Automatic computation of Feynman integrals containing linear propagators via auxiliary mass flow

TL;DR

This paper introduces a systematic method using auxiliary mass flow to compute Feynman integrals with linear propagators, demonstrated by calculating complex vacuum integrals up to four loops.

Contribution

The paper presents a novel recipe that employs auxiliary mass flow and differential equations to evaluate Feynman integrals with linear propagators, expanding computational techniques in quantum field theory.

Findings

Successfully calculated all master integrals of vacuum integrals with gauge links up to four loops.

Validated results using nontrivial dimensional recurrence relations.

Provided a systematic approach applicable to complex Feynman integrals.

Abstract

We proposed a recipe to systematically calculate Feynman integrals containing linear propagators using the auxiliary mass flow method. The key of the recipe is to introduce a quadratic term for each linear propagator and then using differential equations to get rid of their effects. As an application, we calculated all master integrals of vacuum integrals containing a gauge link up to four loops, and we checked the results by nontrivial dimensional recurrence relations.