Rare exclusive semileptonicb→stransitions in the standard model

We study long-distance effects in rare exclusive semileptonic decays $\overrightarrow{B}{(K,K}^{*}\left)\right({\mathcal{l}}^{+}{\mathcal{l}}^{-},\nu \overline{\nu })$ and analyze dilepton spectra and asymmetries within the framework of the standard model. The form factors, describing the meson transition amplitudes of the effective Hamiltonian, are calculated within the lattice-constrained dispersion quark model: the form factors are given by dispersion representations through the wave functions of the initial and final mesons, and these wave functions are chosen such that the $\overrightarrow{B}{K}^{*}$ transition form factors agree with the lattice results at large $q^2$. We calculate branching ratios of semileptonic $\overrightarrow{B}{K,K}^{*}$ transition modes and study the sensitivity of observables to the long-distance contributions. The shape of the forward-backward asymmetry and the longitudinal lepton polarization asymmetry are found to be independent of the long-distance effects and mainly determined by the values of the Wilson coefficients in the standard model.