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 $ellell$ are various combinations of $mu$ and $tau$, and also lepton flavor violation in the $tau$ decays.