The problem of flavour

TL;DR

This paper reviews the longstanding flavour problem in particle physics, discussing new solutions involving discrete symmetries and dark-technicolour models, and explores their implications for dark matter and grand unification.

Contribution

It introduces novel discrete flavour symmetry mechanisms and a dark-technicolour paradigm that unify hierarchical VEV models with dark matter predictions.

Findings

Discrete flavour symmetry solutions can produce flavonic dark matter.

A relation between flavon mass and symmetry-breaking scale is established.

The framework suggests possible connections to grand unified theories.

Abstract

We review the problem of flavour tracing back to the days when the standard model was just coming together. We focus on the recently discussed new solutions of this problem, namely the Froggatt and Nielsen mechanism based on a novel discrete $\mathcal{Z}_{\rm N} \times \mathcal{Z}_{\rm M}$ flavour symmetry, and the standard hierarchical VEVs model. The standard HVM, and the Froggatt and Nielsen mechanism based on the $\mathcal{Z}_{\rm N} \times \mathcal{Z}_{\rm M}$ flavour symmetry, can be recovered from a new dark-technicolour paradigm, where the hierarchical VEVs or the flavon VEV may appear as the chiral multifermion condensates. In particular, there appears a novel feature that the solution of the flavour problem based on the discrete flavour symmetry can provide the so-called flavonic dark matter. This predicts a specific relation between the mass and the symmetry-breaking scale, which can be contrasted with the standard QCD axion. Moreover, a possible direction towards the Grand Unified framework is also discussed.