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Study of $b\to c$ induced $\bar{B}^* \to V \ell \barν_\ell$ decays

In this paper, we investigate the tree-dominated $\bar{B}^*_{u,d,s,c} \to V \ell^- \barν_\ell$ ($V=D^*_{u,d}\,,D^*_s\,,J/ψ$ and $\ell=e\,,μ\,,τ$) 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 $\bar{B}^* \to P \ell^- \barν_\ell$ and $\bar{B} \to V \ell^- \barν_\ell$ 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 $R_V^{\ast(L)}\equiv \frac{\mathcal{B}(\bar{B}^*\to Vτ^- \barν_τ)}{\mathcal{B}(\bar{B}^*\to V \ell^{\prime-} \barν_{\ell^{\prime}})}$ ($\ell'=e\,,μ$). Numerically, the branching fractions of $\bar{B}^* \to V \ell^{\prime-} \barν_{\ell^{\prime}}$ decays are at the level of ${\cal O}(10^{-7})$, and are hopeful to be observed by LHC and Belle-II experiments. The ratios $R_{D^*\,,D^*_s\,,J/ψ}^{\ast(L)}$ have relatively small theoretical uncertainties and are close to each other, $R^{*(L)}_{D^*}\simeq R^{*(L)}_{D^*_s}\simeq R^{*(L)}_{J/ψ} \simeq [0.26,0.27]~([0.27,0.29])$, which are a bit different from the predictions in some previous works. The future measurements are expected to make tests on these predictions.