Abstract
It 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.
Highlights
We are interested here in addressing the infrared (IR) behaviour of theories with both charged scalars and fermions, interacting with neutral singlets or doublets, at finite temperature
We have collected all the known results related to the IR behaviour of both thermal pure fermionic QED and pure scalar QED. With these results in hand, we examine the IR behaviour at finite temperature of the typical process, χ χ → f f, arising from interactions governed by the Lagrangian given in Eq 1
The “WIMP miracle” is oft-quoted as an argument for the viability of a generic cold Dark Matter candidate χ. This is because, for such a particle having interactions with known species with a strength comparable to the electroweak gauge coupling, the relic abundance naturally turns out to be of the same order as the observed one
Summary
We are interested here in addressing the infrared (IR) behaviour of theories with both charged scalars and fermions, interacting with neutral singlets or doublets, at finite temperature. We use a similar approach to address the issue of IR finiteness of the thermal field theory corresponding to Eq 1, thereby combining and extending the results of the earlier work on thermal fermions and thermal charged scalars. The divergences factorise and exponentiate and cancel order by order between virtual and real photon contributions (the latter include both emission and absorption terms); this same approach will be used to prove the IR finiteness to all orders in perturbation of the thermal theory corresponding to the Lagrangian, Eq 1. After this overview, we set up the relevant machinery in Sect. We will see that the results we obtain do not depend on the exact form of the χ – f –φ vertex and is applicable to a larger class of such theories
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