Four Loop Renormalisation Group Equations in general Gross-Neveu-Yukawa Theories

TL;DR

This paper provides comprehensive four-loop beta functions and anomalous dimensions for general renormalisable theories with fermions and scalars, with applications to Higgs and top couplings, addressing dimensional continuation challenges.

Contribution

It offers the first complete four-loop formulas for arbitrary theories in the MS scheme and applies them to key Standard Model couplings, highlighting new computational insights.

Findings

Derived all four-loop beta functions and anomalous dimensions.

Identified novel contributions to Higgs and top Yukawa couplings.

Addressed dimensional continuation issues from four to three dimensions.

Abstract

We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel contributions to the $\beta$-functions of the Higgs and top coupling are extracted. We discuss how four loops present a challenge to dimensional continuation from four to three dimensions and propose a solution.