Correlations between quark mass and flavor mixing hierarchies

Abstract

We calculate the quark flavor mixing matrix $V$ based on the Hermitian quark mass matrices $M_{\mathrm{u}}^{}$ and $M_{\mathrm{d}}^{}$ 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 $M_{\mathrm{u}}^{}$ or $M_{\mathrm{d}}^{}$ characterized by an approximate seesaw-like relation among its $(2,2)$, $(2,3)$ and $(3,3)$ elements.

Comments: 18 pages, the version accepted for publication in NPB