The Neutrino Magnetic Moment Portal and Supernovae: New Constraints and Multimessenger Opportunities

We scrutinize the hypothesis that gauge singlet fermions -- sterile neutrinos -- interact with Standard Model particles through the transition magnetic moment portal. These interactions lead to the production of sterile neutrinos in supernovae followed by their decay into photons and active neutrinos which can be detected at $\gamma$-ray telescopes and neutrino detectors, respectively. We find that the non-observation of active neutrinos and photons from sterile-neutrino decay associated to SN1987A yields the strongest constraints to date on magnetic-moment-coupled sterile neutrinos if their masses are inside a $0.1-100$ MeV window. Assuming a near-future galactic supernova explosion, we estimate the sensitivity of several present and near-future experiments, including Fermi-LAT, e-ASTROGAM, DUNE, and Hyper-Kamiokande, to magnetic-moment-coupled sterile neutrinos. We also study the diffuse photon and neutrino fluxes produced in the decay of magnetic-moment coupled sterile neutrinos produced in all past supernova explosions and find that the absence of these decay daughters yields the strongest constraints to date for sterile neutrino masses inside a $1-100$ keV window.


Introduction -While the Standard Model (SM)
shows remarkable consistency with numerous experiments, it fails to account for nonzero neutrino masses, dark matter, and the baryon asymmetry of the Universe.The addition of gauge-singlet fermions -sterile neutrinos -to the SM allows one to address these shortcomings.Sterile neutrinos allow for tiny active neutrino masses via the type-I seesaw scenario [1][2][3][4], a model that can also dynamically generate the baryon asymmetry via leptogenesis [5,6].Further, light sterile neutrinos have been widely discussed as viable dark matter candidates [7].In the absence of more degrees of freedom, at the renormalizable level, a sterile neutrino N can only interact with SM particles through Yukawa interactions.These are constrained at different levels by a variety of experimental probes across a plurality of mass scales [8,9].
Active-to-sterile neutrino transition magnetic mo-ments are described by a Lagrangian that includes, after electroweak symmetry breaking, Here, ν α (α = e, µ, τ ) are the active neutrino fields while F µν is the field strength tensor of the electromagnetic field.d α are the interaction strengths, with units of inverse energy; for simplicity, we assume flavor universal interactions and define d α ≡ d, ∀α.M N is the mass of the sterile neutrino.Throughout, we assume that N and the active neutrinos are Majorana fermions.
Given the large flux of neutrinos associated to corecollapse supernova explosions (SN) [30], sterile neutrinos can be efficiently produced via magnetic-moment interactions; the process νe − → N e − is the dominant production channel for M N 100 MeV [26].The observed properties of the SN1987A neutrinos, including their total energy [31][32][33] and the estimated cooling time [34][35][36] -around 10 s -imply that hypothetical sterile neutrinos produced in SN1987A did not carry away O(1) of the available energy.This energy loss argument has been widely employed in the literature in order to constrain various BSM scenarios, including keV-scale sterile neutrinos interacting through active-sterile mixing [37][38][39], axion-like particles [40,41], and dark photons [42,43].For the model in Eq. (1), a detailed analysis based on the energy loss argument was carried out in [26] and allows one to exclude 10 −13 MeV −1 d 10 −10 MeV −1 for M N 100 MeV [26] (see also [44]).The lower bound on d was set assuming the new interaction is such that sterile neutrinos carry at most 10% of the energy released in the explosion, as is typically done in the literature.
Eq. ( 1) also mediates the decay of the sterile neutrinos, N → νγ, which potentially lead to observable signatures at neutrino detectors and γ-ray telescopes.We explore such multimessenger signatures and derive new limits and sensitivity projections.These turn out to be stronger than the standard energy-loss bounds discussed above when M N is in the 0.01 − 100 MeV range.
Sterile neutrino production -The differential number of sterile neutrinos N s produced via the magnetic moment portal per unit time t and position r is Here, σn e is related to the interaction rate for the process νe − → N e − which dominates, for M N 100 MeV, due to large neutrino and electron number densities inside the star.The cross section, σ, is proportional to d 2 and includes finite temperature effects as well as those of Pauli blocking on the final state electron; the latter means that a time and radius-dependent chemical potential has also been employed.Further, n e and n ν are, respectively, the number densities of electrons and neutrinos.(1/n ν ) dn ν /dE = f (E)/E where E is the mean neutrino energy and f (E) is the neutrino distribution function [45].The approximate relation between the sterileneutrino and active-neutrino energy is E = 1 2 (E N + p N ), where p N is the sterile-neutrino momentum.We solve Eq. ( 2) using data associated to the simulation performed by the Garching group of an 8.8M progenitor star [33].For more details, see Appendix A. In addition to νe − scattering, we also include contributions from the inverse decay process, γν → N , which is known to be relevant when M N 100 MeV [26].Requiring the total energy carried away by N to be less than 10% of the total available neutrino energy leads to the "cooling" bound depicted in Fig. 1 (gray region).Our estimate is in agreement with the one obtained in [26].
While active neutrinos exit the SN with energies of a few tens of MeV, they are copiously produced at higher temperatures in the dense SN core.Sterile neutrinos, instead, in the parameter space of interest, promptly exit the SN after production.This implies that the typical sterile-neutrino energies are O(100 MeV) (see Appendix A).Sterile neutrinos will decay en route to the Earth via N → νγ, producing O(100 MeV) active neutrinos and photons.
Sterile neutrino decay -The decay width for N → νγ is Γ N = 6d 2 M 3 N /4π [46].For d values of interest, sterile neutrinos produced in the SN core do not interact before decaying.The daughter particles are emitted at an angle α relative to the direction of N , given by where E γ and E ν denote the energies of the daughter photon and neutrino, respectively.For a small range of α, < l a t e x i t s h a 1 _ b a s e 6 4 = " w E I 8 J z t g P f 6 2. Geometry of sterile neutrino decays en route to the Earth.
the daughter particle can reach the Earth, as sketched in Fig. 2. The angle θ at which the daughter particle arrives at the Earth is given by D SN sin θ = L 1 sin α, where D SN is the distance between the SN and the Earth, and L 1 is the distance propagated by N before decaying, see Fig. 2.
In the frame of an observer at the Earth, the differential decay rate of a Majorana N is given by the box distribution [46][47][48] ) where N /E N , the speed of N .Here, we sum over all final-state photon and neutrino polarizations.
The time delay ∆t, the arrival time of the daughter γ/ν relative to the arrival time of the neutrinos produced in the explosion via SM processes, is [49] where L 2 = D SN cos θ − L 1 cos α.For a given ∆t, One finds that θ is bounded: The flux of daughter γ/ν is obtained by integrating over all N decays that occur at R L max 1 corresponds to the distance L 1 associated to the largest time delay considered or the largest angle θ max allowed by observations.R γ/ν SN is the smallest decay distance for which the decay daughter can escape the explosion unperturbed.For daughter photons, N should decay beyond the photosphere, otherwise the associated photon flux is severely attenuated.Conservatively, we take the photosphere radius to match the radius of the star; we adopt R γ SN = 3 × 10 10 m, the estimated radius of the SN1987A progenitor [50].For neutrinos, R ν SN is chosen to be the radius of the neutrinosphere, assumed to be R ν SN = 30 km.In what follows, we will consider different observation time windows and take θ max to be the angular resolution of the γ-ray telescope.The differential flux of daughter particles per unit energy and area A at the Earth is where Gamma-ray detection -We calculate the photon flux at the Earth using Eq. ( 6).Our results are depicted in Fig. 3 for a time window ∆t < 223 s (solid), and a nominal longer exposure ∆t < 3600 s (dashed), assuming D SN = 51.4kpc.We choose θ max = 5 • which, for ∆t < 3600 s, always exceeds the angles at which the photons arrive.The "plateau" for E γ M N is a reflection of the aforementioned box energy distribution while the suppression at larger E γ is a consequence of the fact that the production of sterile neutrinos with energies above the SN core temperature is inefficient.The total number of observed photons N BSM γ , taking into account detection inefficiencies, is obtained by integrating Eq. ( 6) over the photon energy range and the detection area of the γ-ray telescope of interest.
Keeping in mind the small number of decay-daughter gamma rays and neutrinos from the SN explosion, we define the log likelihood (7) and consider constraints at the 2σ level, associated with −2lnL = 3.841.Here, N exp is the number of expected events for a particular point in the (d × M N ) parameter space and N obs is the number of observed events.
At the time of SN1987A, the Gamma-Ray Spectrometer (GRS), mounted on the satellite-borne Solar Maximum Mission (SMM) [51], was operating and observed N obs = 1393 events from the direction of SN1987A in the time window up to 223 s after the neutrino burst and in the energy band 25-100 MeV, with a full field view of the detector [52,53].This event number is consistent FIG. 3. Flux, at the Earth, of photons produced via sterile neutrino decay, for two benchmark points: ∆t < 223 s (solid) and ∆t < 3600 s (dashed).
with expectations from the galactic diffuse photon flux and several other sources, including scintillation light induced by primary cosmic rays [51].We use θ max = 5 • to calculate the number of BSM events, N BSM γ , in the time window ∆t < 223 s.In the parameter space of interest, the angular distribution is very narrow (θ 5 • ).Using Eq. ( 7), we require N BSM γ ≤ 76, a 2σ fluctuation of N obs = 1393.The corresponding constraint is depicted in Fig. 1 as a blue shaded region labeled "SN1987A(γ)."For M N ∼ 100 MeV, we can exclude d ≈ 10 −15 MeV −1 , a constraint that significantly exceeds those of other probes, including the energy loss argument discussed earlier (gray region in Fig. 1).For small M N , the constraints are much weaker because the ∆t < 223 s condition becomes increasingly more difficult to satisfy.
In the event of a future core-collapse SN, current and near future experiments will be able to probe a much larger region of the parameter space.Assuming the SN event happens in the galaxy at a distance D SN = 10 kpc, which is not unlikely [54,55], we consider the currentlyoperating Fermi-LAT, which has a total detection area of 9500 cm 2 and angular resolution around 5 • in all directions [56], together with near-future experiments such as e-ASTROGAM [57] (detection area 9025 cm 2 and angular resolution of 1.25 • ), ComPair [58], and PANGU [59], which will provide better sensitivity for E γ 100 MeV.e-ASTROGRAM, ComPair, and PANGU may be relevant for the small M N region, where a potentially significant portion of the flux has E γ < 100 MeV; see Fig. 3, where fluxes for low and high M N benchmarks are compared.To estimate the sensitivity of these experiments to transition magnetic moments, we consider the same time windows as before, 223 s and 3600 s.With these choices, for E N and M N values of interest, the arrival angle θ is, roughly, less than 5 • .
When estimating the sensitivity of Fermi-LAT, we restrict E γ > 100 MeV [60].For e-ASTROGAM, we instead consider photons with E γ > 1 MeV.The sensitivity projections are depicted in Fig. 1 as dashed lines for both Fermi-LAT, with ∆t < 223 s (3600 s) and N BSM γ < 2.5 (4.9) (blue); and e-ASTROGAM with ∆t < 3600 s and N BSM γ < 4.4 (black).These correspond to 2σ sensitivity, assuming all backgrounds can be eliminated.Future sensitivity is expected to improve on SN1987A constraints by roughly two orders of magnitude throughout the parameter space.PANGU will likely be able to measure the polarization of the gamma rays, allowing one to, for example, distinguish photons from different origins.We leave this to a future study.
To appreciate the fundamental physics impact of possible future Fermi-LAT and e-ASTROGAM measurements, we compute the transition magnetic moment predicted by a specific UV-complete model of neutrino masses involving leptoquarks [25].There, active neutrino masses m ν are obtained via the type-I seesaw mechanism.The expected values of the transition magnetic moment d are related to the mechanism that generates the Dirac masses, connecting the active and sterile neutrinos.One obtains d 10 −13 MeV −2 √ m ν M N for leptoquark masses at the TeV scale.For m ν = 0.1 eV, the expected value of d as a function of M N is depicted in Fig. 1 as a green line, well within the reach of the projected sensitivity for the next galactic SN event.
Neutrino detection -Besides the photon signal, the production of N can also lead to a new, higher energy SN neutrino flux.For active neutrinos produced in radiative N decay, we investigate two water-Cherenkov detectors, Kamiokande-II and IMB, that recorded, respectively, 11 and 8 neutrino events from SN1987A.In these experiments, antineutrinos were detected through inverse beta decay, the most relevant interaction channel for ν e detection in the E ν ∼ 10 − 50 MeV window.Since we assume the magnetic moments are flavor universal, radiative N decays lead to identical numbers of all three neutrino flavors -electron, muon, and tau -and polarizations -referred to as "neutrinos" (left-handed) and "antineutrinos" (right-handed).At low neutrino energies, IMB and Kamiokande-II are only sensitive to the daughter electron antineutrinos and in this case only 1/6 of the flux in Eq. ( 6) is accessible.
We perform two complementary analyses, dubbed "low energy" and "high energy".For the former, we investigate if decaying sterile neutrinos can significantly enhance the number of reported events in the energy interval E ν ∈ [10,50] MeV.We set the time windows to be ∆t < 13 (6) s for Kamiokande-II (IMB) since these are the time windows inside which SN1987A neutrinos were detected.The event rates are given by where N tgt is the number of hydrogen atoms in the detector -Kamiokande-II (IMB) contains 2.14 (6.8) kton of water [61] -and σ IBD (E ν ) is the cross section for inverse beta decay.Detection efficiencies ε(E ν ) are also included [61].We use Eq. ( 7) and take the number of SN events from our simulation as a proxy for N obs in order to keep the estimates of N exp and N obs on equal footing.In Eq. ( 7), we sum the contributions of the two experiments under consideration.In this low-energy analysis, we find that the exclusion limits are at most comparable with the cooling limit.
Regarding the high-energy analysis, restricted to E ν > 70 MeV, we make use of the fact that no significant excess of neutrino events was reported by either Kamiokande-II [34] or IMB [35] in a detailed search for neutrino events inside a two-day interval surrounding the observation of the burst.Atmospheric neutrinos are the main source of background in this analysis.We estimate the number of atmospheric neutrino events inside ∆t < 1 day.Further, taking into account that, for E ν 70 MeV, the cross sections for both ν e and ν e scattering on oxygen dominate over that for inverse beta decay [61], we again perform an analysis following Eqs.( 7) and (8).For N obs , we use the reported atmospheric neutrino background from IMB (2 events/day), and for Kamiokande-II we rescale the IMB number by the ratio of the fiducial masses of the detectors, a factor of 0.32.The excluded region, combining both IMB and Kamiokande-II data, is depicted in Fig. 1 (cyan).We observe that this neutrino limit is stronger than the cooling bound by, roughly, a factor of two.Unlike the photon bound (blue shaded), the neutrino limit extends to higher M N values since daughter neutrinos can come from sterile neutrinos decaying deep inside the photosphere (and still outside of the neutrinosphere).The neutrino limit on d is mostly independent from M N for M N ∼ [0.1, 100] MeV.The limit weakens for lower values of M N , when ∆t fails to fulfill our selection criteria.
The near-future neutrino experiments DUNE [62] and Hyper-Kamiokande [63] are expected to identify several thousands of neutrino events from a future galactic SN.For a hypothetical future galactic SN at D SN = 10 kpc, we estimate the sensitivity of the equivalent of the highenergy analysis for these next-generation experiments.For Hyper-Kamiokande, the strategy is very similar to that of Kamiokande-II; we simply rescale both the new physics and atmospheric background events according to the ratio of fiducial masses.In the case of DUNE, for E ν < 100 MeV, we use the antineutrino cross sections on argon presented in [64].For higher energies (up to 400 MeV), we use GENIE [65] to estimate the relevant cross sections.The results are depicted in Fig. 1 as dashed yellow lines.One is sensitive to FIG. 4. Diffuse photon flux from sterile neutrino decays compared to the measured extragalactic photon background in Eγ ∼ 1 − 100 MeV window.Measurements shown in green (purple) are made by COMPTEL [68] (EGRET [69]); for more data in this energy regime see [53].d 10 −14 MeV −1 , roughly an order of magnitude improvement with respect to current limits from SN1987A.Notice that the upturn in the sensitivity occurs at larger masses relative to the constraints from Kamiokande-II and IMB.This is because for relatively smaller values of d relatively larger values of M N are required to ensure the decay length is shorter than the SN distance.
Diffuse γ-ray and neutrino background -We also investigate the cumulative effect from all past SN explosions and explore the prospects of detecting the related diffuse γ-rays and neutrinos from radiative sterile neutrino decays.The number density of sterile neutrinos from all past SN is [53,66] where z is the redshift, n cc is the derivative with respect to z of the number of SN per comoving volume, from [67], and dN s /dE is the sterile neutrino spectrum evaluated at E z ≡ E(1 + z).In order to estimate the number density of photons or neutrinos from N decays, we also need the fraction f D (z) of sterile neutrinos that have decayed by the present time; see [53] for an exact expression.In a nutshell, (dn γ,ν /dE γ,ν ) is obtained by replacing dN s /dE in Eq. ( 9) with ).The diffuse photon spectrum for two benchmark points is depicted in Fig. 4.
We rule out the region of the d × M N parameter space where the expected photon energy distribution over-shoots the extragalactic differential photon background measured by COMPTEL and EGRET [53], depicted in Fig. 4.These constraints are shown in Fig. 1 (magenta).The shape of the constrained region is different from the constraints associated to a single SN explosion, including the SN1987A constraint, mostly due to effects associated to the cosmological redshift.
When it comes to the diffuse neutrino flux from the radiative decay of sterile neutrinos produced in all past SN, we find it to be unobservable given existing constraints on the model.More details are presented in Appendix B.
Summary and Conclusions -We considered the neutrino magnetic moment portal between light neutrinos and hypothetical sterile neutrinos with masses M N 100 MeV.The new interaction allows for the production of these sterile neutrinos inside SN and mediates their subsequent decays into active neutrinos and photons.If the decay is neither too fast nor too slow, these daughter neutrinos and photons should find their way to the Earth and into our detectors and telescopes.We estimated new constraints on the magnetic moment portal from the absence of such neutrinos and photons associated to SN1987A and found that these are more powerful probes than the more standard cooling bounds.We also considered the flux of neutrinos and photons from the radiative decays of sterile neutrinos produced in all previous SN events and showed that constraints from the observed diffuse γ-ray flux are competitive with those from SN1987A for M N 1 MeV.With an eye towards the future, we estimated the sensitivity of next SN explosion, given the capabilities of current and next-generation neutrino detectors and γ-ray telescopes.active neutrinos (flux  10 -3 ) M N =1 MeV, =3.5610 -13 MeV -1 M N =100 MeV, =1.5510 -13 MeV -1 FIG. 5. Thermal active neutrino spectrum (blue) relative to that of sterile neutrinos (red, green) produced through the magnetic moment portal.See text for details ergy distribution of the active neutrinos as a function of radius and time.In particular, α [70] parameterizes the deviation of the SN neutrino energy distribution from a Maxwell-Boltzmann one; all α-dependent terms in Eq. (A1) are building blocks of f (E), see [45].All parameters are evaluated at "snapshots" in time and space (provided by SN simulation data) between which we interpolate.The radial integral runs from the center of the star (close to R = 0) to its outer layers; in our calculations we stop at 40 km since the production of sterile neutrinos is concentrated inside the neutrinosphere (∼ 30 km) due to the larger number densities of neutrinos and electrons.The time integration encompasses the neutronization, accretion, and cooling phases of the SN explosion and, for the simulation at hand, data are available until 8.85 s after core bounce.
We used data associated to the simulation of a 8.8M progenitor star performed by the Garching group [33] and do not explore potential uncertainties associated to SN modeling [71,72].We expect these not to impact our results in a meaningful way.Fig. 5 depicts sterile neutrino spectra calculated using Eq.(A1) for two benchmark points with M N = 1 MeV (red) and M N = 100 MeV (green) and comparable values of d.For comparison, the figure also contains the active neutrino spectrum (summed over all flavors, in blue).The typical sterile neutrino energies (as well as the energies of its decay products, see Fig. 3) are roughly an order of magnitude larger than the energies of the thermal active neutrinos.The production of active neutrinos from the decay of sterile neutrinos hypothetically produced inside all past SN explosions is discussed in the main body of this manuscript, see text around around Eq. ( 9).The detection of electron antineutrinos via inverse beta decay in water Cherenkov detectors is the most sensitive channel, on which we concentrate.We consider results from [73] and utilize their 90% CL upper limit on the diffuse ν e flux (see Fig. 25 in [73], where previous results from Super-Kamiokande [74] and KamLAND [75] are also summarized).In Fig. 6, we compare the fluxes expected from two benchmark points with the existing upper limits.As can be inferred from the figure, for values of d 10 −13 MeV −1 , the BSM-induced neutrino diffuse flux is significantly smaller than the existing upper limits.These values of d roughly correspond to the neutrino limits from the SN1987A energy loss argument (gray boundary in Fig. 1) so current bounds from the diffuse neutrino background are not competitive.For E ν 40 MeV, there are no upper limits on the diffuse flux in the literature; for these and higher energies, the atmospheric neutrino background is relatively large.

F
FIG. 1. 2σ constraints and future sensitivity for the transition magnetic moment d as a function of the sterile neutrino mass MN .See text for detail.

1 FIG. 6 .
FIG. 6. Diffuse neutrino flux from sterile neutrino decays compared to the flux sensitivity of KamLAND and Super-Kamiokande.