General quartic β-function at three loops

Abstract

Abstract We determine the three-loop MS ¯ $$ \overline{\textrm{MS}} $$ quartic β-function for the most general renormalisable four-dimensional theories. A general parametrisation of the β-function is compared to known β-functions for specific theories to fix all coefficients. Three-loop β-functions for the cubic coupling and scalar mass terms also follow from the result, which is made available in software packages.

Keywords

• Renormalization Group
• Renormalization and Regularization