Radiative and semileptonic B decays involving higher K-resonances in the final states

Hisaki Hatanaka; Kwei-Chou Yang

doi:10.1140/epjc/s10052-010-1293-7

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Particles and Fields

Eur. Phys. J. C (2010) 67: 149-162
https://doi.org/10.1140/epjc/s10052-010-1293-7

Regular Article - Theoretical Physics

Radiative and semileptonic B decays involving higher K-resonances in the final states

Hisaki Hatanaka and Kwei-Chou Yang^*

Department of Physics, Chung-Yuan Christian University, Chung-Li, Taiwan, 320, ROC

^* e-mail: kcyang@cycu.edu.tw

Received: 13 January 2010
Published online: 1 April 2010

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.