再一次变弱：中微子寿命的质量谱一致宇宙学约束
Weaker yet again: mass spectrum-consistent cosmological constraints on the neutrino lifetime
摘要：
我们考虑了在超相对论极限下的不可见中微子衰变$ν_H \to ν_l + ϕ$，并计算了与宇宙微波背景（CMB）各向异性有关的中微子各向异性损失率。改进我们以前的工作，假设无质量$ν_l$和$ϕ$，我们恢复在这项工作中的子中微子质量$m_{νl}$的方式与实验确定的中微子质量分裂。我们发现，一个非零的$m_{νl}$引入了一个新的相空间因子的损失率$Γ_{\rm T}$成比例的$(Δm_ν^2/m_{ν_H}^2)^2$在一个小的平方之间的父中微子和子中微子，即，$Γ_{\rm T} \sim (Δm_ν^2/m_{νH}^2)^2 (m_{νH}/E_ν)^5 (1/τ_0)$，其中$τ_0$是$ν_H$休息帧寿命。使用该结果的一般形式，我们使用普朗克2018 CMB数据更新了$τ_0$的极限。我们发现，对于质量为$m_{νH} \lesssim 0.1 {\rm eV}$的母中微子，新的相空间因子削弱了对它的寿命的约束，如果$Δm_ν^2$对应于大气质量差距的50倍和$10^{5}$，如果太阳质量差距，与天真的估计相比，假设$m_{νl}=0$。修正后的约束条件是：（i）如果只有一个中微子衰变为子中微子，分别由大气和太阳的质量差距，$τ^0 \gtrsim (6 \to 10) \times 10^5~{\rm s}$和$τ^0 \gtrsim (400 \to 500)~{\rm s}$，和（ii）$τ^0 \gtrsim (2 \to 3) \times 10^7~{\rm s}$的情况下，两个衰变通道与一个近共同的大气质量差距。与以前的朴素限制（如$m_{νH}^5$）相比，这些质谱一致的$τ_0$限制明显独立于母质量，并在未来20年内在冰立方和其他中微子望远镜的预计范围内开辟了一条参数空间。
英文摘要：
We consider invisible neutrino decay $ν_H \to ν_l + ϕ$ 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 $ν_l$ and $ϕ$, we reinstate in this work the daughter neutrino mass $m_{νl}$ in a manner consistent with the experimentally determined neutrino mass splittings. We find that a nonzero $m_{νl}$ introduces a new phase space factor in the loss rate $Γ_{\rm T}$ proportional to $(Δm_ν^2/m_{ν_H}^2)^2$ in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., $Γ_{\rm T} \sim (Δm_ν^2/m_{νH}^2)^2 (m_{νH}/E_ν)^5 (1/τ_0)$, where $τ_0$ is the $ν_H$ rest-frame lifetime. Using a general form of this result, we update the limit on $τ_0$ using the Planck 2018 CMB data. We find that for a parent neutrino of mass $m_{νH} \lesssim 0.1 {\rm eV}$, the new phase space factor weakens the constraint on its lifetime by up to a factor of 50 if $Δm_ν^2$ corresponds to the atmospheric mass gap and up to $10^{5}$ if the solar mass gap, in comparison with naive estimates that assume $m_{νl}=0$. The revised constraints are (i) $τ^0 \gtrsim (6 \to 10) \times 10^5~{\rm s}$ and $τ^0 \gtrsim (400 \to 500)~{\rm s}$ if only one neutrino decays to a daughter neutrino separated by, respectively, the atmospheric and the solar mass gap, and (ii) $τ^0 \gtrsim (2 \to 3) \times 10^7~{\rm s}$ in the case of two decay channels with one near-common atmospheric mass gap. In contrast to previous, naive limits which scale as $m_{νH}^5$, these mass spectrum-consistent $τ_0$ 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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