Classifying Accidental Symmetries in Multi-Higgs Doublet Models

TL;DR

This paper develops a systematic method to classify accidental symmetries in multi-Higgs doublet models, explicitly listing all possible symmetries for 2HDM and 3HDM, advancing understanding of scalar potential symmetries.

Contribution

It introduces prime invariants and irreducible representations to classify accidental symmetries in n-Higgs doublet models, providing complete symmetry lists for 2HDM and 3HDM.

Findings

Maximum 13 accidental symmetries in 2HDM identified

Complete list of 40 accidental symmetries in 3HDM provided

Method enables explicit construction of symmetric potentials

Abstract

The potential of $n$-Higgs Doublet Models ($n$HDMs) contains a large number of SU(2)$_L$-preserving accidental symmetries as subgroups of the symplectic group Sp(2$n)$. To classify these, we introduce prime invariants and irreducible representations in bilinear field space that enable us to explicitly construct accidentally symmetric $n$HDM potentials. We showcase the classifications of symmetries and present the relationship among the theoretical parameters of the scalar potential for; (i) the Two Higgs Doublet Model (2HDM) and (ii) the Three Higgs Doublet Model (3HDM). We recover the maximum number of $13$ accidental symmetries for the 2HDM potential and for the first time, we present the complete list of $40$ accidental symmetries for the 3HDM potential.