Dark Matter Decay to Neutrinos Carlos A. Arg uelles 1Diyaselis Delgado

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Dark Matter Decay to Neutrinos

Carlos A. Arg¨

uelles ,1Diyaselis Delgado ,1, ∗Avi Friedlander ,2, 3

Ali Kheirandish ,4, 5 Ibrahim Safa ,6, 7, 1 Aaron C. Vincent ,2, 3, 8 and Henry White 2, 3

1Department of Physics & Laboratory for Particle Physics and Cosmology,

Harvard University, Cambridge, MA 02138, USA

2Department of Physics, Engineering Physics and Astronomy,

Queen’s University, Kingston ON K7L 3N6, Canada

3Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Kingston ON K7L 3N6, Canada

4Department of Physics & Astronomy, University of Nevada, Las Vegas, NV, 89154, USA

5Nevada Center for Astrophysics, University of Nevada, Las Vegas, NV 89154, USA

6Department of Physics, Columbia University, New York, NY, 10027, USA

7Department of Physics & Wisconsin IceCube Particle Astrophysics Center,

University of Wisconsin, Madison, WI 53706, USA

8Perimeter Institute for Theoretical Physics, Waterloo ON N2L 2Y5, Canada

It is possible that the strongest interactions between dark matter and the Standard Model occur

via the neutrino sector. Unlike gamma rays and charged particles, neutrinos provide a unique avenue

to probe for astrophysical sources of dark matter, since they arrive unimpeded and undeﬂected from

their sources. Previously, we reported on annihilations of dark matter to neutrinos; here, we review

constraints on the decay of dark matter into neutrinos over a range of dark matter masses from MeV

to ZeV, compiling previously reported limits, exploring new electroweak corrections and computing

constraints where none have been computed before. We examine the expected contributions to the

neutrino ﬂux at current and upcoming neutrino experiments as well as photons from electroweak

emission expected at gamma-ray telescopes, leading to constraints on the dark matter decay lifetime,

which ranges from τ∼1.2×1021 s at 10 MeV to 1.5×1029 s at 1 PeV.

I. INTRODUCTION

The angular power spectrum of the cosmic microwave

background (CMB) as well as the matter distribution

on large scales, the clustering of galaxies, and the mea-

sured kinematics of stars and gas within those galaxies

all point to a large component of weakly-interacting dark

matter (DM), constituting 85% of all matter in the Uni-

verse [1,2]. While these observations imply an equation

of state consistent with a cold, collisionless ﬂuid, no mi-

crophysical connection has yet been found between DM

and the Standard Model (SM) of particle physics. Nu-

merical coincidences such as the one-to-ﬁve ratio of dark-

to-ordinary matter sustain our hope that DM decoupled

late enough in the history of the Universe to require a

coupling well below the Planck scale and thus be describ-

able in the language of particle physics.

The parameter space of such nongravitational in-

teractions is immense, and myriad portals are poten-

tially available. Traditional searches for electroweak and

supersymmetry-inspired WIMPs in the GeV-TeV mass

range that scatter with or annihilate to quarks have ex-

panded in the past decades to encompass light axion-

like [3] and minicharged particles [4–8], sub-GeV nonther-

mal DM candidates [9,10], primordial black holes [11],

and other exotic objects. In some of these scenarios, dark

matter can be unstable and decay to Standard Model

particles.

∗Corresponding author: ddelgado@g.harvard.edu

Direct searches for such DM rely on elastic scatter-

ing with electrons or nuclei, while indirect searches look

for signatures of decay or annihilation into SM particles.

Products of DM decay (or annihilation) into SM parti-

cles eventually create a ﬂux of stable particles, i.e., pro-

tons, electrons, photons, or neutrinos. Here, we focus on

the latter. A direct neutrino portal would render direct

detection impracticable, and indirect detection very dif-

ﬁcult, owing to the minuscule cross section of neutrinos

at low energies. However, at high energies, the neutrino

cross section grows and is no longer suppressed by the

mass of the heavy bosons but by the momentum trans-

fer as is the case of photon-nucleon interactions [12–14].

Additionally, high-energy gamma rays can be attenuated

as they travel from their sources of production to Earth,

while neutrinos voyage unimpeded. Therefore, the study

of neutrinos represents a ﬁnal frontier in the search for

indirect signatures of DM. The study of this channel is

further motivated by connections between the dark sec-

tor and neutrinos. These have been proposed in a variety

of diﬀerent contexts, including the scotogenic scenarios

where neutrinos gain their mass via interacting with the

dark sector [15–21], the Majoron scenario [22] or see-saw

models [23]. In many of these models, UV physics can

destabilize the DM, leading to a decay to ¯νν, which may

dominate over other channels. These models have moti-

vated numerous dedicated studies, mainly in the context

of discovering heavy DM using neutrino line searches [24–

35], and many neutrino experiments have hunted for DM

signatures in their observations [36–42], so far yielding

null results.

arXiv:2210.01303v3 [hep-ph] 6 Nov 2023

Previously, we presented an updated compendium of

constraints on particle DM annihilation to neutrinos [43].

Here, we turn our attention to the production of neutri-

nos from DM decay, directing special attention to the

higher-mass region. At masses greater than ∼TeV, elec-

troweak (EW) corrections can“decloak” the DM, produc-

ing high-energy photons, even when directly decaying to

neutrinos that can be detectable at current and future

gamma-ray observatories [44]. We thus present limits

from current measurements and sensitivities for upcom-

ing experiments covering a DM mass range starting at

20 MeV and spanning well into the ultra-heavy domain

up to 1011 GeV. Although recent LHAASO results are on

par with IceCube’s recent analyses, we will ﬁnd that cur-

rent and future neutrino telescopes retain superior sen-

sitivity across nearly the entire range of masses that we

consider. This is due to three factors: the loop suppres-

sion of the gamma-ray production rate, the growth of

the electroweak cross section with energy, and the loss of

high-energy gamma rays to interactions in the interstellar

and intergalactic medium.

We begin by brieﬂy describing the signature of DM

decaying to neutrinos at both neutrino telescopes and

gamma-ray observatories. We present our new results

in Section III and oﬀer parting words of wisdom in Sec-

tion IV.

II. DARK MATTER DECAYS TO NEUTRINOS

The expected ﬂux per neutrino ﬂavor at Earth from

decay of DM with mass mχand lifetime τχis

dΦν+¯ν

dEν

4π

τχmχ

dNν

dEν

D(Ω).(1)

Below the electroweak scale, the neutrino spectrum per

decay is dNν/dEν= 2δ(1 −2E/mχ)mχ/2E2; at higher

masses a low-energy tail arises as discussed in Ref. [44].

Because relevant backgrounds follow a power-law distri-

bution, only the delta contribution is relevant for neu-

trino constraints. The so-called D-factor, D(Ω), is an

integral of the DM distribution ρ(x) along the line of

sight and solid angle ∆Ω:

D≡ZdΩZl.o.s.

ρχ(x)dx. (2)

We assume the Galactic DM spatial distribution is mod-

eled by an Navarro-Frenk-White (NFW) proﬁle with a

slope parameter γ= 1.2 and a scale radius rs= 20 kpc,

and we set the local DM density to ρ0= 0.4 GeV cm−3.

These parameters are consistent with the results of, e.g.,

Ref. [45], which point out a strong dependence on how

the baryonic potential is modeled. We take the distance

to the galactic centre to be R0= 8.127 kpc [46]. Here, we

mainly strive to make results as self-consistent as possible

by using common halo parameters in all of our analyses.

We have assumed equal production of each ﬂavor, which

leads to equal ﬂavors at Earth. Due to neutrino oscil-

lation, this will remain approximately true regardless of

the initial ﬂavor composition.

The D-factor depends on the ﬁeld of view of each ex-

periment. Eﬀective areas are reported as a function of

elevation (or equivalently, zenith angle). Given each ex-

periment’s latitude and altitude, we integrate these ac-

ceptances over a period of 24 hours, where the solid angle

integral is weighted by the fractional acceptance. This

deﬁnes an eﬀective D-factor:

Deﬀ =Zdt ZdΩZl.o.s.

ρχ(x)F(Ω, t)dx, (3)

where F(Ω, t) is the fractional acceptance in equatorial

coordinates. This procedure is simpliﬁed for experiments

at the South Pole (IceCube, ANITA), where elevation

and declination are equivalent.

In computing the yield of dark matter in a given ex-

periment, we convolve the experimental eﬃciency with

ﬂux from neutrinos from a given direction. For our back-

ground agnostic constraints, the ﬂux obtained by this

procedure is then compared to the unfolded neutrino

ﬂuxes. When published experimental results on dark

matter annihilation use a directional analysis, such as the

case of ANTARES, we rescale the result by the eﬃciency-

weighted ratio of the dark matter Jto Dfactors; namely

the ratio of expected signal yield in the annihilation to

decay scenarios. Eﬃciencies used for each experiment are

given in Suppl. Table III.

Based on Eq. 1, we produce limits on the DM de-

cay rate, using results from diﬀerent analyses of exist-

ing data [28,43,50,54,61,73–83] or forecasted sensi-

tivities [84–89]. The full list of neutrino experiments is

given in the top section of Table I. We also list the neu-

trino energy range covered by each experiment, spanning

from 10 MeV at Borexino to >1011 GeV at IceCube and

AUGER, as well as each experiment’s neutrino ﬂavor sen-

sitivity. For a detailed description of each experiment and

its sensitivity, we point the reader to Ref. [43]. The D-

factors for each experiment are computed by integrating

the exposure of each telescope over 24 hours. The result-

ing exposures and D-factors are tabulated in Table III in

the Supplementary Material.

The decay lifetime constraints result from a com-

parison between the ﬂux sensitivities from each exper-

iment and the expected neutrino ﬂux from DM de-

cay. This approach assumes a branching ratio of 100%

of DM decay to neutrinos can describe the total neu-

trino ﬂux measurements in the Galactic Center region.

Our forecasts assume ﬁve years of exposure for each

of the following experiments: JUNO [49], DUNE [51],

Hyper-Kamiokande (HK) [51], RNO-G [60], IceCube-

Gen2 [59], KM3NeT [57], P-ONE [56], TAMBO [58], and

GRAND [61]. Constraints that are not derived by us,

but are reported by experiments or other groups, are

rescaled to match the D-factors used in this work. This

enables a fair comparison between diﬀerent experimental

constraints.

TABLE I: Neutrino (top) and gamma-ray

(bottom) observatories considered in this work.

Here, “All Flavors” denotes both neutrinos and

antineutrinos of electron, muon, and tau ﬂavor. The

experiments given in italic font are upcoming or

proposed detectors.

Energy (GeV) Experiment Dir. Particles

(2.5−15) ×10−3Borexino [47]×¯νe

(8.3−18.3) ×10−3KamLAND [48] ¯νe

(10 −40) ×10−3JUNO [49] ¯νe

(1.5−100) ×10−2SK [50]×¯νe

0.1−30 DUNE [51]×νe,¯νe, ντ,¯ντ

0.1−30 HK [51]×νe,¯νe, ντ,¯ντ

1−104SK [52,53] All Flavors

20 −104IceCube [54] All Flavors

50 −105ANTARES [55]νµ,¯νµ

103−107P-ONE [56] All Flavors

104−107KM3NeT [57] All Flavors

106−108TAMBO [58]ντ,¯ντ

>107

IceCube-

Gen2 [59] All Flavors

>108RNO-G [60] All Flavors

>108GRAND [61]ντ,¯ντ

108−1011 Auger [62] All Flavors

10−1−102Fermi-LAT [63]γ

103−109CTA [64]γ

104−109HAWC [65]γ

105−109LHAASO [66]γ

106−109IceTop [67]γ

107−2×109KASCADE [68]γ

108−2×1010 CASA-MIA [69]γ

109−2×1012 EAS-MSU [70]γ

1011.5−1014 TA-SD [71]γ

>1012 Auger-SD [72]γ

Data are available at various stages of the analysis

pipeline. The closer to event-level, the stronger the con-

straining power. Depending on how data are reported,

we are able to compute lifetime limits with varying preci-

sion. The methods by which these diﬀerent data sets are

converted into a lower bound on DM lifetime is outlined

below. Further, Table II outlines the type of data used

to calculate all lifetime limits within this work. Below

we discuss the approach applied to each individual data

set according to the exposure time and neutrino ﬂavor

detected by the experiment.

The full list of references for each experiment is pro-

vided in Tab. I.

1. Lifetime limit

Constraints labeled IceCube (Bhattacharya) are

based on Ref. [28]. They performed an event-level

calculation of limits on dark matter decay and an-

nihilation. They present separate constraints for

decays to electron, mu, and tau ﬂavor. We take

the least constraining (most conservative) limit for

each energy bin, and divide by three to account for

our assumption of equal decay to all ﬂavors. These

limits were not scaled by the ratio of Dfactors due

to matching NFW halo proﬁle assumptions.

Similarly, for the sensitivities of JUNO, based on

Ref. [85], the D-factor deﬁnition matches the halo

parameters used for this analysis and does not re-

quire rescaling.

2. Rescaled annihilation cross section limits

A number of experiments have presented con-

straints on dark matter annihilation cross section

⟨σv⟩, but not decay. These annihilation limits can

be converted into a limit on DM lifetime by rescal-

ing by the appropriate ratio of D-factor to J-factor,

i.e.

τlimit

χ=2mχ

DJ⟨σv⟩limit .(4)

Note that the J-factor refers to the annihilation

equivalent of Eq. (2) with ρ2

χ.

This is done for IceCube, IceCube-DeepCore, and

SuperKamiokande. This procedure is used for sen-

sitivity forecasts for DUNE, HyperKamiokande and

KM3NeT. For our ANTARES constraint, based on

[90], eﬀective areas were presented in Ref. [91] for

three diﬀerent nadir angle bins, as a function of

neutrino energy. This allows us to perform a more

accurate rescaling of the eﬀective ⟨σv⟩to τχcon-

version, by combining Eqs. (4) and (3) to take into

account the acceptance for each mass for a given

time of day.

3. Upper limit on neutrino ﬂux

Borexino, KamLand, SuperKamiokande (¯νesearch)

have presented energy-binned neutrino ﬂux limits.

We translate these to limits on the DM lifetime

using Eq. (1). Limits on only neutrinos or an-

tineutrinos were scaled by an additional factor of

to translate them to a limit on Φν+¯ν. These lim-

its are not derived using angular information in the

data, and are thus less sensitive than a dedicated

analysis.

4. Diﬀuse Neutrino Flux

Limits on the diﬀuse neutrino ﬂux are typically pre-

sented under the assumption of a power-law spec-

trum. We label the size of the logarithmic energy

bins, ∆ ≡log10 Ei−log10 Ei+1 for the ith bin, and

the power law, E−α, such that the limit on the dif-

fuse ﬂux can be written as

dϕ

dE 



lim

=f0E−α,(5)

where f0is constant. This ﬁrst needs to be inte-

grated to turn this limit into a limit on the total

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DarkMatterDecaytoNeutrinosCarlosA.Arg¨uelles,1DiyaselisDelgado,1,∗AviFriedlander,2,3AliKheirandish,4,5IbrahimSafa,6,7,1AaronC.Vincent,2,3,8andHenryWhite2,31DepartmentofPhysics&LaboratoryforParticlePhysicsandCosmology,HarvardUniversity,Cambridge,MA02138,USA2DepartmentofPhysics,EngineeringPhysicsandAs...

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Dark Matter Decay to Neutrinos Carlos A. Arg uelles 1Diyaselis Delgado

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