Detecting the radiative decay of the cosmic neutrino background with line-intensity mapping

We study the possibility to use line-intensity mapping (LIM) to seek photons from the radiative decay of neutrinos in the cosmic neutrino background. The Standard Model prediction for the rate for these decays is extremely small, but it can be enhanced if new physics increases the neutrino electromagnetic moments. The decay photons will appear as an interloper of astrophysical spectral lines. We propose that the neutrino-decay line can be identified with anisotropies in LIM clustering and also with the voxel intensity distribution. Ongoing and future LIM experiments will have -- depending on the neutrino hierarchy, transition and experiment considered -- a sensitivity to an effective electromagnetic transition moment $\sim 10^{-12}\, -\,10^{-8}\, (m_ic^2/{0.1 \rm eV})^{3/2}\mu_{\rm B}$, where $m_i$ is the mass of the decaying neutrino and $\mu_{\rm B}$ is the Bohr magneton. This will be significantly more sensitive than cosmic microwave background spectral distortions, and it will be competitive with stellar cooling studies. As a byproduct, we also report an analytic form of the one-point probability distribution function for neutrino-density fluctuations, obtained from the Quijote simulations using symbolic regression.

Considerable efforts are underway to study the properties of neutrinos, including their masses, mixing angles, and nature (e.g., Dirac or Majorana) . The stability of neutrinos is also of interest. An active massive neutrino ν i can decay into a lighter eigenstate ν j and photon, γ, ν i → ν j + γ with a rate determined by electromagnetic transition moments induced via loops involving gauge bosons. The Standard Model (SM) prediction for the lifetime is τ SM = 7.1 × 10 43 m −5 eV s [22][23][24][25], where m eV ≡ m ν c 2 /eV is the neutrino mass in eV/c 2 units, significantly longer than the age of the Universe.
Here we study the use of line-intensity mapping (LIM) to seek photons from radiative decays of neutrinos in the cosmic neutrino background. LIM [44,45] exploits the integrated intensity at a given frequency induced by a well-identified spectral line to map the three-dimensional distribution of matter in the Universe. Photons from particle decays will appear in these maps as an unidentified line [46] that can be distinguished from astrophysical lines through its clustering anisotropies and through the voxel probability distribution function [47]. We find that LIM has the potential to be significantly more sensitive to radiative decays than current cosmological probes and compete with the strongest bounds to electromagnetic moments coming from astrophysical observations. While neutrino radiative decays are characterized by the electromagnetic transition moments, LIM experiments are sensitive to the luminosity density ρ L of the photons produced in each point x, which, for the decay between the i and j states, is given by where ρ ν is the total neutrino density, Γ ij ≡ τ −1 ij is the decay rate, and m i are the neutrino masses. We assume that the density of each state is 1/3 of the total density, as expected apart from small mass differences and flavor corrections that have negligible consequences for the precision goals of this Letter [48]. The corresponding arXiv:2103.12099v2 [hep-ph] 22 Oct 2021 brightness temperature T at redshift z is where H is the Hubble expansion and k B is the Boltzmann constant and f is the rest-frame frequency [49]. Thus, the brightness temperature from neutrino decays traces the neutrino density field. Decay photons are then an emission line with restframe frequency given by where T ν is the cosmic neutrino temperature), which holds true for our cases of interest, the neutrinos are non-relativistic and we can neglect the linewidths due to their velocity dispersion. 1 The restframe frequency of the emission lines is then uniquely characterized by the neutrino hierarchy and the sum m ν of neutrino masses, as shown in Fig. 1, with the observed frequency redshifted accordingly. The transitions not included in the figure have a very similar frequency than one of the other two (e.g., f 31 ≈ f 32 for the normal hierarchy) and are not distinguished hereinafter.
We now consider two LIM observables: the power spectrum and the voxel intensity distribution (VID). The observed anisotropic LIM power spectrum associated to the neutrino decay between i and j states is [47,50] where k is the modulus of the Fourier mode, µ ≡ k·k /k 2 is the cosine of the angle between the Fourier mode and the line of sight, W is a window function modeling the effects from instrumental resolution and finite volume observed, the brackets denote the spatial mean, F RSD is a redshift-space distortions factor [50], P ν is the neutrino power spectrum, computed using CAMB [51], and all redshift dependence is implicit. We consider the Legendre multipoles of the LIM power spectrum with respect to µ up to the hexadecapole. Similarly, the VID is related to the probability distribution function (PDF) Pρ of the normalized total neutrino densityρ ν ≡ ρ ν / ρ ν , as P ij (T ) = Pρ(ρ ν )/ T ij . We estimate the neutrino density PDF from high-resolution simulations of the Quijote simulation suite [52], that model the gravitational evolution of more than 2 billion cold dark matter and neutrino particles in a comoving box of (1 h −1 Gpc) 3 volume. Degenerate neutrino mass eigenstates are assumed. First, neutrino particle positions are assigned to a regular grid with 1500 3 voxels employing the cloud-in-cell mass-assignment scheme. Next, the 3D field is convolved with a Gaussian kernel of a given width. Then, the PDF is estimated by computing the fraction of voxels with a givenρ ν . We do this for m ν c 2 = {0.1, 0.2, 0. 4} eV, at z = {0, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9} and for 6 smoothing scales {2, 3, 4, 5, 7.5, 10} h −1 Mpc. We have checked that the computed PDFs, in the range of interest for this study, are converged in our simulations. Note that all dependences can be condensed in the root-mean square σ of smoothed density field, which depends on m ν , z and the smoothing scale. Finally, we use symbolic regression to approximate this grid of PDFs using the Eureqa package (https://www.datarobot.com/nutonian/) finding where  a normalization factor. LIM experiments will not target the emission line from neutrino decays, but known astrophysical lines. In turn, the neutrino decay line will redshift into the telescope frequency band from a different redshift. All emission lines other than the main target that contribute to the total signal tracing other cosmic volumes are known as line interlopers. These contributions, if known, can be identified and modeled (see e.g., [53][54][55][56][57][58][59][60][61]). However, the neutrino decay line will be an unknown line interloper. From Fig. 1 we can see that the frequencies of interest lie in the frequency bands of experiments like COMAP [62] (which targets the CO line) and CCAT-prime [63] and AtLAST [64] (which target the CII line); their instrumental specifications are summarized in Table I.
We assume the fiducial astrophysical model for the CO and the CII lines from Refs. [65] and [66], and model their power spectrum and VID, with their corresponding covariances, following Refs. [47,50,67]. For the VID analysis, we use a modified Schechter function with the parameters reported in Ref. [47]. We take ΛCDM cosmology with best-fit parameter values from Planck temperature, polarization and lensing power spectra [68] assuming m ν c 2 = 0.06 as our fiducial model. We consider normal (NH) and inverted (IH) neutrino hierarchies. 2 Recently, a similar situation, regarding decaying dark matter, was described in Ref. [47], where strategies to detect such decays were proposed. Here we adapt that modeling to the neutrino decay case, considering neutrino decays happening at z < 10, and perform a Fishermatrix analysis [69][70][71][72], accounting for the uncertainity in the astrophysical model. In summary, the contribution from neutrino decays to the VID can be modeled by convoluting P ij (T ) with the astrophysical and noise 2 In the Fisher-matrix analysis, the variation of mν and the change of the neutrino hierarchy are included in our fiducial model: we only consider deviations due to the neutrino decay and not to the varying neutrino masses.
VIDs: the total VID is the result of the sum of the three contributions. In turn, the contribution to the power spectrum consists of the addition of the projected power spectrum from neutrino decays to a different redshift, which introduces a strong anisotropy in the power spectrum, altering the ratio between the Legendre multipoles. For the power spectrum, we do not consider decays from the same cosmic volumes probed by the astrophysical line because they are very degenerate with astrophysical uncertainties.
We show the forecasted minimum values of Γ ij which LIM experiments will be sensitive to at the 95% confidence level, as function of the neutrino hierarchy, transition, and m ν in Fig. 2. We limit the minimum m ν at the minimum mass allowed for each hierarchy from neutrino oscillations experiments [73]. As expected from Fig. 1, COMAP and the experiments targeting CII are sensitive to the transitions between close and far mass eigenstates, respectively (with the exception of low m ν in the normal hierarchy).
After marginalizing over the astrophysical uncertainties of the target line as in Ref. [47], we find that for all cases considered LIM experiments can improve current cosmological bounds on the neutrino decay rate from CMB spectral distortions [42,43] by several orders of magnitude. This shows that LIM has the potential to provide the strongest cosmological sensitivity on neutrino radiative decays. Furthermore, LIM will be competitive to the most stringent limits to date, coming from stellar cooling [39][40][41], as we see below.
As mentioned above, at the microscopic level radiative neutrino decays may result from an effective term in the Lagrangian like ∝ν i σ αβ (µ ij + ij γ 5 )ν j F αβ + hermitian conjugates [14,37,74], where F αβ is the electromagnetic field tensor, σ αβ is the Dirac gamma matrices commutator, and µ ij and ij are the magnetic and electric moments, respectively. For a transition (i.e., i = j), we can relate an effective electromagnetic moment µ eff ij to the decay rate as where |µ eff ij | 2 ≡ |µ ij | 2 +| ij | 2 , and µ B is the Bohr magneton.
According to Eq. (5), the forecasted LIM sensitivity of Γ ij ∼ 10 −28 − 10 −25 s −1 at 95% confidence level translates to µ eff ij ∼ 10 −12 − 10 −8 (m i c 2 /0.1eV) 3/2 µ B , while current and forecasted CMB limits are ∼ 10 −7 − 10 −8 µ B and ∼ 10 −8 − 3 × 10 −11 µ B , respectively [43]. Note that the sensitivity to µ eff ij depends on the mass of the original neutrino, which in turn depends on the transition, hierarchy and m ν considered. In turn, the most stringent direct detection limit was obtained in the Borexino experiment and is related to an effective moment accounting for all magnetic direct and transition moments: µ eff ν < 2.8×10 −11 µ B at 90% confidence level [75]. Finally, astrophysical studies of stellar cooling set the strongest COMAP1 COMAP2 CCAT-prime AtLAST P(k) VID CMB . The left panels refer to the NH case, while the right ones to the IH case. In both cases we also indicate the considered transition between eigenstates. The dotted purple lines indicate the CMB limits from ref. [42,43].
This demonstrates the great potential that LIM surveys have to unveil neutrino properties: on top of having a sensitivity competitive to and in some cases even improving current strongest limits, LIM experiments may probe neutrino decays in a very different context than the rest of experiments and observations discussed above. Instead of neutrinos produced in the interior of stars, LIM will be sensitive to the cosmic neutrino background (as CMB studies are, but at very different redshifts). Moreover, the energy of the neutrinos involved in each probe also varies, which may inform about a potential energy dependence of the electromagnetic transition moments [76]. These synergies are very timely, since an enhanced magnetic moment may explain the ∼ 3σ excess observed by XENON1T [36], but the values require are close to the limits found by Borexino and in tension with stellar cooling constraints.
Finally, LIM may provide additional information about the cosmic neutrino background beyond the effect of m ν in the growth of perturbations: combining the information about m ν with the frequency of the photons produced in the decay, LIM might be the only cosmological probe sensitive to individual neutrino masses and their hierarchy [77].
The complementarity between different probes of neutrino decays will also help as a cross-check for eventual caveats or systematic uncertainties in the measurements. In the case of LIM experiments, these are the same as for the search for radiative dark matter decays, which are discussed in Ref. [47]. In summary, astrophysical uncertainties are already accounted for in our analysis, there are efficient strategies to deal with known astrophysical line interlopers [53][54][55][56][57][58][59][60][61], and galactic foregrounds are expected to be under control at the frequencies of interest. Moreover, the neutrino decay contribution to the LIM power spectrum and VID is very characteristic, and the combination of both summary statistics will not only improve the sensitivity but also the robustness of the measurement. 3 Finally, we have assumed that the neutrino decay line is a delta function, and neglected any widening due to the neutrino velocity distributions. While this is a good approximation for the regime of interest at this stage, it is also possible to model the neutrino decay emissivity with a generic momentum distribution [43]; this will allow to adapt our analysis to neutrino production models that alter their momentum distribution [79].
The neutrino decay contribution might be confused with other exotic radiation injection such as dark matter decay. However, the shape of the neutrino power spectrum and density PDF is different. Moreover, while the contribution from dark matter decays will appear in LIM cross-correlations with galaxy clustering [46] and lensing [80], the contribution from neutrino decays will barely do, since galaxy surveys do not trace the neutrino density field.
In this letter we have proposed the use of LIM for the detection of a possible radiative decay of the cosmic neutrino background, focusing on its contribution to the LIM power spectrum and VID. We have also provided a first parametric fit of the neutrino density PDF using N-body simulations and symbolic regression, that was required to compute the contribution to the VID. Our results show that LIM have the potential to achieve sensitivities competitive to current limits, improving other cosmological probes by several orders of magnitude. The complementarity of LIM and other existing probes of neutrino decays opens exciting synergies, as well as checks for systematics, that will lead the way to new studies of neutrino properties.
Acknowledgments-JLB is supported by the Allan C.