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

We perform a thorough analysis of the 3-Higgs doublet model with a scalar potential invariant under a global $\Delta(27)$ discrete symmetry. The three scalar doublets are chosen to transform as triplets under the discrete group. For each of the known tree-level minima, we study the mass spectra and use the oblique parameters $STU$ and perturbative unitarity to constrain the parameter space of this model. We then consider phenomenological consequences of some leading order quark Yukawa couplings by considering the flavour violation process $b \to s \gamma$. We show that unitarity constraints greatly limit the parameter space of the model, conversely $b \to s \gamma$ is automatically tamed by the symmetry.Comment: 26 pages, 3 figures; minor text revisio