Semileptonic B decay as a test of CKM unitarity

I point out that $B \to X_q \l^+ \l^-$ decays $(q = s, d)$ are sensitive probes of possible violation of CKM unitarity. I compute the decay rates and asymmetries in a minimal extension of the Standard Model containing an additional isosinglet charge (-1/3) quark, which leads to a deviation from CKM unitarity. It is shown that even for small mixing ratios $|{z_{qb}}/{(V_{tq}^\ast V_{tb})}| \sim O({10}^{-2})$, the contribution of the tree-level $Z-$FCNC appearing in the model should change the rates and asymmetries significantly. Especially the CP asymmetry, $A_{CP} (B \to X_s \l^+ \l^-)$, can be enhanced to be few percents, while in the standard model the size is less than $O({10}^{-3})$. On the other hand, $A_{CP} (B \to X_d \l^+ \l^-)$ is not altered so much. Constraints for the mixing ratios are extracted from the experiments of $B \to X_s \gamma$ for $q = s$ and $B_d^0 - \bar{B}_d^0$ mixing for $q = d$ under a natural assumption that the couplings of the tree-level $Zf\bar{f}$ are almost unity, i.e. $z_{\alpha \alpha} \sim 1$.