Correlations between quark mass and flavor mixing hierarchies

Abstract

We calculate the quark flavor mixing matrix $V$ based on the Hermitian quark mass matrices $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with vanishing $(1,1)$, $(1,3)$ and $(3,1)$ entries. The popular leading-order prediction $|V^{}_{ub}/V^{}_{cb}| \simeq \sqrt{m^{}_u/m^{}_c}$ is significantly modified, and the result agrees with the current experimental value. We find that behind the strong {\it mass} hierarchy of up- or down-type quarks is the weak {\it texture} hierarchy of $M^{}_{\rm u}$ or $M^{}_{\rm d}$ characterized by an approximate seesaw-like relation among its $(2,2)$, $(2,3)$ and $(3,3)$ elements.