Textures and hierarchies in quark mass matrices with four texture-zeros

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A systematic analysis on the phenomenologically allowed textures in Hermitian quark mass matrices with four texture-zeros is presented. The current data allow a full determination of the mass matrix elements, provided that the actual number of the parameters in the matrices is less than or equal to ten. Besides the standard texture with zeros located in (1,1) and (1,3) positions, we find four new type of parallel mass matrices. All of them are found to have similar hierarchical structures: three of the nonzero matrix elements are at the same order of magnitude with a small geometric hierarchy, while the remaining one is relatively much smaller. These textures show a possibility that a realistic quark mass matrix may have an approximate flavor S(2)ₗ⊗ S(2)ᵣ symmetry, i.e. a partial flavor democracy. The absolute values of the CP violating phases in the matrix elements are found to be either close to their maximum (≈ 90∘) or very small (≤ 10∘). We also find twenty-six quasi-parallel and seventeen non-parallel textures allowed by the experimental data.