Special symmetric quark mass matrices

Abstract

We give a procedure to construct a special class of symmetric quark mass matrices near the democratic limit of equal Yukawa couplings for each sector. It is shown that within appropriate weak-bases, the requirements of symmetry and arg[det( M)]=0 are very strong conditions, that necessarily lead to a Cabibbo angle given by |V us|= m d/m s , and to | V cb |∼ m s / m b , in first order. In addition, we prove that the recently classified ansätze, which also reproduce these mixing matrix relations, and which were based on the hypothesis of the Universal Strength for Yukawa couplings, where all Yukawa couplings have equal moduli while the flavour dependence is only in their phases, are, in fact, particular cases of the generalized symmetric quark mass matrix ansätze we construct here. In an excellent numerical example, the experimental values on all quark mixings and masses are accommodated, and the CP violation phase parameter is shown to be crucially dependent on the values of m u and V us .