The CP violating phase δ_{13} and the quark mixing angles θ_{13}, θ_{23} and θ_{12} from flavour permutational symmetry breaking

Abstract

The phase equivalence of the theoretical mixing matrix ${\bf V}^{th}$ derived from the breaking of the flavour permutational symmetry and the standard parametrization ${\bf V}^{PDG}$ advocated by the Particle Data Group is explicitly exhibited. From here, we derive exact explicit expressions for the three mixing angles $θ_{12}$, $θ_{13}$, $θ_{23}$, and the CP violating phase $δ_{13}$ in terms of the quark mass ratios $(m_{u}/m_{t}, m_{c}/m_{t}, m_{d}/m_{b}, m_{s}/m_{b})$ and the parameters $Z^{*1/2}$ and $Φ^*$ characterizing the preferred symmetry breaking pattern. The computed values for the CP violating phase and the mixing angles are: $δ^*_{13}=75^\circ$, $\sinθ^*_{12}=0.221$, $\sinθ^*_{13}=0.0034$, and $\sinθ^*_{23}=0.040$, which coincide almost exactly with the central values of the experimentally determined quantities.