Geometrical CP Violation

TL;DR

This paper explores spontaneous CP violation through calculable phases in models with three Higgs doublets and non-Abelian symmetries, analyzing their potential to explain fermion masses and mixings.

Contribution

It demonstrates how the non-Abelian group Delta(54) can produce calculable CP-violating phases similar to Delta(27), expanding the understanding of symmetry-based CP violation.

Findings

Delta(54) leads to calculable phases akin to Delta(27)

Models with three Higgs doublets can incorporate observed fermion properties

Non-Abelian symmetries can naturally generate CP violation

Abstract

Spontaneous CP-violating phases that do not depend on the parameters of the Higgs sector - the so-called calculable phases - are investigated. The simplest realization is in models with 3 Higgs doublets, in which the scalar potential is invariant under non-Abelian symmetries. The non-Abelian discrete group Delta(54) is shown to lead to the known structure of calculable phases obtained with Delta(27). We investigate the possibily of accommodating the observed fermion masses and mixings.