New quark mass matrix based on the BCS form

A new quark mass matrix based on the BCS form is proposed. At the first stage, the desirable two mass gaps are derived and generation mixing occurs between the second and third generations. At the second stage, the first-generation quarks obtain masses and the $\mathrm{CP}$-violating phase appears. An interesting prediction is found in the $V_{\mathrm{cb}}$ element of the Kobayashi-Maskawa matrix, which is favorable to the heavy top quark. The new mass matrix is consistent with the observed $B_d^0-{\overline{B}}_d^0$ mixing.