RGBeta: A Mathematica Package for the Evaluation of Renormalization Group $ \beta $-Functions

TL;DR

RGBeta is a Mathematica package that simplifies the extraction of renormalization group beta-functions in generic four-dimensional gauge-Yukawa theories, making complex calculations more accessible for specific models.

Contribution

The paper introduces RGBeta, a new Mathematica package that automates the calculation of beta-functions in broad classes of gauge-Yukawa theories, based on general three-loop results.

Findings

RGBeta enables efficient extraction of beta-functions for specific models.

The package is publicly available on GitHub with example notebooks.

It facilitates application of high-order loop calculations to practical model analysis.

Abstract

In completely generic four-dimensional gauge-Yukawa theories, the renormalization group $ \beta $-functions are known to the 3-2-2 loop order in gauge, Yukawa, and quartic couplings, respectively. It does, however, remain difficult to apply these results to specific models without the use of dedicated computer tools. We describe a procedure for extracting $ \beta $-functions using the general results and introduce RGBeta, a dedicated Mathematica package for extracting the $ \overline{\text{MS}} $ $ \beta $-functions in broad classes of models. The package and example notebooks are available from the GitHub repository at https://github.com/aethomsen/RGBeta .