Co-positivity of tensors and bounded from below conditions of CP conserving two-Higgs-doublet potential

TL;DR

This paper derives analytic necessary and sufficient conditions for the boundedness from below of CP-conserving two-Higgs-doublet potentials using tensor co-positivity, addressing a key stability issue in particle physics models.

Contribution

It introduces a novel tensor-based approach to determine stability conditions for two-Higgs-doublet potentials, providing explicit analytic criteria.

Findings

Derived necessary and sufficient conditions for potential stability.

Applied tensor co-positivity theory to Higgs potential analysis.

Provided a method to analyze misalignment in Higgs doublets.

Abstract

In this paper, the analytic sufficient and necessary conditions are obtained for the CP conserving two-Higgs-doublet potential to be bounded from below by using the co-positivity of tensors. This is achieved by treating the potential as a quartic homogeneous polynomial about the moduli of the two Higgs doublet fields, where the 'angles' is described as the misalignment of the two doublets, then solving three minimum problems with respect to the misalignment. Finally, the analytic conditions are established with the help of the corresponding theory and methods of higher order tensors.