Multiloop Bubbles for hot QCD

TL;DR

This paper develops analytical expansion techniques for complex four-loop vacuum integrals in hot QCD, utilizing hypergeometric representations and nested sums to advance computational methods in quantum field theory.

Contribution

Introduces new hypergeometric and nested sum algorithms for expanding four-loop vacuum integrals in hot QCD, implemented in FORM.

Findings

Derived hypergeometric representations with half-integer coefficients.

Successfully expanded integrals using nested sums algorithms.

Enhanced computational tools for high-loop quantum field theory calculations.

Abstract

In this article, we present analytical expansion results of two single mass scale four-loop vacuum integrals in d=3-2*ep dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we implemented in FORM to expand these in terms of nested sums.