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arXiv 2201.04661hep-phastro-ph.COastro-ph.HE
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共振区费米子和标量背景中的中微子有效势和阻尼

Neutrino effective potential and damping in a fermion and scalar background in the resonance region

Jose F. Nieves, Sarira Sahu

备注：
20 pages, 3 figures, identical to the published version
发表信息：
PRD 105, 095022 (2022)
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摘要：

我们考虑中微子或反中微子在由费米子$f$和标量$ϕ$通过$\bar fνϕ$形式的Yukawa型耦合相互作用组成的介质中的传播，对于中微子能量，如$ν+ ϕ\leftrightarrow f$或$ν+ \bar f \leftrightarrow \barϕ$，以及相应的反中微子的过程，是运动学上可接近的。相关能量值约为$|m^2_ϕ- m^2_f|/2m_ϕ$或$|m^2_ϕ- m^2_f|/2m_f$，其中$m_ϕ$和$m_f$分别为$ϕ$和$f$的质量。我们将这些区域中的任一个称为共振能量范围。在这些点附近，中微子自能的单圈公式有一个奇点。从技术角度来看，这一特征表明，自能获得虚部，虚部与阻尼效应有关，不能忽略，而实部的积分公式必须使用积分的主值来计算。我们进行计算明确的某些情况下，使我们能够给出分析结果。将色散关系写成$ω= κ+ V_{\text{eff}} - iγ/2$的形式，我们给出了所考虑情况下的$V_{\text{eff}}$和$γ$的显式公式。当中微子能量比共振能量大得多或小得多时，$V_{\text{eff}}$分别在高动量区或低动量区降低到文献中已经确定的有效势。我们为$V_{\text{eff}}$给出的公式的优点是，它在\emph{resonance energy range}中也是有效的，它在所提到的两个极限之外。作为可能的应用指南，我们给出了相关的公式为$V_{\text{eff}}$和$γ$，并考虑解决方案的振荡方程，包括阻尼项，在一个简单的两代的情况下。

英文摘要：

We consider the propagation of a neutrino or an antineutrino in a medium composed of fermions $f$ and scalars $ϕ$ interacting via a Yukawa-type coupling of the form $\bar fνϕ$, for neutrino energies at which the processes like $ν+ ϕ\leftrightarrow f$ or $ν+ \bar f \leftrightarrow \barϕ$, and the corresponding ones for the antineutrino, are kinematically accessible. The relevant energy values are around $|m^2_ϕ- m^2_f|/2m_ϕ$ or $|m^2_ϕ- m^2_f|/2m_f$, where $m_ϕ$ and $m_f$ are the masses of $ϕ$ and $f$, respectively. We refer to either one of these regions as a resonance energy range. Near these points, the one-loop formula for the neutrino self-energy has a singularity. From a technical point of view, that feature is indicative that the self-energy acquires an imaginary part, which is associated with damping effects and cannot be neglected, while the integral formula for the real part must be evaluated using the principal value of the integral. We carry out the calculations explicitly for some cases that allow us to give analytic results. Writing the dispersion relation in the form $ω= κ+ V_{\text{eff}} - iγ/2$, we give the explicit formula for $V_{\text{eff}}$ and $γ$ for the cases considered. When the neutrino energy is either much larger or much smaller than the resonance energy, $V_{\text{eff}}$ reduces to the effective potential that has been already determined in the literature in the high or low momentum regime, respectively. The virtue of the formula we give for $V_{\text{eff}}$ is that it is valid also in the \emph{resonance energy range}, which is outside the two limits mentioned. As a guide to possible applications we give the relevant formulas for $V_{\text{eff}}$ and $γ$, and consider the solution to the oscillation equations including the damping term, in a simple two-generation case.

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