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

Abstract

We consider invisible neutrino decay nu _H rightarrow nu _l + phi 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 masslessnu _l and phi , we reinstate in this work the daughter neutrino mass m_{nu l} in a manner consistent with the experimentally determined neutrino mass splittings. We find that a nonzero m_{nu l} introduces a new phase space factor in the loss rate varGamma _mathrm{T} proportional to (varDelta m_nu ^2/m_{nu _H}^2)^2 in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., varGamma _mathrm{T} sim (varDelta m_nu ^2/m_{nu H}^2)^2 (m_{nu H}/E_nu )^5 (1/tau _0), where tau _0 is the nu _H rest-frame lifetime. Using a general form of this result, we update the limit on tau _0 using the Planck 2018 CMB data. We find that for a parent neutrino of mass m_{nu H} lesssim 0.1 eV, the new phase space factor weakens the constraint on its lifetime by up to a factor of 50 if varDelta m_nu ^2 corresponds to the atmospheric mass gap and up to 10^{5} if the solar mass gap, in comparison with naïve estimates that assume m_{nu l}=0. The revised constraints are (i) tau ^0 > rsim (6 rightarrow 10) times 10^5 s and tau ^0 > rsim (400 rightarrow 500) s if only one neutrino decays to a daughter neutrino separated by, respectively, the atmospheric and the solar mass gap, and (ii) tau ^0 > rsim (2 rightarrow 6) times 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_{nu H}^5, these mass spectrum-consistent tau _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.