Single mass scale diagrams: construction of a basis for the $\epsilon$-expansion

TL;DR

This paper develops a method to construct a basis of transcendental numbers for the epsilon-expansion of single mass scale Feynman diagrams with two massive particles, and demonstrates it through new multi-loop integral calculations.

Contribution

It introduces an ansatz for building a transcendental basis for epsilon-expansions in specific Feynman diagrams, advancing computational techniques in quantum field theory.

Findings

Calculated several new two- and three-loop master integrals.

Proposed a basis construction method based on Broadhurst's idea.

Enhanced understanding of epsilon-expansions in single mass scale diagrams.

Abstract

Exploring the idea of Broadhurst on the ``sixth root of unity'' we present an ansatz for construction of a basis of transcendental numbers for the epsilon-expansion of single mass scale diagrams with two particle massive cut. As example, several new two- and three-loop master integrals are calculated.