The Effects of Flavor Changing Neutral Current and Cabibbo-Kobayashi-Maskawa Matrix

Abstract

We study the effects of tree-level flavor changing neutral current and its present status with Cabibbo-Kobayashi-Maskawa matrix. Especially, we remark the effects of flavor changing neutral current on the unitary triangle of Cabibbo-Kobayashi-Maskawa matrix. In the case when the unitarity is nearly conserved, we find that the allowed FCNC in the $db$ sector is $\left| {{z_d}^{db}}/{{V_{CKM}}^{td} {{V_{CKM}}^{tb}}^\ast} \right| \sim O({10}^{-2})$, from the evaluation of the present bounds for the mixing size of neutral $B$ meson ($x_d$), and the $CP$ violation parameter in the neutral $K$ meson ($\epsilon$). Although the size is small, the new physics due to the tree-level FCNC in the $db$ sector is expected to be visible in the $B \rightarrow X_d \, l^+ \, l^- $ and the $CP$ asymmetries in the neutral $B$ meson system. In the case when the unitarity is violated and the quadrangle is conserved, the FCNC is large enough, i.e. $\left| {{z_d}^{db}}/{{V_{CKM}}^{td} {{V_{CKM}}^{tb}}^\ast} \right| \sim O(1)$. Then, a significant contribution is also expected in the inclusive $B \rightarrow X_d \, \gamma$ decay.