Weaker yet again: mass spectrum-consistent cosmological constraints on the neutrino lifetime
(2022) European Physical Journal C — Vol. 82 (2022)
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- 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 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 $\varGamma _\mathrm{T}$ 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.
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Oldengott, I., & et al. (2022). Weaker yet again: mass spectrum-consistent cosmological constraints on the neutrino lifetime. European Physical Journal C, 82. https://doi.org/10.1140/epjc/s10052-022-10518-3 (Original work published 2022)