The discrete charm of flavour and CP violation

We point out that in the Standard Model (SM) there is no explanation why $|V_{23}|^2 + |V_{13}|^2$ is of order $10^{-3}$. A framework is described for explaining this small mixing, involving the introduction of vector-like quarks. A symmetry is introduced so that at a first stage $V_{CKM} = 1\>\!\!\!\mathrm{I}$ and only the third generation of quarks acquires a mass. It is shown that when interactions of vector-like quarks are taken into account a realistic quark mass spectrum is generated together with a correct $V_{CKM}$ matrix.
Comment: 10 pages, no figures. Prepared for the proceedings of DISCRETE2016: the Fifth Symposium on Prospects in the Physics of Discrete Symmetries, 28 November-3 December 2016, University of Warsaw, Poland, to appear in the Journal of Physics: Conference Series (JPCS)