The CP violating phase \delta_{13} and the quark mixing angles \theta_{13}, \theta_{23} and \theta_{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 $\theta_{12}$, $\theta_{13}$, $\theta_{23}$, and the CP violating phase $\delta_{13}$ 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 $\Phi^*$ characterizing the preferred symmetry breaking pattern. The computed values for the CP violating phase and the mixing angles are: $\delta^*_{13}=75^\circ$, $\sin\theta^*_{12}=0.221$, $\sin\theta^*_{13}=0.0034$, and $\sin\theta^*_{23}=0.040$, which coincide almost exactly with the central values of the experimentally determined quantities.