Semi-leptonic $B$ decays to tensor mesons

Abstract

Using the form factors of the transtions $B\to T$ with $T$ refering to a tensor meson, such as $a_2(1320),f_2(1270),K_2^{\ast }(1430),D_2^{\ast }(2460)$ and $D_{2s}^{\ast }(2573)$, within the covariant light-front quark model (CLFQM), we provide a detailed investigation of the corresponding semi-leptonic decays $B\to T\ell \hat{I}{½}_{\ell }$ with $\ell =e,\hat{I}½,\ddot{I}„$. All the branching ratios of these decays are larger than $10^{-5}$, in which the maximum value can reach up to $10^{-3}$, indicating promising prospects for experimental observation. Furthermore, we also calculate the longitudinal polarization fractions $f_L$ and forward-backward asymmetries $A_{FB}$ for these considered decays. All the decays $B\to T\ell \hat{I}{½}_{\ell }$ are dominated by the longitudinal polarization, where the polarization fractions can reach up to $\sim 70\%$ for the decays $B\to T{\ell }^{\prime }\hat{I}{½}_{{\ell }^{\prime }}$ with ${\ell }^{\prime }=e,\hat{I}¼$, those of the decays $B\to T\ddot{I}„\hat{I}{½}_{\ddot{I}}„$ are a little smaller. The $A_{FB}$ values of the decays $B\to T{\ell }^{\prime }\hat{I}{½}_{{\ell }^{\prime }}$ and $B\to T\ddot{I}„\hat{I}{½}_{\ddot{I}}„$ have opposite signs.

18 pages, 4 figures