论文标题
中微子有效潜力和在共振区域中的费米和标量背景中进行阻尼
Neutrino effective potential and damping in a fermion and scalar background in the resonance region
论文作者
论文摘要
我们考虑中微子或抗肿瘤在由费米斯$ f $组成的介质中的传播和标量$ ϕ $通过Yukawa型$ \ bar fνϕ $进行交互，用于中微子能量，例如$ c $ n f $或bartright off $或bar $ b f $或bar f $ b f $ b f。抗肿瘤的相应抗性，可以在运动学上访问。相关的能量值约为$ | m^2_2_2_f |/2m_ϕ $或$ | m^2_2_2_2_2_f |/2m_f $，其中$ m_ϕ $和$ m_f $分别是$ ϕ $和$ f $的群众。我们将其中一个区域称为共振能量范围。在这些点附近，中微子自我能源的一环公式具有奇异性。从技术的角度来看，该特征表明自我能源获得了一个虚构的部分，该部分与阻尼效应相关并且不能忽略，而实际部分的积分公式必须使用积分的主要价值来评估。对于某些情况，我们可以明确执行计算，以使我们能够给出分析结果。以$ω=κ+ v _ {\ text {eff}}-Iγ/2 $的形式编写分散关系，我们为$ v _ {\ text {eff}} $和$γ$提供明确的公式。当中微子能量要么比共振能量大得多，要么小得多，$ v _ {\ text {eff}} $降低了在高或低动量制度的文献中已经确定的有效潜力。我们给出的公式的优点是$ v _ {\ text {eff}} $，它在\ emph {resonance encomence范围}中也是有效的，这是在提到的两个限制之外的。作为可能的应用程序的指南，我们为$ v _ {\ text {eff}} $和$γ$提供了相关公式，并在简单的两生中考虑振荡方程的解决方案，包括阻尼项。
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.
