The H-graph with unequal masses in quantum field theory

TL;DR

This paper computes Feynman integrals for the H-graph with unequal masses in quantum field theory, presenting a differential equation approach and expressing results in terms of iterated integrals and polylogarithms.

Contribution

It introduces an $ ext{ε}$-factorised differential equation for 40 master integrals involving algebraic arguments and square roots, advancing the computation of complex Feynman integrals.

Findings

Derived an $ ext{ε}$-factorised differential equation for master integrals.

Expressed integrals in terms of iterated integrals with algebraic arguments.

Provided compact expressions for the H-graph in terms of multiple polylogarithms.

Abstract

We compute the family of Feynman integrals related to the H-graph with unequal masses in relativistic quantum field theory. We present an $\varepsilon$-factorised differential equation for the 40 master integrals. The alphabet consists of 29 dlog-forms with algebraic arguments, involving six square roots. As these square roots are not simultaneously rationalizable, we express the master integrals in terms of iterated integrals. In addition, we express the H-graph with unit powers of the propagators up to weight four in terms of multiple polylogarithms in compact form.