Precision constraints on radiative neutrino decay with CMB spectral distortion

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 formulas for the decay of a heavier neutrino into a lighter neutrino and a photon, ν_j→ν_i+γ, and of absorption as its inverse, ν_i+γ→ν_j, by accounting for the precise form of the neutrino momentum distribution. Our calculations show that if the neutrinos are heavier than O(0.1) eV the exact formulas give results that differ by ∼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 ∼10 going from a neutrino mass of 0.01-0.1 eV). By analyzing the CMB spectral data measured with COBE-FIRAS, we obtain lower limits on the neutrino lifetime of τ₁₂ ≥ 4 × 10²¹ s (95% C.L.) for the smaller mass splitting and τ₁₃∼τ₂₃ ≥ 10¹⁹ s for the larger mass splitting. These represent up to 1 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 μ_ν < 3 × 10^-11 μ_B, where μ_B is the Bohr magneton. Such constraints would make future precision CMB measurements competitive with lab-based constraints on neutrino magnetic moments.