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

Abstract

We consider invisible neutrino decay $$\nu _H \rightarrow \nu _l + \phi $$ 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$$\nu _l$$ ν l and $$\phi $$ ϕ , we reinstate in this work the daughter neutrino mass $$m_{\nu l}$$ m ν l in a manner consistent with the experimentally determined neutrino mass splittings. We find that a nonzero $$m_{\nu l}$$ m ν l introduces a new phase space factor in the loss rate $$\varGamma _\mathrm{T}$$ Γ T proportional to $$(\varDelta m_\nu ^2/m_{\nu _H}^2)^2$$ ( Δ m ν 2 / m ν H 2 ) 2 in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., $$\varGamma _\mathrm{T} \sim (\varDelta m_\nu ^2/m_{\nu H}^2)^2 (m_{\nu H}/E_\nu )^5 (1/\tau _0)$$ Γ T ∼ ( Δ m ν 2 / m ν H 2 ) 2 ( m ν H / E ν ) 5 ( 1 / τ 0 ) , where $$\tau _0$$ τ 0 is the $$\nu _H$$ ν H rest-frame lifetime. Using a general form of this result, we update the limit on $$\tau _0$$ τ 0 using the Planck 2018 CMB data. We find that for a parent neutrino of mass $$m_{\nu H} \lesssim 0.1$$ m ν H ≲ 0.1 eV, the new phase space factor weakens the constraint on its lifetime by up to a factor of 50 if $$\varDelta m_\nu ^2$$ Δ m ν 2 corresponds to the atmospheric mass gap and up to $$10^{5}$$ 10 5 if the solar mass gap, in comparison with naïve estimates that assume $$m_{\nu l}=0$$ m ν l = 0 . The revised constraints are (i) $$\tau ^0 > rsim (6 \rightarrow 10) \times 10^5$$ τ 0 ≳ ( 6 → 10 ) × 10 5 s and $$\tau ^0 > rsim (400 \rightarrow 500)$$ 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) $$\tau ^0 > rsim (2 \rightarrow 6) \times 10^7$$ τ 0 ≳ ( 2 → 6 ) × 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 $$m_{\nu H}^5$$ m ν H 5 , these mass spectrum-consistent $$\tau _0$$ 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.

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