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

Abstract

We consider invisible neutrino decay ${\nu }_H\to {\nu }_l+\varphi$ 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 $\varphi$, 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 ${\Gamma }_{\mathrm{T}}$ 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., ${\Gamma }_{\mathrm{T}}\sim (\Delta m_{\nu }^2/m_{\nu H}^2{)}^2(m_{\nu H}/E_{\nu }{)}^5(1/{\tau }_0)$, 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 $m_{\nu H}\lesssim 0.1\mathrm{eV}$, 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) ${\tau }^0\gtrsim (6\to 10)\times 10^5\mathrm{s}$ and ${\tau }^0\gtrsim (400\to 500)\mathrm{s}$ if only one neutrino decays to a daughter neutrino separated by, respectively, the atmospheric and the solar mass gap, and (ii) ${\tau }^0\gtrsim (2\to 3)\times 10^7\mathrm{s}$ 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.

Comments: 23 pages, 6 figures. v3 accepted for publication by EPJC. Updated the paragraph explaining the separable ansatz on page 5 and added some extra text and equations in appendix B for the Legendre polynomials expansion. Minor additions and small correction to figure 3 bounds