Momentum expansion of massive two-loop Feynman graphs around a finite value

TL;DR

This paper presents an algorithm for expanding massive two-loop Feynman graphs around a finite, nonzero external momentum, combining algebraic reduction to special functions with numerical integration for precise calculations.

Contribution

It introduces a novel expansion algorithm for two-loop Feynman graphs around finite momentum values, enhancing computational methods in quantum field theory.

Findings

Applied to top-dependent corrections of O(g^2 alpha_s) to the b quark self-energy.

Successfully extracted on-shell momentum expansion of the b quark self-energy.

Demonstrated the algorithm's effectiveness in complex two-loop calculations.

Abstract

We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. This is based on our general two-loop formalism to reduce massive two-loop graphs with renormalizable interactions into a standard set of special functions. After the algebraic reduction, the final results are obtained by numerical integration. We apply the expansion algorithm to treat the top-dependent corrections of O(g^2 alpha_s) to the b quark self-energy and extract its momentum expansion on-shell.