(g − 2)μ versus flavor changing neutral current induced by the light (B − L)μτ boson

We propose the local (B − L)μτ model, which minimally retains the local B − L extension for the sake of neutrino phenomenologies, and at the same time presents an invisible gauge boson Z′ with mass ∼ 𝒪 (10) MeV to account for the discrepancy of the muon anomalous magnetic moment. However such a scenario is challenged by flavor physics. To accommodate the correct pattern of Cabibbo-Kobayashi-Maskawa matrix, we have to introduce either a SU(2)L doublet flavon or vector-like quarks plus a singlet flavon. In either case Z′ induces flavor changing neutral current (FCNC) in the quark sector at tree-level. We find that the former scheme cannot naturally suppress the FCNC from the down-type quark sector and thus requires a large fine-tuning to avoid the stringent K → πν$$ \overline{v} $$ bound. Whereas the latter scheme, in which FCNC merely arises in the up-type quark sector, is still free of strong constraint. In particular, it opens a new window to test our scenario by searching for flavor-changing top quark decay mode t → u/c+(invisible), and the typical branching ratio ∼ 𝒪 (10−4).