3HDM with softly broken $Δ(54)$ and $Σ(36)$

TL;DR

The paper investigates the scalar sector of three-Higgs-doublet models with Δ(54) and Σ(36) discrete symmetries under softly broken potentials. It derives and analyzes the vacuum alignments, the resulting mass spectra, and how soft-breaking terms lift degeneracies across alignments A, A', B, and C, using both analytical formulas and numerical examples. A key finding is that soft breaking generically lifts degeneracies, but certain SBP-induced alignments can preserve a residual Z2 symmetry, stabilizing a scalar as a dark matter candidate. These results illuminate the phenomenology of multi-Higgs sectors with discrete symmetries and inform constraints on scalar spectra and possible DM scenarios in such models.

Abstract

We perform an analysis of the scalar sector of 3-Higgs doublet models with softly broken $Δ(54)$ and $Σ(36)$ symmetries. We consider the various vacuum expectation value alignments and consider, for each, softly broken terms that deviate the alignment. We check the evolution of the minima, present analytical and numerical results for the lifting of degeneracies of the physical eigenstates, and describe the decays of the states considering any residual symmetries.

Figures (5)

• Figure 1: Evolution of the parameters $v/v_0$ and $u/v_0$ as a function of $m_{22}^2$ for $\Sigma(36)$. Where $v_0$ corresponds to $m_{22}^2=0$
• Figure 2: Masses evolution as a function of $m_{22}^2$ for $\Sigma(36)$.
• Figure 3: Evolution of the parameters $v$ and $u$ as a function of $m_{22}^2$ for $\Sigma(36)$.
• Figure 4: Masses evolution as a function of $m_{22}^2$ for $\Delta(54)$.
• Figure 5: Evolution of the parameters $a$ and $b$ as a function of $m_{22}^2$ for $\Sigma(36)$ and $\Delta(54)$.