Z-Sum Approach to Loop Integrals using Taylor Expansion

TL;DR

This paper evaluates the Z-Sum method for calculating loop integrals in quantum field theory, analyzing its effectiveness for one-loop scalar integrals and applying it to heavy-flavor corrections in deep-inelastic scattering.

Contribution

It systematically assesses the Z-Sum approach's applicability to one-loop scalar integrals and extends the analysis to specific physical calculations.

Findings

Z-Sum approach effectively computes certain one-loop integrals

Identifies limitations of Z-Sum in complex cases

Successfully applies Z-Sum to heavy-flavor corrections

Abstract

We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of any higher-loop calculation. We focus in particular on triangle one-loop integrals and identify strengths and limitations of the Z-Sum approach, extending our results to the case of one-loop box integrals when appropriate. We conclude with the calculation of a specific physical example: the calculation of heavy-flavor corrections to deep-inelastic-scattering structure functions.