SYMMETRICAL CABIBBO-KOBAYASHI-MASKAWA MATRIX AND QUARK MASS MATRICES

In this article we aim to find the constraints on the quark mass matri ces for the symmetric Cabibbo-Kobayashi-Maskawa (CKM) matrix V. We wor k in the bases, where (i) M(u) is diagonal, (ii) M(d) is diagonal, and (iii) M(d) = f(M(u)), i.e., U = D* P, where U and D are matrices tha t diagonalize the up- and down-quark mass matrices, respectively, and P is the phase matrix. We find that none of the moduli of the off-diag onal elements of these interesting forms of the quark mass matrices M( u) and M(d), which lead to the symmetric CKM matrix, are consistent wi th zero for these Ansatze, which means that such forms for mass matric es are difficult to obtain from any symmetry. We then give the symmetr y constraint for V written in terms of the mass eigenvalues in a basis -independent form.