General scalar renormalisation group equations at three-loop order

Abstract

Abstract For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the MS ¯ $$ \overline{\mathrm{MS}} $$ scheme. Utilising pre-existing literature expressions for a specific model, loop integrals are avoided and templates for general theories are obtained. We reiterate known four-loop expressions, and from those derive β functions for scalar masses and cubic interactions. As an example, the results are applied to compute all renormalisation group equations in U(n) × U(n) scalar theories.

Keywords

• Renormalization Group
• Renormalization Regularization and Renormalons