Fermion mass hierarchy and lepton flavor violation using $CP$ symmetry

We present a model which employs $CP\times Z_3$ symmetries where quark mixing and charged leptons masses are explained by following some texture. To achieve neutrino mass and mixing, we write a non-renormalizable Lagrangian using type-II seesaw mechanism by assuming ${\mathcal{O}}(1)$ couplings predicting no $CP$ violation. Then, we calculate the value of the couplings for both normal and inverted ordering of neutrino masses. We propose a mechanism of ultra-violet (UV) completion that motivates the higher dimensional Lagrangian in the neutrino sector. We also calculate the branching fraction of lepton flavor violating decays driven by triplet scalar for the model. Later, it is shown that the model can also accommodate maximal $CP$ violation by breaking the $CP$ symmetry spontaneously.