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

Abstract

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

Comments: 27 pages, 4 figures, 7 tables;contents and figures corrected, title and references revised