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

TL;DR

This paper refines cosmological constraints on neutrino lifetime by incorporating realistic neutrino mass differences, revealing significantly weaker bounds than previous estimates and expanding the accessible parameter space for future neutrino observations.

Contribution

It introduces a mass spectrum-consistent calculation of neutrino decay effects on CMB anisotropies, updating lifetime constraints with realistic neutrino mass splittings.

Findings

Mass spectrum effects weaken lifetime constraints by up to 50,000 times.

Revised bounds on neutrino lifetime are around 10^5 to 10^7 seconds.

Constraints are largely independent of the parent neutrino mass.

Abstract

We consider invisible neutrino decay $\nu_H \to \nu_l + \phi$ 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 massless $\nu_l$ 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 $\Gamma_{\rm T}$ proportional to $(\Delta m_\nu^2/m_{\nu_H}^2)^2$ in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., $\Gamma_{\rm T} \sim (\Delta m_\nu^2/m_{\nu H}^2)^2 (m_{\nu H}/E_\nu )^5 (1/\tau_0)$, 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 $m_{\nu H} \lesssim 0.1 {\rm eV}$, the new phase space factor weakens the constraint on its lifetime by up to a factor of 50 if $\Delta m_\nu^2$ corresponds to the atmospheric mass gap and up to $10^{5}$ if the solar mass gap, in comparison with naive estimates that assume $m_{\nu l}=0$. The revised constraints are (i) $\tau^0 \gtrsim (6 \to 10) \times 10^5~{\rm s}$ and $\tau^0 \gtrsim (400 \to 500)~{\rm s}$ if only one neutrino decays to a daughter neutrino separated by, respectively, the atmospheric and the solar mass gap, and (ii) $\tau^0 \gtrsim (2 \to 3) \times 10^7~{\rm s}$ in the case of two decay channels with one near-common atmospheric mass gap. In contrast to previous, naive 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.