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 ${\mathbf{V}}^{th}$ derived from the breaking of the flavour permutational symmetry and the standard parametrization ${\mathbf{V}}^{PDG}$ 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 $Z^{\ast 1/2}$ and ${\Phi }^{\ast }$ characterizing the preferred symmetry breaking pattern. The computed values for the CP violating phase and the mixing angles are: ${\delta }_{13}^{\ast }=75^{\circ }$, $\sin {\theta }_{12}^{\ast }=0.221$, $\sin {\theta }_{13}^{\ast }=0.0034$, and $\sin {\theta }_{23}^{\ast }=0.040$, which coincide almost exactly with the central values of the experimentally determined quantities.

Comments: 25 pages, we added an estimation of a reasonable range of values for the quark mass ratios and the corresponding quark mixing matrix elements. Accepted in Phys. Rev. D, 01 April 2000