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 $B \to K_J^{(*)}\nu \bar{\nu}$. 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.