Controlled fermion mixing and FCNCs in a $\Delta(27)$ 3+1 Higgs Doublet Model

Understand

We propose a 3+1 Higgs Doublet Model based on the $\Delta(27)$ family symmetry supplemented by several auxiliary cyclic symmetries leading to viable Yukawa textures for the Standard Model fermions, consistent with the observed pattern of fermion masses and mixings.

• The charged fermion mass hierarchy and the quark mixing pattern is generated by the spontaneous breaking of the discrete symmetries due to flavons that act as Froggatt-Nielsen fields.
• The tiny neutrino masses arise from a radiative seesaw mechanism at one loop level, thanks to a preserved $Z_2^{\left( 1\right)}$ discrete symmetry, which also leads to stable scalar and fermionic dark matter candidates.
• The leptonic sector features the predictive cobimaximal mixing pattern, consistent with the experimental data from neutrino oscillations.