Exclusive B → Mℓ⁺ℓ^-(M = π, K, ρ, K *) decays and determinations of |V_ts| (and |V_td/V_ts|)

We examine the possibility for precise determination of |V_ts| (and |V_td/V_ts\) from the exclusive decays, B → Kℓ⁺ℓ^-, B → K * ℓ⁺ℓ^- (and B → π ℓ⁺ℓ^-, B → ρℓ⁺ℓ^-). We show that the ratio |V_ts| can be extracted experimentally with a small theoretical uncertainty from hadronic form-factors, if we appropriately constrain kinematical regions of q². We also give detailed analytical and numerical results on the differential decay width dΓ(B → K * ℓ⁺ℓ^-)/dq², and the ratios of integrated branching fractions, ℬ(B → ρℓ⁺ℓ^-)/ℬ(B → K * ℓ⁺ℓ^-). We estimate that one can determine the ratio |V_ts\ from those decays within theoretical accuracy of ∼ 10%.