介质中双圈中微子自能的收缩奇异性抑制
Taming the pinch singularities in the two-loop neutrino self-energy in a medium
摘要：
本文考虑了在由费米子和标量通过Yukawa型耦合相互作用组成的介质中传播的中微子的热自能的计算，在这种情况下，中微子的能量远大于费米子和标量的质量，以及背景的温度和化学势。在这种运动状态下，单圈对自能虚部的贡献可以忽略不计。我们考虑了两圈的贡献，我们遇到了所谓的箍缩奇点，这是已知的热场论中较高的圈自能计算中出现的。通过对热传播子的性质和参数化的合理利用，奇异性得到了有效的处理，并且实际上消失了。从自能的虚部，我们得到一个精确的公式表示的阻尼矩阵的积分在背景粒子分布。该公式预测的阻尼项对中微子能量的特定依赖性，这取决于背景条件。为了指导在特定情况下估计的影响，我们计算阻尼项的几个限制情况下的动量分布函数的背景粒子。我们简要地讨论了阻尼矩阵的计算结果与用林德布拉德方程描述的退相干效应之间的联系。
英文摘要：
We consider the calculation of the thermal self-energy of a neutrino that propagates in a medium composed of fermions and scalars interacting via a Yukawa-type coupling, in the case that the neutri no energy is much larger than the fermion and scalar masses, as well as the temperature and chemical potentials of the background. In this kinematic regime the one-loop contribution to the imaginary part of the self-energy is negligible. We consider the two-loop contribution and we encounter the so-called pinch singularities which are known to arise in higher loop self-energy calculations in Thermal Field Theory. With a judicious use of the properties and parametrizations of the thermal propagators the singularities are treated effectively and actually disappear. From the imaginary part of the self-energy, we obtain a precise formula for the damping matrix expressed in terms of integrals over the background particle distributions. The formulas predict a specific dependence of the damping terms on the neutrino energy, depending on the background conditions. For guidance to estimating the effects in specific contexts, we compute the damping terms for several limiting cases of the momentum distribution functions of the background particles. We discuss briefly the connection between the results of our calculations for the damping matrix and the decoherence effects described in terms of the Lindblad equation.
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