# Infrared finiteness of a thermal theory of scalar electrodynamics to all orders

## TL;DR

This paper demonstrates that the thermal scalar electrodynamics theory remains free of infrared divergences at all orders in perturbation theory, which is crucial for accurate dark matter modeling.

## Contribution

It extends the proof of IR finiteness from fermionic to scalar charged fields at finite temperature using the Grammer and Yennie method.

## Key findings

- Infrared divergences are identified and factorized for scalar theories.
- IR finite pieces from scalar-photon interactions are crucial for exponentiation.
- The results support the IR finiteness of thermal scalar theories relevant to dark matter.

## Abstract

Models explaining dark matter typically include interactions with charged scalar and fermion fields. The Infra-Red (IR) finiteness of thermal field theories of charged fermions (fermionic QED) has been proven to all orders in perturbation theory. Here we reexamine the IR behaviour of charged scalar theories at finite temperature. Using the method of Grammer and Yennie, we identify and factorise the infra-red divergences to all orders in perturbation theory. The inclusion of IR finite pieces arising from the 4-point interaction terms of scalars with photon fields is key to the exponentiation. We use this in a companion paper to prove the IR finiteness of the corresponding thermal theory which is of relevance in dark matter calculations.