Quark mixing angles and CP-violating phase from flavor permutational symmetry breaking

Different Ansaetze for the breaking of flavor permutational symmetry according to SL(3)(multiply-in-circle sign)SR(3)→SL(2)(multiply-in-circle sign)SR(2) give different Hermitian mass matrices of the same modified Fritzsch type, which differ in the symmetry breaking pattern. A clear and precise indication on the preferred symmetry breaking scheme is obtained from a fit of the predicted vertical bar Vth vertical bar to the experimentally determined absolute values of the elements of the CKM matrix. The preferred scheme leads to simple mass textures and allows us to compute the CKM mixing matrix, the Jarlskog invariant J, and the three inner angles of the unitarity triangle in terms of four quark mass ratios and only two free parameters: Z and the CP violating phase Φ. Excellent agreement with the experimentally determined absolute values of the entries in the CKM matrix is obtained for Z*=2.53125 and Φ*=90 deg. The corresponding computed values of the Jarlskog invariant and the inner angles are J=0.000028, α=83 deg., β=22 deg. and γ=75 deg. in very good agreement with current data on CP violation in the kaon-antikaon system and oscillations in the B-antiB system. It is also shown that the theoretical mixing matrix Vth derived from the breaking of the flavor permutational symmetry and the standard parametrization VPDG advocated by the Particle Data Group are equivalent, up to a redefinition of the unobservable phases of the quark fields in the mass representation. From here, we derive exact explicit expressions for the three mixing angles θ12, θ13, θ23, and the CP violating phase δ13 in terms of the quark mass ratios (mu/mt,mc/mt,md/mb,ms/mb) and the parameters Z*1/2 and Φ* characterizing the preferred symmetry breaking pattern. The predicted values for the CP violating phase and the mixing angles are: δ13*=75 deg., sin θ12*=0.2208, sin θ13*=0.0034, and sin θ23*=0.040, which coincide almost exactly with the central values of the experimentally determined quantities