The High-Temperature Expansion of the Thermal Sunset

TL;DR

This paper presents a systematic method for calculating the high-temperature expansion of the thermal sunset integral, including all odd-temperature terms, with analytical and numerical validation.

Contribution

It introduces a new prescription for arbitrary order expansion and rederives known results up to zero order for bosonic and fermionic cases.

Findings

Derived all odd-in-temperature terms in the expansion.

Validated results through analytical and numerical cross-checks.

Extended previous calculations to arbitrary order.

Abstract

We give a prescription for calculating the high-temperature expansion of the thermal sunset integral to arbitrary order. We derive all terms odd in $T$, and rederive previous results up to $\mathcal{O}(T^0) $ for both bosonic and fermionic thermal sunsets in dimensional regularisation. We perform analytical and numerical cross-checks. Intermediate steps involve integrals over three Bessel functions.