# Discrete Minimal Flavour Violation

## TL;DR

This paper explores replacing continuous flavour symmetry with discrete groups to avoid Goldstone bosons, enabling TeV-scale minimal flavour violation with specific discrete groups providing sufficient protection.

## Contribution

It introduces a novel approach of using discrete flavour symmetries to prevent Goldstone bosons, allowing for TeV-scale minimal flavour violation models.

## Key findings

- Discrete groups Sigma(168), Sigma(72phi), Sigma(216phi), Sigma(360phi) protect TeV-scale MFV.
- Goldstone bosons impose strong bounds on continuous symmetry models.
- Discrete symmetries can suppress flavor-changing processes effectively.

## Abstract

We investigate the consequences of replacing the continuous flavour symmetry of minimal flavour violation by a discrete group. Goldstone bosons, resulting from the breaking of the continuous flavour symmetry, generically lead to bounds on new flavour structure by many orders of magnitude above the TeV-scale. The absence of Goldstone bosons for discrete symmetries constitutes the primary motivation of our work. The four crystal-like groups Sigma(168), Sigma(72phi), Sigma(216phi) and Sigma(360phi)$ provide enough protection for a discrete TeV-scale MFV scenario in the case where Delta F = 2 processes are generated by two subsequent Delta F = 1 transitions.