We study the exclusive decays of $\overrightarrow{B}{K}^{\left(*\right)}{\mathcal{l}}^{+}{\mathcal{l}}^{-}$ by results in perturbative QCD with the heavy quark effective theory and lattice calculations. We obtain the form factors for the $\overrightarrow{B}{K}^{\left(*\right)}$ transitions in the whole allowed region. Our predictions for the branching ratios of $\overrightarrow{B}K{\mathcal{l}}^{+}{\mathcal{l}}^{-},$ $\overrightarrow{B}{K}^{*}{e}^{+}{e}^{-},$ and $\overrightarrow{B}{K}^{*}{\mu }^{+}{\mu }^{-}$ are $0.53\pm {0.05}_{-0.07}^{+0.10\mathrm{}},$ $1.68\pm {0.17}_{-0.09}^{+0.14\mathrm{}},$ and $1.34\pm {0.13}_{-0.06}^{+0.11\mathrm{}}\times {10}^{-6},$ where the errors are from the quark mixing elements and hadronic effects, respectively. We also find that our definitions of the T-odd observable and the up-down asymmetry of the K meson in $\overrightarrow{B}{K}^{*}{\mathcal{l}}^{+}{\mathcal{l}}^{-}\to K\pi {\mathcal{l}}^{+}{\mathcal{l}}^{-}$ can be used to probe new physics.

• Received 18 June 2002

DOI:https://doi.org/10.1103/PhysRevD.66.094018