Dirac Algebra Formalism for Two Higgs Doublet Models: the One-Loop Effective Potential

TL;DR

This paper introduces a covariant Dirac algebra formalism for the Two Higgs Doublet Model, providing an O(1,3)-covariant, IR-safe one-loop effective potential and a method to analyze symmetry breaking invariantly.

Contribution

It develops a novel Dirac algebra-based covariant formalism for 2HDM that simplifies the calculation of the one-loop effective potential and symmetry breaking analysis.

Findings

Derived a fully covariant, IR-safe one-loop effective potential.

Demonstrated the formalism's ability to evaluate symmetry breaking.

Provided a reparameterisation-invariant analysis method.

Abstract

We present a novel covariant bilinear formalism for the Two Higgs Doublet Model (2HDM) which utilises the Dirac algebra associated with the SL(2,C) group that acts on the scalar doublet field space. This Dirac-algebra approach enables us to obtain a fully O(1,3)-covariant and IR-safe expression for the one-loop effective potential. We illustrate how the formalism can be used to evaluate the breaking of global symmetries of the 2HDM potential by loop effects, in a field-reparameterisation invariant manner.