Towards realistic models of quark masses with geometrical CP violation

TL;DR

This paper proposes a novel model for quark masses and mixing that incorporates geometrical CP violation via a elta(27) symmetry, using an additional U(1)_F or Z_N symmetry to control scalar potential terms and generate Yukawa hierarchies.

Contribution

It introduces a new framework combining elta(27) with a Froggatt-Nielsen mechanism to produce realistic quark mass hierarchies and CP violation.

Findings

Successfully reproduces quark mass hierarchies

Achieves realistic CKM mixing angles

Maintains calculable CP-violating phases

Abstract

We present a model for quark masses and mixing, featuring geometrical CP violation through a \Delta(27) triplet. By employing a single U(1)_F or Z_N symmetry in addition to \Delta(27), we forbid all terms in the scalar potential that would spoil the calculable phases the triple acquires. The quark sector is realised by mimicking an existing scheme that reproduces the masses and CKM mixing, with the extra symmetry enabling the hierarchies in the Yukawa couplings through a Froggatt-Nielsen mechanism.