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In this paper, we investigate the tree-dominated $\bar{B}^*_{u,d,s,c} \to V\ell^- \bar{\nu}_\ell$ ($V=D^*_{u,d}\,,D^*_s\,,J/\psi$ and$\ell=e\,,\mu\,,\tau$) decays in the Standard Model with the relevant formfactors obtained in the light-front quark model. These decays involve much morehelicity states relative to the corresponding $\bar{B}^* \to P \ell^-\bar{\nu}_\ell$ and $\bar{B} \to V \ell^- \bar{\nu}_\ell$ decays, and moreover,the contribution of longitudinal polarization mode ($V$ meson) is relativelysmall, $\sim 30\%$, compared with the corresponding $B$ meson decays. We havealso computed the branching fraction, lepton spin asymmetry, forward-backwardasymmetry and ratio $R_V^{\ast(L)}\equiv \frac{\mathcal{B}(\bar{B}^*\to V\tau^-\bar{\nu}_\tau)}{\mathcal{B}(\bar{B}^*\to V \ell^{\prime-}\bar{\nu}_{\ell^{\prime}})}$ ($\ell'=e\,,\mu$). Numerically, the branchingfractions of $\bar{B}^* \to V \ell^{\prime-} \bar{\nu}_{\ell^{\prime}}$ decaysare at the level of ${\cal O}(10^{-7})$, and are hopeful to be observed by LHCand Belle-II experiments. The ratios $R_{D^*\,,D^*_s\,,J/\psi}^{\ast(L)}$ haverelatively small theoretical uncertainties and are close to each other,$R^{*(L)}_{D^*}\simeq R^{*(L)}_{D^*_s}\simeq R^{*(L)}_{J/\psi} \simeq[0.26,0.27]~([0.27,0.29])$, which are a bit different from the predictions insome previous works. The future measurements are expected to make tests onthese predictions.

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