Infrared finiteness of a complete theory of charged scalars and fermions at finite temperature

Abstract

AbstractIt is known that the infrared (IR) divergences accruing from pure fermion–photon interactions at finite temperature cancel to all orders in perturbation theory. The corresponding infrared finiteness of scalar thermal QED has also been established recently. Here, we study the IR behaviour, at finite temperature, of theories where charged scalars and fermions interact with neutrals that could potentially be dark matter candidates. Such thermal field theories contain both linear and sub-leading logarithmic divergences. We prove that the theory is IR-finite to all orders in perturbation, with the divergences cancelling order by order between virtual and real photon corrections, when both absorption and emission of photons from and into the heat bath are taken into account. The calculation follows closely the technique used by Grammer and Yennie for zero temperature field theory. The result is generic and applicable to a variety of models, independent of the specific form of the neutral-fermion–scalar interaction vertex.