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 $(g-2)_μ$ 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 ${(g-2)_μ},\ R_{K^{(*)}},\ R_{D^{(*)}}$, $B \to (K) \ell \ell'$ where $\ell\ell'$ are various combinations of $μ$ and $τ$, and also lepton flavor violation in the $τ$ 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.

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