3HDM with $\Delta(27)$ symmetry and its phenomenological consequences

TL;DR

This paper analyzes a 3-Higgs doublet model with $(27)$ symmetry, exploring its scalar potential, mass spectra, and flavor violation constraints, revealing how the symmetry constrains new physics contributions.

Contribution

It provides a comprehensive analysis of the $(27)$ symmetric 3HDM, including scalar potential minima, mass spectra, and flavor violation effects, highlighting the symmetry's constraining power.

Findings

Perturbative unitarity constrains model parameters.

The $(27)$ symmetry suppresses flavor violation effects.

Model predictions are consistent with experimental bounds.

Abstract

We perform a comprehensive analysis of a version of the 3-Higgs doublet model whose scalar potential is invariant under a global $\Delta(27)$ discrete symmetry and where the three scalar doublets are chosen to transform as a triplet under this discrete group. For each of the known tree-level minima we study the mass spectra and use the oblique parameters $STU$ as well as perturbative unitarity to constrain the parameter space of the model. We then discuss phenomenological consequences of some leading order flavour mixing quark Yukawa couplings by considering the flavour violation process $b \to s \gamma$. We show that perturbative unitarity significantly constrains parameters of the model while, conversely, the beyond the Standard Model contributions to the $b \to s \gamma$ decay are automatically tamed by the symmetry.