New physics effects of the vector leptoquark on $${\bar{B}}^{*}\rightarrow P\tau {\bar{\nu }}_{\tau }$$ B ¯ ∗ → P τ ν ¯ τ decays

Motivated by the $$R_{\mathrm{D}^{(*)}}$$ anomalies which may imply hints of New Physics in the flavor sector and which can be explained by adding a single vector leptoquark $$ U_{3}(3,3,2/3)$$ to the Standard Model as well as by the abundant $$B^{*}$$ data samples at high-luminosity collider experiments in the future, we further probe the New Physics effects of the vector leptoquark in the semileptonic $${\bar{B}}^{*}_\mathrm{d,s}\rightarrow P \tau {\bar{\nu }}_{\tau }(P=D,D_\mathrm{s},\pi ,K)$$ decays which are induced by the transitions $$b\rightarrow (u,c)\tau {\bar{\nu }}_{\tau }$$ at the quark level. We investigate the New Physics leptoquark effects in the observables including the differential branching fractions and their ratios, lepton forward–backward asymmetry and lepton polarization asymmetry. We find the contributions of the vector leptoquark to the differential branching fractions and their ratios to be significant, and they show large deviations from the corresponding Standard Model predictions, while the lepton forward–backward asymmetry and the lepton polarization asymmetry in the leptoquark scenario show the same behaviors as that in the Standard Model.