtain these results.The plot in Fig. 3 also shows the current SuperK

bound [37] and the future IC sensitivity bound [22] onσSD (dashed and dotted curves respectively). For 100%DM annihilation to W ’s, the experiments have derivedbounds on σSD by applying appropriate energy and an-gular cuts on the muon spectrum. No limit has beenplaced yet for DM annihilation to primary neutrinos byeither experiment. In the absence of a thorough analysis,we have used a simple criterion to find an approximatebound on σSD for the neutrino final states. We comparedthe total number of contained muon events with a 40 GeVenergy threshold and 5◦ angular cut for the two finalstates. In the case of primary neutrinos, the flux of µ’s isabout eight times larger than the flux from W ’s, as ex-pected from the harder neutrino spectrum. We assumedthe limit on σSD in this case is also tighter by the samefactor. A dedicated analysis for the neutrino final state,with optimized angular and energy cuts, would result ina more precise bound. Indeed, theoretical motivation formodels with DM annihilation to primary neutrinos war-rants such a study by experimental collaborations. Inthe presence of both ν and W final states, the limits are

7

approximately given by

σSD (1 + 7 BRν) ≤ σmax . (3)

The current bound from SuperK [37] and the future ICsensitivity bound [22] correspond to σmax ≈ 2.5× 10−40

and 4× 10−41 cm2 respectively.It is seen from the shape of the contours that higher

σSD and smaller BRν are difficult to distinguish fromlower σSD and larger BRν . The number of muon eventsat the DM mass mainly comes from the peak of primaryneutrinos, which is determined by BRν . This holds af-ter smoothing of the spectrum because of the kinematiccutoff that appears well below the DM mass for annihila-tion to W ’s, see Fig. 1b. This implies that after smearingthe main contribution to the total spectrum at energiesaround and above the DM mass still comes from primaryneutrinos. On the other hand, the main contribution tolower energy muons comes from secondary neutrinos pro-duced by W decay. For small values of σSD or large val-ues of BRν , this contribution is small and overwhelmedby the Poisson error from the atmospheric background.Therefore, one can compensate for a change in σSD by acorresponding change in BRν and obtain spectra that arestatistically indistinguishable. For larger values of σSD

or smaller values of BRν , the contribution of secondaryneutrinos becomes significant, which limits simultaneousvariations in σSD and BRν that keep the peak height un-changed. As a result, the 2σ contours are tighter for re-construction points toward the right and bottom of theplot in Fig. 3. As expected, an energy reconstructionerror of 40 GeV does a poorer job because it further sup-presses the features discussed above.

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FIG. 4: The same as Fig. 3, but for annihilation to ν and τ

final states.

In Fig. 4 we show the 2σ confidence contours froma similar analysis for annihilation to ν’s and τ ’s. The

contours are wider in this case, which implies the recon-struction is significantly more difficult. This is due tothe different shapes for the W and τ final state spectra,see Figs. 1b and 1c. In the case of the τ final state, thespectrum resulting from secondary neutrinos is softer andextends all the way to the DM mass. Therefore secondaryneutrinos can make a significant contribution to the to-tal spectrum at energies around and above the DM massafter energy reconstruction and are also affected more bythe background at lower energies. Both of these effectsimply a poorer reconstruction of the branching ratios inthis case.Some comments are in order. In producing these fig-

ures, a scan of angular cuts in 1◦ increments within the1◦ − 10◦ range was made. While visually a 1◦ cut maybe optimal in distinguishing the presence of the neu-trino channel, a 5◦ cut was optimal in reconstructing thebranching ratios in the presence of the broad, low energyW or τ spectrum.We also note that the muon event rates for both the sig-

nal and background must be convolved with the effectivevolume of the detector for contained muon events, whichis a function of energy. IC/DC maintains significant vol-ume above 10 GeV [11]. While the geometric volumefor IC/DC is about 3% of the volume of IC, the moredense spacing of DOMs in IC/DC make it more efficientat event detections for energies below 100 GeV [11]. Theeffective volume in this range increases with energy aslonger muon tracks are more likely to produce detectablelight. This can make the effect of the peak at the DMmass from primary neutrinos even more distinctive abovethe smeared W or τ spectrum. The reconstruction cantherefore be better than shown here after accounting forthe energy dependence of the effective volume.Finally, one year results for a km3 effective volume,

with the sun below the horizon, translate to roughly tenyears of a 0.05 km3 detector capable of operating for afull year. Thus, in the region of IC and IC/DC sensi-tivity that would yield a discovery of prompt neutrinosafter one year, 10 years of data could allow reconstructionof the branching ratios for the IC/DC effective volume.A larger detector with the same capabilities can signifi-cantly improve these prospects.

V. DISTINGUISHING NEUTRINO FLAVORS

Once the presence of direct DM annihilation to neutri-nos is confirmed, it is desirable to also learn the flavor ofthe final state neutrinos. This will provide specific infor-mation about models that connect DM to the neutrinosector. For example, in the U(1)B−L extension of MSSMwhere the lightest RH sneutrino is the DM candidate [19],flavor composition of final state neutrinos is related to theneutrino Yukawa couplings. Therefore, knowledge of theneutrino flavors will yield useful information pertainingto the underlying neutrino mass model and leptogenesis.Here we show how regeneration of ντ inside the sun and

8

its effect on the muon spectrum may be used as a novelmethod to distinguish the flavor of primary neutrinos inthe final state.6

A. The ντ Regeneration Effect

DM annihilation produces neutrinos in flavor eigen-states in the sun. Neutrinos then undergo charged cur-rent interactions with matter as they propagate throughthe sun. These interactions convert νe, νµ, ντ to e, µ, τrespectively. e’s and µ’s are stopped immediately due toelectromagnetic interactions. On the other hand, the τdecays quickly before losing too much energy because ofits very short lifetime of 3×10−13 s [38]. This decay pro-duces a ντ , which has a lower energy than the originalone. Charged current interactions therefore suppress thepeak of the neutrino spectrum at the DM mass for all fla-vors.7 However, in the case of the ντ , the regeneration ofneutrinos via three-body decay populates the spectrumat energies well below the DM mass.The cross section for charged current interactions is

proportional to the energy of primary neutrinos producedat the center of the sun, which is essentially equal tothe DM mass. Neutrino absorption becomes significantwhen the absorption length of neutrinos Labs is roughlyequivalent to the core size of the sun RC ∼ 70, 000 km.Using the charged current neutrino-nucleon cross sec-tion [39] and a core density of 150 g/cm

3, we find that

Labs ∼ 70, 000 km at energiesEν ∼ 300 GeV. Oscillationsamong different flavors should be taken into account asneutrinos travel through the sun. We note that for νethe flavor and mass eigenstates are the same deep insidethe sun. This implies that upon production at the cen-ter of the sun νe’s propagate through the core withoutchanging their flavor. Thus absorption via charged cur-rent interactions start to suppress the flux of νe for DMmasses above 300 GeV as discussed above.On the other hand, νµ and ντ are not mass eigenstates

inside the sun, and hence undergo oscillations. Sincematter effects are the same for these two flavors, theνµ − ντ oscillation length inside the sun is set by the at-mospheric mass splitting Losc = Eν/4π∆m2

atm. As longas Labs >∼ Losc/4, oscillations mix νµ and ντ efficientlybefore the absorption becomes important. As a result,νµ final states also feel the regeneration effect. Since

6 It has been proposed that seasonal variation of the neutrino sig-nal may also be used to extract information about the flavor ofprimary neutrinos [40].

7 Neutrinos also have neutral current interactions with matter in-side the sun. Scatterings via neutral current interactions resultin energy loss of the neutrinos and further suppress the peak atthe DM mass. However, the cross section for neutral current in-teractions is a factor of 3 smaller than that for charged currentinteractions, which makes them subdominant. More importantly,neutral current scatterings affect all flavors equally.

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FIG. 5: Contained muon spectra for DM annihilation to νe(dotted), νµ (solid) and ντ (dashed) for 400 (Fig. 5a) and 600GeV (Fig. 5b) DM masses and σDM = 10−41 cm2. Normalmass hierarchy and θ13 = 10◦ are chosen here, but substan-tive features of the spectra do not depend on the neutrinooscillation scenario. A 5◦ cut has been placed on the events.Corresponding neutrino spectra are shown in thin lines. Theregeneration effect is evident for the ντ final state and resultsin a peak in the muon spectrum at low energies. For a 400GeV DM particle, regeneration also affects the νµ final statedue to efficiency of νµ − ντ oscillations inside the sun.

Labs ∝ E−1ν and Losc ∝ Eν , at sufficiently high ener-

gies Labs drops below Losc/4. This happens for a DMmass of about 500 GeV. Starting at this point, νµ − ντoscillations cease to be effective. Hence νµ gets absorbedthrough charged current interactions similar to νe. Inconsequence, only the ντ final state retains a significantregeneration signature for DM masses above 500 GeV.In Fig. 5 we show the muon and neutrino spectra

for different flavors of primary neutrinos. As we see inFig. 5a, the νµ channel shows some regeneration effect fora 400 GeV particle, which makes it distinguishable fromthe νe channel. For a 600 GeV DM particle, see Fig. 5b,the νµ−ντ oscillations are inefficient. Therefore, only theντ channel shows significant regeneration, which makesit distinguishable from the νµ and νe channels. The re-generation effect results in a peak in the muon spectrum

9

at low energies, which becomes more pronounced as theDM mass increases. These figures are for the normal hi-erarchy of neutrinos and θ13 = 10◦, but variations in theneutrino oscillation scheme do not change the substantivefeatures of the spectra.

B. Signals of Neutrino Flavor

As we saw, the ντ regeneration effect becomes signifi-cant at DM masses above 300 GeV. The background fromatmospheric neutrinos is relatively small at such energiesdue to the power law decrease in cosmic ray background.However, the neutrino signal from DM annihilation isalso kinematically suppressed for heavier DM masses.This leaves few events to detect in the interesting range ofthe spectrum where a regeneration peak is evident. Ad-ditionally, energy reconstruction for the contained muonspectrum above 300 GeV begins to suffer from logarith-mic error in energy since the reconstruction also dependson the amount of light produced in Brehmsstrahlung ra-diation and pair production. Events cannot be fully con-tained at these energies, so reconstruction efforts basedon track length are imprecise.8

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FIG. 6: Integrated muon spectra from 60 GeV to the DMmass with a 5◦ angular cut as a function of DM mass forσSD = 10−40 cm2. The dotted, solid and dashed lines denotethe νe, νµ and ντ final states respectively. The bands of linesfor each flavor depict different oscillation scenarios (normaland inverted mass hierarchy as well as 0 ≤ θ13 ≤ 10◦). Theseparation between the ντ and νe exceeds the Poisson error ofthe signal and background (black line) for DM masses above300 GeV, and the ντ becomes distinguishable from νµ above600 GeV as well.

To mitigate these experimental challenges, we inte-grate the contained muon events above a threshold toconsider if the cumulative effect of the regeneration isvisible. In Fig. 6 we show the integrated events above 60

8 If the energy of the corresponding cascades accompanying themuon event can also be captured, energy reconstruction wouldbe improved.

GeV with a 5◦ angular cut, which readily retains the lowenergy regeneration effect. One can see the separationbetween the νe channel and the νµ, ντ channels above300 GeV, and between the ντ channel and the νe, νµchannels above 500 GeV (as discussed above). Separationbetween signals from different channels is typically largerthan the Poisson error of the background and signal to-gether. The background and signal are shown separatelysince the background may be subtracted from the signalby observing away from the sun, off-source, as is donein galactic center DM searches [22]. We also note thatthe oscillation scenario does not significantly affect theseresults. The bands of lines depicting the normal and in-verted hierarchies as well as θ13 ranging from 0 to 10◦ foreach flavor do not overlap at DM masses above 300 GeV.These results assume σSD = 10−40cm2, which is compat-ible with the current bounds from IC for heavier DM,and is within the reach of IC/DC sensitivity limits [22].

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FIG. 7: The same as in Fig. 6 after normalization to accountfor unknown value of the DM elastic scattering cross section.The normalized spectra give the same number of events (whenintegrated from 200 GeV to the DMmass for a 1◦ angular cut)as the νµ final state for normal mass hierarchy and θ13 = 10◦.The separation between the ντ and other flavors still exceedsthe Poisson error of the signal and background (black line).

If the elastic scattering cross section of the DM isknown, then a simple integration as in Fig. 6 will be suf-ficient to distinguish the flavor of primary neutrinos byusing the regeneration effect. However, a confirmationof annihilation to primary neutrinos would likely comefrom the presence of a monochromatic peak alone, theheight of which depends on the scattering cross section.In the absence of information about the cross section,we then need to normalize the signal to extract informa-tion about the neutrino flavor. The height of the peakin the muon spectrum is closely related to the height ofthe neutrino peak. However, for DM masses above 300GeV, for which the regeneration effect becomes impor-tant, muon events at the peak are not fully contained. Itwill be most difficult to reconstruct the energy of theseevents without track-length information. Instead, we in-tegrate muon events above 200 GeV, which are essentiallythe through-going muons, using a 1◦ angular cut on the

10

muon spectrum in order to best capture the monochro-matic peak. We then use this to normalize the integratedmuon flux above 60 GeV with a 5◦ cut to retain the max-imum effect of regeneration at low energies.The normalization accounts for the lack of knowledge

in the value of the DM elastic scattering cross section,and to a lesser extent the oscillation parameters. Afternormalization, see Fig. 7, the separation between the ντchannel and the νe, νµ channels remains and is still largerthan the statistical error of the background and signaltogether. Using the regeneration effect, the IC/DC ef-fective volume could reasonably yield a determination ofthe neutrino flavor after 10 full years of operation.

VI. CONCLUSION

We have investigated prospects of determining DM an-nihilation final states with neutrino telescopes by usingthe spectrum of contained muon tracks from conversionof neutrinos that are produced in the annihilation of DMparticles trapped inside the sun. Our focus was on distin-guishing neutrino final states from gauge boson and taufinal states and on discriminating the flavor of final stateneutrinos. Gauge boson and tau final states are typi-cally the dominant annihilation channels in supersym-metric models with neutralino DM, while direct annihi-lation into neutrinos can occur in models that connectDM to the neutrino sector. The theoretical motivationfor the latter could provide the grounds for a dedicatedanalysis by the IceCube Collaboration to put stringentbounds on annihilation to primary neutrinos, similar towhat has been done for annihilation to gauge bosons [6].Primary neutrinos from DM annihilation result in a

distinct peak in the muon spectrum at the DM mass.For DM masses below 300 GeV we can expect that thepeak will be accessible to a detector the size of IC. Thespectrum is smeared as a result of the experimental errorin energy reconstruction, but primary neutrinos may bedistinguished from gauge boson and tau final states after

this effect is taken into account. We showed that foran energy resolution of 10 GeV (as in IC/DC) and bymaking an optimal angular cut on the muons (which wefound to be 5◦), the branching ratios may be determinedin the parameter space within the reach of the one-yearsensitivity limits of IC/DC with a km3/yr of data. This isroughly equivalent to 10 years of data for a detector withthe same capabilities and effective volume as IC/DC.The regeneration of ντ inside the sun may be used to

distinguish the flavor of final state primary neutrinos.This effect becomes important for DM masses above 300GeV and populates the spectrum with muons whose en-ergy is well below the energy of primary neutrinos. ForDM masses up to about 500 GeV, oscillations mix νµ andντ effectively, which implies that regeneration affects fi-nal states with νµ and ντ similarly. Final states with νeare therefore distinguishable within this mass range. Forheavier DM particles, the νµ − ντ oscillation becomes in-efficient. As a result, ντ final states are picked out by theregeneration effect for DM masses above 500 GeV. Weshowed that final states with ντ stand out at a statisti-cally significant level for DM masses as heavy as 800 GeV,even after normalizing the muon spectrum to the totalevent count (to account for the unknown DM-nucleonelastic scattering cross section). Again, such a distinc-tion may be achieved with 10 years of data from IC/DC.In summary, using the the IC results in tandem with

independent measurements of the DM mass (for example,from the LHC), will allow us to identify the annihilationchannels of DM with multi-year data. Improved energyresolution and increased effective volume of the detectorwill greatly help in achieving this goal.

VII. ACKNOWLEDGEMENTS

The authors wish to thank Bernard Becker, Tyce DeY-oung, Arman Esamili, Yasaman Farzan, Alexander Fried-land, Francis Halzen, Spencer Klein, Robert Lauer, IrinaMocioiu, and Carsten Rott for valuable discussions.

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