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In recent years, the experimental results about the ratio of the branching ratios    $$R_{D^{(*)}}$$  R D ( ∗ ) and    $$R_{K^{(*)}}$$  R K ( ∗ ) , which are in the semileptonic    $$b\rightarrow c l \bar{\nu }_{l}$$  b → c l ν ¯ l and    $$b\rightarrow s l^+l^-$$  b → s l + l - decays, have been observed to deviate from the Standard Model prediction by    $$1.4\sigma $$  1.4 σ ,    $$2.5\sigma $$  2.5 σ ,    $$2.4\sigma $$  2.4 σ and    $$2.2\sigma $$  2.2 σ respectively. Motivated by these anomalies and by the abundant    $$B^*$$  B ∗ data samples, we investigate possible New Physics effects of the vector leptoquark in the semileptonic decay    $$\bar{B}^*_{u,d,s,c} \rightarrow V \tau ^-\bar{\nu }_{\tau }$$  B ¯ u , d , s , c ∗ → V τ - ν ¯ τ (   $$V=D^*_{u,d,s},J/\psi $$  V = D u , d , s ∗ , J / ψ ). which is induced by    $$b\rightarrow c \tau ^-\bar{\nu }_{\tau }$$  b → c τ - ν ¯ τ at the quark level. Using the best fit solutions for the new operator Wilson coefficients and the relevant form factors which are obtained in the light-front quark model, we find that (i) the contributions of the vector leptoquark to    $$d{\varGamma }^{(L)}/dq^2(\bar{B}^*_{u,d,s,c} \rightarrow V \tau ^-\bar{\nu }_{\tau })$$  d Γ ( L ) / d q 2 ( B ¯ u , d , s , c ∗ → V τ - ν ¯ τ ) and    $$R^{*(L)}_{V}(q^2)$$  R V ∗ ( L ) ( q 2 ) to be significant; (ii) the two best fit solutions in the vector leptoquark are indistinguishable from each other and give similar amounts of enhancements to these two observables; (iii) both two cases of the vector leptoquark give nearly same results as those of the Standard Model for    $$A_{FB}^{\tau }(q^2)$$  A FB τ ( q 2 ) ,    $$P_{\tau }(q^2)$$  P τ ( q 2 ) and    $$F_{L}^{*V}(q^2)$$  F L ∗ V ( q 2 ) . We hope that the numerical results in this work will be tested in the future high energy experiments.

Investigation on the New Physics effects of the vector leptoquark on semileptonic $$\bar{B}^*\rightarrow V \tau ^-\bar{\nu _{\tau }}$$ decays