The breaking of the flavour permutational symmetry: Mass textures and   the CKM matrix
  Different ansaetze for the breaking of the flavour permutational symmetry according to S(3)L X S(3)R in S(2)L X S(2) give different Hermitian mass matrices of the same modified Fritzsch type, which differ in the symmetry breaking pattern. In this work we obtain a clear and precise indication on the preferred symmetry breaking scheme from a fit of the predicted theoretical Vckm 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 one free parameter: the CP violating phase Phi. Excellent agreement with the experimentally determined absolute values of the entries in the CKM matrix is obtained for Phi = 90 deg. The corresponding computed values of the Jarlskog invariant and the inner angles are J = 3.00 X 10^-5, alpha= 84 deg, beta= 24 deg and gamma =72 deg in very good agreement with current data on CP violation in the neutral kaon-antikaon system and oscillations in the B-Bbar system. 
A. Mondragon and E. Rodriguez-Jauregui (IF, Nat. Autonomous Univ. of   Mexico)