Gauge theory on $Z_2 \times Z_2 \ti Z_2 $ Discrete Group and a Spontaneous $CP$ Violation Toy Model

TL;DR

This paper constructs a toy model of spontaneous CP violation using non-commutative differential calculus on a discrete group, involving three Higgs doublets and a specific $Z_2 imes Z_2 imes Z_2$ symmetry.

Contribution

It introduces a novel spontaneous CP violation model based on discrete group gauge theory, distinct from the Weinberg-Branco model, with preserved neutral flavor current conservation.

Findings

Model achieves spontaneous CP violation with three Higgs doublets.

Uses $Z_2 imes Z_2 imes Z_2$ symmetry to constrain Yukawa couplings.

Maintains neutral flavor current conservation.

Abstract

In the spirit of Non-commutative differential calculus on discrete group, we construct a toy model of spontaneous $CP$ violation (SCPV). Our model is different from the well-known Weinberg-Branco model although it involves three Higgs doublets and preserve neutral flavor current conservation (NFC) after using the $Z_2 \ti Z_2 \ti Z_2$ discrete symmetry and imposing some constraints on Yukawa couplings.