A comprehensive study of vector leptoquark 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 $(g-2)$ 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.