Exclusive B --> M l^+ l^- (M=π, K, ρ, K^*) Decays and Determinations of |V_{ts}| (and |V_{td}/V_{ts}|)

Abstract

We examine the possibility for precise determination of |V_{ts}| (and |V_{td}/V_{ts}|) from the exclusive decays, $B --> K \ell^+ \ell^-, B --> K^* \ell^+ \ell^-$ (and $B --> π\ell^+ \ell^-, B --> ρ\ell^+ \ell^-$). We show that the ratio |V_{ts}| can be extracted experimentally with a small theoretical uncertainty from hadronic form--factors, if we {\bf appropriately constrain} kinematical regions of $q^2$. We also give detailed analytical and numerical results on the differential decay width $dΓ(B --> K^* \ell^+ \ell^-)/dq^2$, and the ratios of integrated branching fractions, ${\cal B}(B --> ρ\ell^+ \ell^-)/{\cal B}(B --> K^* \ell^+ \ell^-)$. We estimate that one can determine the ratio |V_{ts}| from those decays within theoretical accuracy of $\sim 10%$.