Precision constraints on radiative neutrino decay with CMB spectral distortion

TL;DR

This paper derives precise formulas for neutrino radiative decay effects on CMB spectral distortion, providing new constraints on neutrino lifetimes and magnetic moments from COBE-FIRAS data, with future experiments promising significant improvements.

Contribution

The paper introduces exact decay and absorption formulas accounting for neutrino momentum distribution, improving previous approximations and deriving tighter CMB-based neutrino constraints.

Findings

Lower limits on neutrino lifetime: τ > 10^{19} s.

Improved constraints on neutrino magnetic moments: μ_ν < 3×10^{-11} μ_B.

Future experiments could enhance limits by four orders of magnitude.

Abstract

We investigate the radiative decay of the cosmic neutrino background, and its impact on the spectrum of the cosmic microwave background (CMB) that is known to be a nearly perfect black body. We derive exact formulae for the decay of a heavier neutrino into a lighter neutrino and a photon, $\nu_j \to \nu_i + \gamma$, and of absorption as its inverse, $\nu_i + \gamma \to \nu_j$, by accounting for the precise form of the neutrino momentum distribution. Our calculations show that if the neutrinos are heavier than $\mathcal O(0.1)$ eV, the exact formulae give results that differ by $\sim$50%, compared with approximate ones where neutrinos are assumed to be at rest. We also find that spectral distortion due to absorption is more important for heavy neutrino masses (by a factor of $\sim$10 going from a neutrino mass of 0.01 eV to 0.1 eV). By analyzing the CMB spectral data measured with COBE-FIRAS, we obtain lower limits on the neutrino lifetime of $\tau_{12} \gtrsim 4 \times 10^{21}$ s (95% C.L.) for the smaller mass splitting and $\tau_{13} \sim \tau_{23} \gtrsim 10^{19}$ s for the larger mass splitting. These represent up to one order of magnitude improvement over previous CMB constraints. With future CMB experiments such as PIXIE, these limits will improve by roughly 4 orders of magnitude. This translates to a projected upper limit on the neutrino magnetic moment (for certain neutrino masses and decay modes) of $\mu_\nu < 3 \times 10^{-11}\, \mu_B$, where $\mu_B$ is the Bohr magneton. Such constraints would make future precision CMB measurements competitive with lab-based constraints on neutrino magnetic moments.