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

Matheo Escobar, Sebastian Olivares

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 $κ$, minimization conditions combined with global symmetries enforce a phase alignment that yields a real vacuum. In the singular limit $κ\to 0$, 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.

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

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 , minimization conditions combined with global symmetries enforce a phase alignment that yields a real vacuum. In the singular limit , 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.
Paper Structure (15 sections, 17 equations)

This paper contains 15 sections, 17 equations.

Table of Contents

  1. Introduction
  2. Model and Scalar Potential
  3. Generalization to Complex Vacuum
  4. Phase Constraints from Minimization
  5. Vacuum Parametrization
  6. Absence of Spontaneous CP Violation in the Scalar Sector
  7. The Coupled Case: $\kappa \neq 0$
  8. The Decoupling Limit and Physical Consequences
  9. Discussion and Implications
  10. Comparison with the 2HDM
  11. Implications for Leptogenesis
  12. Conclusions
  13. Scalar Mass Structure and Zero Modes
  14. CP Conservation in the General Case
  15. The CP-Odd Sector and the Singular Limit