Towards general scalar-Yukawa renormalisation group equations at three-loop order

TL;DR

This paper derives three-loop renormalisation group equations for general four-dimensional quantum field theories with scalars and fermions, providing comprehensive formulas for various interactions and applying them to a specific model.

Contribution

It provides the first complete three-loop RG equations for arbitrary scalar-fermion theories, including new expressions for anomalous dimensions and interaction evolutions.

Findings

Derived general three-loop RG equations for scalars and fermions.

Applied the formulas to the Litim-Sannino model to analyze its RG flow.

Identified unknown coefficients in scalar interaction evolutions.

Abstract

For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature results, general expressions are obtained for field anomalous dimensions, Yukawa interactions, as well as fermion masses. The renormalisation group evolution of scalar quartic, cubic and mass terms is determined up to a few unknown coefficients. The combined results are applied to compute the renormalisation group evolution of the gaugeless Litim-Sannino model.