On the Classification of Accidental Symmetries of the Two Higgs Doublet Model Potential

TL;DR

This paper classifies the 13 possible accidental symmetries of the two-Higgs-doublet-model potential using a bilinear formalism, providing detailed transformation relations and confirming the classification's completeness.

Contribution

It explicitly derives the transformation relations for each symmetry and establishes a one-to-one correspondence with the bilinear space, supporting the completeness of the symmetry classification.

Findings

Confirmed the 13 distinct accidental symmetries of the 2HDM potential.

Provided explicit transformation relations for each symmetry.

Established a one-to-one correspondence between scalar field space and bilinear space.

Abstract

Recently, it has been shown [arXiv:1106.3482] that the two-Higgs-doublet-model potential may exhibit a maximum of 13 distinct accidental symmetries. Such a classification is based on a six-dimensional bilinear scalar field formalism realizing the SO(1,5) symmetry group. This note presents the transformation relations for each of the 13 symmetries in the original scalar field space and their one-to-one correspondence to the space of scalar bilinears, thereby providing firm support for the completeness of the classification.