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

For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the (MS) over bar 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.

Automated summary

This article investigates the renormalisation group equations for arbitrary four-dimensional quantum field theories with scalars and fermions, up to three-loop order in perturbation theory. General expressions for field anomalous dimensions, Yukawa interactions, and fermion masses are obtained, and applied to compute the renormalisation group evolution of a specific model.