Six-loop beta functions in general scalar theory

Abstract

Abstract We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $$ \overline{\mathrm{MS}} $$ MS ¯ -scheme. We do not explicitly compute relevant loop integrals but utilize O(n)-symmetric model counter-terms available in the literature. We consider dimensionless couplings and parameters with a mass scale, ranging from the trilinear self-coupling to the vacuum energy. We use obtained results to extend renormalization-group equations for several vector, matrix, and tensor models to the six-loop order. Also, we apply our general expressions to derive new contributions to beta functions and anomalous dimensions in the scalar sector of the Two-Higgs-Doublet Model.