A Scaling Law for Quark Masses and the CKM matrix

We have recently argued that quark masses may follow a simple scaling law. In this paper we build a simple mass matrix for quarks that can reproduce the scaling law expression. The simple mass matrices of the model are then generalized through general rotations in the flavor space, including phase transformations. In turn they will be used to construct the quark-mixing matrix. It has been found that the model can predict the entries of the $CKM$ matrix in excellent agreement with current values. We give precise values for the light quark masses and determine the magnitude of the CP violation and also the quark-mixing angles in the flavor space. The main motivation behind this work is to relate the scaling law predictions with quark-mixing, through a simple mass matrix and its generalized Hermitian form.