Generating and evaluating 1PI Feynman diagrams for an MSR field theory

TL;DR

This paper presents computational methods combining FeynArts and SecDec to automate the generation, regularization, and evaluation of Feynman diagrams in MSR field theories, demonstrated on the NSAPS three-vector model.

Contribution

It introduces a semi-automated approach for generating and evaluating 1PI Feynman diagrams in MSR field theories, with specific modifications to existing packages for improved efficiency.

Findings

Automated generation of Feynman diagrams using FeynArts.

Dimensional regularization and epsilon expansion with SecDec.

Application to the NSAPS three-vector model.

Abstract

We discuss certain computational methods and analytical techniques that can be used to automatize the various steps involved in the renormalization group analysis of an MSR field theory. The methods rely mainly on the well known packages FeynArts and SecDec. The former is used with minor modifications for generating the Feynman diagrams and obtaining the corresponding expressions, and the latter for dimensional regularization and epsilon expansion of the Feynman integrals. We first discuss how suitable classes and generic model files required by FeynArts are created, present the minor modifications made in the internal file Analytic.m, and then show how the diagrams and the expressions are generated. We then discuss the procedure followed in further simplifying the integrals obtained from the Feynman diagrams to render them in the form of standard scalar Feynman integrals so that the package SecDec can be used to dimensional regularize and epsilon expand them. We discuss these methods as it is applied to a particular theory, namely, the NSAPS three-vector model. However, they can be easily generalized to be applied to other similar MSR field theories.