Dark Matter Decay to Neutrinos

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 × 10 21 s at 10 MeV to 1 . 5 × 10 29 s at 1 PeV.

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 × 10 21 s at 10 MeV to 1.5 × 10 29 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 measured 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 Universe [1,2].While these observations imply an equation of state consistent with a cold, collisionless fluid, no microphysical connection has yet been found between DM and the Standard Model (SM) of particle physics.Numerical coincidences such as the one-to-five ratio of darkto-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 describable in the language of particle physics.
The parameter space of such nongravitational interactions is immense, and myriad portals are potentially available.Traditional searches for electroweak and supersymmetry-inspired WIMPs in the GeV-TeV mass range that scatter with or annihilate to quarks have expanded in the past decades to encompass light axionlike [3] and minicharged particles [4][5][6][7][8], sub-GeV nonthermal 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.
Direct searches for such DM rely on elastic scattering 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 particles eventually create a flux of stable particles, i.e., protons, electrons, photons, or neutrinos.Here, we focus on the latter.A direct neutrino portal would render direct detection impracticable, and indirect detection very difficult, 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 transfer as is the case of photon-nucleon interactions [12][13][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 sector 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][16][17][18][19][20][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 motivated numerous dedicated studies, mainly in the context of discovering heavy DM using neutrino line searches [24][25][26][27][28][29][30][31][32][33][34][35], and many neutrino experiments have hunted for DM signatures in their observations [36][37][38][39][40][41][42], so far yielding null results.
Previously, we presented an updated compendium of constraints on particle DM annihilation to neutrinos [43].Here, we turn our attention to the production of neutrinos from DM decay, directing special attention to the higher-mass region.At masses greater than ∼ TeV, electroweak (EW) corrections can "decloak" the DM, producing 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 upcoming experiments covering a DM mass range starting at 20 MeV and spanning well into the ultra-heavy domain up to 10 11 GeV.Although recent LHAASO results are on par with IceCube's recent analyses, we will find that current and future neutrino telescopes retain superior sensitivity across nearly the entire range of masses that we consider.This is due to three factors: the loop suppression 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 Section IV.

II. DARK MATTER DECAYS TO NEUTRINOS
The expected flux per neutrino flavor at Earth from decay of DM with mass m χ and lifetime τ χ is Below the electroweak scale, the neutrino spectrum per decay is dN ν /dE ν = 2δ(1 − 2E/m χ )m χ /2E 2 ; at higher masses a low-energy tail arises as discussed in Ref. [44].
Because relevant backgrounds follow a power-law distribution, only the delta contribution is relevant for neutrino 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: We assume the Galactic DM spatial distribution is modeled by an Navarro-Frenk-White (NFW) profile with a slope parameter γ = 1.2 and a scale radius r s = 20 kpc, and we set the local DM density to ρ 0 = 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 R 0 = 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 oscillation, this will remain approximately true regardless of the initial flavor composition.Auger-SD [72] γ Based on Eq. 1, we produce limits on the DM decay rate, using results from different analyses of existing data [28,43,50,54,61,[73][74][75][76][77][78][79][80][81][82][83] or forecasted sensitivities [84][85][86][87][88][89].The full list of neutrino experiments is given in the top section of Table I.We also list the neutrino energy range covered by each experiment, spanning from 10 MeV at Borexino to > 10 11 GeV at IceCube and AUGER, as well as each experiment's neutrino flavor sensitivity.For a detailed description of each experiment and its sensitivity, we point the reader to Ref. [43].The Dfactors for each experiment are computed by integrating the exposure of each telescope over 24 hours.The resulting exposures and D-factors are tabulated in Table II in the Supplementary Material.

A. Gamma rays from electroweak corrections
Above the TeV scale, electroweak corrections can lead to the production of photons.These result in two distinct gamma-ray fluxes.First, "prompt" high-energy flux consisting of primary photons emitted during the dark matter decay to neutrinos.Second, lower-energy (GeV-TeV) photon signal due to scattering of primary photons with the CMB and extragalactic background light (EBL).The prompt gamma-ray spectra can be obtained via the HDM-Spectra package [44], which solves the Dokshitzer-Gribo-Lipatov-Altarelli-Parisi (DGLAP) equations above the electroweak scale with initial conditions given by the DM decay channel.At the edge of this scale, HDMSpectra matches its solution with Pythia-8.2[90], which calculates the effects of particle showers, hadronization, and light particle decays.
We use the gamma-ray distribution from this package to derive constraints using gamma-ray data sets in a similar way to how we proceed with neutrinos.One important difference is the inclusion of an additional factor of exp(−τ γγ ) in Eq. 1.This factor accounts for attenuation due to pair-production from scattering of highenergy gamma-rays with CMB photons, the dominant attenuation channel.For the galactic component, we conservatively include this as a constant factor by taking the average attenuation rate over a distance of 10 kpc.We will present limits from Fermi-LAT [63], HAWC [65], LHAASO [66], IceTop [67], KASCADE-Grande [68], CASA-MIA [69], EAS-MSU [70], TA-SD [71], and Auger-SD [72] observations as well as a projected sensitivity for CTA [64].For CTA, we consider the differential sensitivity from [91] and convert it to an upper limit on the total flux per decade of energy, which is defined as the minimum flux required to obtain a 5σ point source detection from CTA Southern array for a total observation time of 50 hours.
In the case of IceTop, we use the differential upper limits at 90% C.L. reported in [92].These are then converted to total integrated emission per energy decade.For KASCADE, KASCADE-Grande, CASA-MIA, EAS-MSU, TA-SD, and Auger-SD, we use the integral gammaray flux upper limits reported in Refs.[93][94][95][96][97].For HAWC, we follow the same procedure for the flux upper limit in each declination band [98] and then further select the most stringent constraint among all bands.All integrated gamma-ray fluxes are then compared to the expected total flux from DM decay to neutrinos with the photon spectrum from electroweak corrections.This comparison then yields our constraints on the DM decay  I.
lifetime.Limits for decaying DM to all neutrino flavors from LHAASO were taken from [99].At sufficiently large masses, gamma rays produced from decays outside our galaxy can scatter down to produce a signal that is observable at lower energies in experiments such as Fermi -LAT.High-energy gamma rays traversing the intergalactic medium (IGM) are absorbed and scattered by photons from the CMB and EBL, attenuating the signal [100]; see Ref. [101] for a recent detailed discussion.Scattering and absorption of gamma rays result in cascades that transform any sufficiently highenergy gamma-ray source into a universal spectrum [102] that peaks within the Fermi telescope's sensitivity range.In what follows we take advantage of this universality to extend gamma-ray limits to higher dark matter masses, and convert them to limits on decay to neutrinos.
Ref. [103] sets constraints on the lifetime of DM decay to SM particles using Fermi observations of the isotropic gamma-ray background.We use the limits presented there for DM decays to neutrino pairs that extend up to m χ = 10 7 GeV.The limits presented in Ref. [103] constrain the channel χ → bb up to 10 10 GeV.We use these to obtain corresponding limits in the channel of interest, DM decay to neutrino pairs.The idea of the universal spectrum means that regardless of the initial gamma-ray spectral shape, the spectrum arriving at Earth is universal.Therefore limits on dark matter decay to neu-trinos are related to the χ → bb limits by a factor of F γ χ→νν /F γ χ→ bb = 0.06, where F γ χ→ XX is the fraction of energy per decay to species X going into photons.Suppl.Fig. 1 shows that this rescaling yields the published νν results below 10 7 to a reasonable accuracy, allowing us to confidently extend these limits up to 10 10 GeV.We find that the Fermi-LAT constraints remain subdominant over the full range of masses considered.

III. RESULTS
Using the methods outlined above, we present constraints on the DM decay lifetime in Fig. 2. We label the results derived for this work with a heart (♥).
Constraints from neutrino telescopes are shown as shaded regions bordered by solid lines.The overlap in experimental sensitivities yields continuous constraints on the DM lifetime that are much greater than the age of the Universe, ranging from τ > 10 19 s at m χ ∼ 50 MeV to τ > 10 27 s for m χ ∼ 10 11 GeV.The expected neutrino flux at Earth from DM decay is independent of mass.Below ∼ 10 7 GeV, this is reflected by sensitivity closely following the growth of the electroweak cross section with energy, with some scaling between experiments owing to differences in effective volumes.Above ∼ 10 7 GeV energies, the Earth becomes opaque to neutrinos, and detection technologies become sensitive to a much smaller solid angle, usually restricted to an area just around the horizon.
Estimated sensitivities of future observatories are shown as dashed lines; these assume five years of data taking.JUNO, Hyper-K, DUNE, KM3NeT, P-ONE, and IceCube-Gen2 should each lead to an improvement of one to two orders of magnitude over current bounds, mainly owing to much larger effective detector volumes.Projected improvements from future radio (GRAND, RNO-G) and modular Cherenkov arrays (TAMBO) are more modest, which we mainly attribute to restricted fields of view.
Limits from gamma-ray observatories are marked with a γ superscript.These are also shown separately in Fig. 3. Four experiments dominate the constraints at three different energy ranges.At masses below ∼ 10 5 GeV, the flux of extragalactic gamma-rays produced by interactions with the IGM is probed by Fermi -LAT, yielding the dominant source of gamma-ray constraints in this mass range.At masses between 10 6 and 10 7 GeV, recent measurements by LHAASO supersede prior experiments and improve constraints by nearly four orders of magnitude compared to HAWC.At masses above 10 7.5 GeV, KASCADE-Grande measurements establish the most competitive constraints on the DM decay lifetime limits, outperforming existing neutrino telescopes; at m χ > ∼ 10 10 GeV, Auger-SD supersedes all other experiments thanks to its monumental effective area.Other experiments considered, such as HAWC or IceTop, remain subdominant over the entire mass range probed here.

IV. FUTURE PROSPECTS & CONCLUSIONS
As shown in Fig. 2, existing neutrino telescopes are able to constrain the lifetime of DM decay to neutrino pairs to values ranging from 10 3 to 10 12 times the age of the Universe.Upcoming neutrino telescopes will make improvements of one to two orders of magnitude: DUNE and Hyper-Kamiokande will fill in the gap around m χ ∼ GeV, while the strongest improvements will take place for the next generation of large-volume water and ice Cherenkov telescopes: KM3NeT, P-ONE, and IceCube-Gen2.Though not included here, the ongoing scintillator phase of SNO+ [104] may also shore up constraints on the low-mass end, depending on the timeline for tellurium filling; the inclusion of directional information in, e.g., Borexino [105] or KamLAND analyses could also yield a modest improvement in reach [106,107].
Above the ∼ TeV range, the electroweak emission of gamma rays opens a new opportunity for discovery, and above 10 8 GeV, gamma rays become the dominant source of information, thanks to the large telescope areas and unsuppressed electroweak emission of photons.What's more the observation of an electromagnetic counterpart will be key in the event of a discovery.Intriguingly, the Square Kilometre Array (SKA) will be sensitive to χ → νν [29] in nearby dwarf galaxies for DM masses above a few hundred GeV.Taken together, these observations highlight the importance of multimessenger observations when it comes to elucidating the nature of dark matter.FIG.2: Constraints on the lifetime of dark matter decaying to neutrinos χ → νν.Solid lines bordering shaded regions represent limits from existing neutrino telescope data, solid lines without shading correspond to limits from existing gamma-ray observatories (as shown in Fig. 3), and dashed lines show the reach of future experiments.Labels with a heart symbol (♥) correspond to limits derived for this work.

FIG. 1 :
FIG. 1: Expected integral gamma-ray fluxes produced by electroweak corrections to dark matter decay to neutrinos overlaid on the observed gamma-ray distributions.Integral fluxes, defined as the integral of the flux from E γ to infinity, for four different dark matter masses and lifetime of τ χ = 10 27 s, are shown as solid lines.Colored symbols indicate observations detailed in the bottom half of TableI.

10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 10 12 FIG. 3 :
FIG.3: Gamma-ray constraints on dark matter decay lifetime χ → νν due to γ emission from electroweak processes.Solid lines correspond to existing constraints, while the dashed line is a projection for a future experiment.Hearts indicate the new constraints derived in this work.Gamma-ray emission below the electroweak scale is suppressed by powers of M W[44].

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.