A comprehensive study of vector leptoquark with $U(1)_{B_3-L_2}$ on the $B$-meson and Muon g-2 anomalies

Recently reported anomalies in various $B$ meson decays and also in the anomalous magnetic moment of muon $(g-2)_\mu$ motivate us to consider a particular extension of the standard model incorporating new interactions in lepton and quark sectors simultaneously. Our minimal choice would be leptoquark. In particular, we take vector leptoquark ($U_1$) and comprehensively study all related observables including ${(g-2)_{\mu}},\ R_{K^{(*)}},\ R_{D^{(*)}}$, $B \to (K) \ell \ell' $ where $\ell\ell'$ are various combinations of $\mu$ and $\tau$, and also lepton flavor violation in the $\tau$ decays. We find that a hybrid scenario with additional $U(1)_{B_3-L_2}$ gauge boson provides a common explanation of all these anomalies.