Spectral Surgery in a Heat Bath: a finite-temperature guide to particle production for phenomenologists

Quantifying the effects of finite temperature and density (FTD) on particle properties is essential for understanding phenomena within and beyond the Standard Model. In this work, we present a simplified framework for calculating particle production rates at FTD without resorting to a full thermal field theory calculation. We do so by relating the imaginary part of a particle's $n$-loop finite temperature self energy, which defines its in-medium damping rate, to a sum of thermally weighted tree-level vacuum rates. Such a mapping results in novel "interference" contributions to particle production which have no vacuum analog and which have been relatively overlooked in the phenomenology literature. These interference terms are known to regulate collinear and infrared divergences that arise when calculating interaction rates in a medium. We demonstrate the impact of these corrections with two toy models and find that properly accounting for these interference terms can alter particle production by an $O(1)$ amount. We additionally compare the size of these corrections to the thermal mass corrections often studied in the literature, finding the sizes of these contributions to be of similar order.