Two-loop Beta Function for Complex Scalar Electroweak Multiplets

TL;DR

This paper derives the two-loop beta function for a complex scalar electroweak multiplet, enabling precise predictions of coupling evolutions in extended Standard Model scenarios.

Contribution

It provides the general form of four-point interactions for complex scalars in SU(2) representations and calculates the two-loop beta function for models with scalar multiplets.

Findings

Derived the algebraic identities for higher-order corrections.

Explicit two-loop beta function for scalar multiplet extensions.

Numerical analysis of coupling evolution in specific models.

Abstract

We present the general form of the renormalizable four-point interactions of a complex scalar field furnishing an irreducible representation of SU(2), and derive a set of algebraic identities that facilitates the calculation of higher-order radiative corrections. As an application, we calculate the two-loop beta function for the SM extended by a scalar multiplet, and provide the result explicitly in terms of the group invariants. Our results include the evolution of the Higgs-portal couplings, as well as scalar "minimal dark matter". We present numerical results for the two-loop evolution of the various couplings.