Six-loop beta functions in general scalar theory

TL;DR

This paper derives six-loop beta functions for general scalar field theories in four dimensions, extending renormalization-group equations and applying results to models like the Two-Higgs-Doublet Model, enhancing precision in theoretical predictions.

Contribution

The paper provides the first six-loop beta functions for all parameters in general scalar theories within the ar{MS} scheme, using existing counter-term results without explicit loop integral calculations.

Findings

Extended RG equations to six-loop order for various models.

Derived new contributions to beta functions in the Two-Higgs-Doublet Model.

Enhanced precision in scalar sector renormalization-group analysis.

Abstract

We consider general renormalizable scalar field theory and derive six-loop beta functions for all parameters in d = 4 dimensions within the $\overline{MS}$-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.