The problem of flavour

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 \(\mathcal {Z}_{\textrm{N}} \times \mathcal {Z}_{\textrm{M}}\) flavour symmetry, and the standard hierarchical VEVs model. The standard HVM, and the Froggatt and Nielsen mechanism based on the \(\mathcal {Z}_{\textrm{N}} \times \mathcal {Z}_{\textrm{M}}\) flavour symmetry, can be recovered from a new dark-technicolour paradigm, where the hierarchical VEVs or the flavon VEV may appear as the chiral multi-fermion 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.