Absence of CP Violation in the Scalar Sector of a Higgs Triplet Model

TL;DR

This paper demonstrates that the scalar sector of a Higgs Triplet Model with a complex singlet scalar cannot produce spontaneous CP violation due to symmetry constraints and potential minimization conditions.

Contribution

It provides a comprehensive analysis showing the absence of spontaneous CP violation in this extended Higgs model, clarifying the role of global symmetries and potential parameters.

Findings

Scalar potential forbids spontaneous CP violation across all parameters.

Global symmetries enforce real vacua when trilinear coupling is non-zero.

Vacuum phases become unphysical in the limit of zero trilinear coupling.

Abstract

We investigate the potential for spontaneous CP violation in a Higgs Triplet Model extension, including a complex singlet scalar. We demonstrate that the scalar potential strictly forbids spontaneous CP violation across the entire parameter space. For a non-zero trilinear coupling $\kappa$, minimization conditions combined with global symmetries enforce a phase alignment that yields a real vacuum. In the singular limit $\kappa \to 0$, we show that the enhancement of global symmetries renders unphysical vacuum phases. Consequently, we conclude that the scalar sector of this model cannot source CP violation.