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 \(K_{J}^{(*)}\) with parity (−1)J for \(K_{J}^{*}\) and (−1)J+1 for K J in the final state. Using 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.