Structure and texture of the quark mass matrix

Abstract

Starting from a weak basis in which the up (or down) quark matrix is diagonal, we obtain an exact set of equations for the quark mass matrix elements in terms of known observables. We make a numerical analysis of the down (up) quark mass matrix. Using the data available for the quark masses and mixing angles at different energy scales, we found a numerical expression for these matrices. We suggest that it is not possible to have an specific texture from this analysis. We also examine the most general case when the complex phases are introduced in the mass matrix. We find the numerical value for these phases as a function of $δ$, the CP-violationg phase.