Study of $b\to c$ induced ${\bar{B}}^{\ast }\to V\ell {\bar{\nu }}_{\ell }$ decays

Abstract

In this paper, we investigate the tree-dominated ${\bar{B}}_{u,d,s,c}^{\ast }\to V{\ell }^{-}{\bar{\nu }}_{\ell }$ ($V=D_{u,d}^{\ast },D_s^{\ast },J/\psi$ and $\ell =e,\mu ,\tau$) decays in the Standard Model with the relevant form factors obtained in the light-front quark model. These decays involve much more helicity states relative to the corresponding ${\bar{B}}^{\ast }\to P{\ell }^{-}{\bar{\nu }}_{\ell }$ and $\bar{B}\to V{\ell }^{-}{\bar{\nu }}_{\ell }$ decays, and moreover, the contribution of longitudinal polarization mode ($V$ meson) is relatively small, $\sim 30\%$, compared with the corresponding $B$ meson decays. We have also computed the branching fraction, lepton spin asymmetry, forward-backward asymmetry and ratio $R_V^{\ast (L)}\equiv \frac{\mathcal{B}({\bar{B}}^{\ast }\to V{\tau }^{-}{\bar{\nu }}_{\tau })}{\mathcal{B}({\bar{B}}^{\ast }\to V{\ell }^{\prime -}{\bar{\nu }}_{{\ell }^{\prime }})}$ (${\ell }^{\prime }=e,\mu$). Numerically, the branching fractions of ${\bar{B}}^{\ast }\to V{\ell }^{\prime -}{\bar{\nu }}_{{\ell }^{\prime }}$ decays are at the level of $\mathcal{O}(10^{-7})$, and are hopeful to be observed by LHC and Belle-II experiments. The ratios $R_{D^{\ast },D_s^{\ast },J/\psi }^{\ast (L)}$ have relatively small theoretical uncertainties and are close to each other, $R_{D^{\ast }}^{\ast (L)}\simeq R_{D_s^{\ast }}^{\ast (L)}\simeq R_{J/\psi }^{\ast (L)}\simeq [0.26,0.27]([0.27,0.29])$, which are a bit different from the predictions in some previous works. The future measurements are expected to make tests on these predictions.

22 pages, 3 figures