Correlations between quark mass and flavor mixing hierarchies.
2021
We calculate nine moduli of 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 now with the current experimental value. We find that behind the strong {\it mass} hierarchies of up- and down-type quarks are the relatively weak {\it texture} hierarchies on the right-bottom corners of $M^{}_{\rm u}$ and $M^{}_{\rm d}$.
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