Explaining the $R_{K}$ and $R_{D^{(*)}}$ anomalies with vector leptoquarks

Recently the $B$ factories BaBar and Belle as well as the LHCb experiment have reported several anomalies in the semileptonic $B$ meson decays such as $R_{K}$ and $R_{D^{(*)}}$ etc. We investigate these deviations by considering the vector leptoquarks relevant for both $b \to s l^+ l^-$ and $b \to c l \bar \nu_l$ transitions. The leptoquark parameter space is constrained by using the experimentally measured branching ratios of $B_s \to l^+ l^-$, $\bar B \to X_s l^+ l^- (\nu \bar \nu)$ and $B_u^+ \to l^+ \nu_l$ processes. Using the constrained leptoquark couplings, we compute the branching ratios, forward-backward asymmetries, $\tau$ and $D^*$ polarization parameters in the $\bar B \to D^{(*)} l \bar \nu_l$ processes. We find that the vector leptoquarks can explain both $R_{D^{(*)}}$ and $R_K$ anomalies simultaneously. Furthermore, we study the rare leptonic $B_{u, c}^* \to l \bar\nu$ decay processes in this model.