Radiative and Semileptonic B Decays Involving Higher K-Resonances in the Final States

We study the radiative and semileptonic B decays involving a spin-$J$ resonant $K_J^{(*)}$ with parity $(-1)^J$ for $K_J^*$ and $(-1)^{J+1}$ for $K_J$ in the final state. Using the large energy effective theory (LEET) techniques, we formulate $B to K_J^{(*)}$ transition form factors in the large recoil region in terms of two independent LEET functions $zeta_perp^{K_J^{(*)}}$ and $zeta_parallel^{K_J^{(*)}}$, the values of which at zero momentum transfer are estimated in the BSW model. According to the QCD counting rules, $zeta_{perp,parallel}^{K_J^{(*)}}$ exhibit a dipole dependence in $q^2$. We predict the decay rates for $B to K_J^{(*)} gamma$, $B to K_J^{(*)} ell^+ ell^-$ and $B to K_J^{(*)} u bar{ u}$. The branching fractions for these decays with higher $K$-resonances in the final state are suppressed due to the smaller phase spaces and the smaller values of $zeta^{K_J^{(*)}}_{perp,parallel}$. Furthermore, if the spin of $K_J^{(*)}$ becomes larger, the branching fractions will be further suppressed due to the smaller Clebsch-Gordan coefficients defined by the polarization tensors of the $K_J^{(*)}$. We also calculate the forward backward asymmetry of the $B to K_J^{(*)} ell^+ ell^-$ decay, for which the zero is highly insensitive to the $K$-resonances in the LEET parametrization.