Infrared finiteness of theories with bino-like dark matter at finite temperature

Models incorporating moderately heavy dark matter (DM) typically need charged (scalar) fields to establish admissible relic densities. Since the DM freezes out at an early epoch, thermal corrections to the cross sections can be important. In a companion paper [arXiv:1812.04247v2] we established that the infrared (IR) divergences accruing from scalar-photon interactions cancel to all orders in perturbation theory. The corresponding infrared finiteness of thermal fermionic QED has already been established. Here, we study the IR behaviour at finite temperatures, of a theory of dark matter interacting with charged scalars and fermions, which potentially contains both both linear and sub-leading logarithmic divergences. We prove that the theory is IR-finite to all orders with the divergences cancelling when both absorption and emission of photons from and into the heat bath are taken into account. While 4-point interaction terms are known to be IR finite, their inclusion leads to a neat exponentiation. The calculation follows closely the technique used for the scalar finite temperature theory.