Weaker yet again: mass spectrum-consistent cosmological constraints on the neutrino lifetime

Abstract

We consider invisible neutrino decay ν H → ν l + φ in the ultra-relativistic limit and compute the neutrino anisotropy loss rate relevant for the cosmic microwave background (CMB) anisotropies. Improving on our previous work which assumed massless ν l and φ, we reinstate in this work the daughter neutrino mass m νl in a manner consistent with the experimentally determined neutrino mass splittings. We find that a nonzero m νl introduces a new phase space factor in the loss rate Γ T proportional to (∆m 2 ν /m 2 ν H ) 2 in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., Γ T ∼ (∆m 2 ν /m 2 νH ) 2 (m νH /E ν ) 5 (1/τ 0 ), where τ 0 is the ν H rest-frame lifetime. Using a general form of this result, we update the limit on τ 0 using the Planck 2018 CMB data. We find that for a parent neutrino of mass m νH 0.1 eV, the new phase space factor weakens the constraint on its lifetime by up to a factor of 50 if ∆m 2 ν corresponds to the atmospheric mass gap and up to 10 5 if the solar mass gap, in comparison with naïve estimates that assume m νl = 0. The revised constraints are (i) τ 0 (6 → 10) × 10 5 s and τ 0 (400 → 500) s if only one neutrino decays to a daughter neutrino separated by, respectively, the atmospheric and the solar mass gap, and (ii) τ 0 (1 → 3) × 10 7 s in the case of two decay channels with one near-common atmospheric mass gap. In contrast to previous, naïve limits which scale as m 5 νH , these mass spectrum-consistent τ 0 constraints are remarkably independent of the parent mass and open up a swath of parameter space within the projected reach of IceCube and other neutrino telescopes in the next two decades.

Decaying warm dark matter revisited

“…Studies of decaying massive neutrinos emerged several decades ago (e.g. [32,33] and references therein) when it was realized that finite neutrino lifetimes may significantly relax the bounds on the neutrino mass sum (for the most recent constraints, see [34][35][36][37]). It is only recently, with the work of reference [38], that decaying warm dark matter (DWDM) has been investigated explicitly.…”