Penguin b→sℓ^′+ℓ^′− and B-meson anomalies in a gauged L_μ − L_τ

The Z^′-gauge boson in an U(1)_Lμ−Lτ gauge symmetry has two interesting features: one is its vector couplings to the charged leptons, and the other is the decoupling from the electron. Based on these properties, we investigate the feasibility to simultaneously resolve the R_K^(⁎) =BR(B→K^(⁎)μ⁺μ⁻)/BR(B→K^(⁎)e⁺e⁻) and R_D^(⁎) =BR(B¯→D^(⁎)τν¯_τ)/BR(B¯→D^(⁎)ℓν¯_ℓ) anomalies in an U(1)_Lμ−Lτ model, where the former is expected to arise from the Z^′-penguin-induced b→sμ⁺μ⁻ process and the latter from the tree-level b→cτν¯_τ decay. In order to achieve the intended purpose, we employ one vector-like doublet lepton and one singlet scalar leptoquark (LQ), in which the new particles all carry the U(1)_Lμ−Lτ charges; the b→sZ^′ effective interaction is generated from the vector-like lepton and LQ loop, and the b→cτν¯_τ decay is induced from the LQ. When the constraints from the b→sγ B⁺→K⁺νν¯ B_c ⁻→τν¯_τ, ΔF=2, and τ→μℓℓ¯ processes are included, it is found that R_D and R_D^⁎ can be enhanced to fit the experimental data, and the Wilson coefficient C₉ from the LQ-loop can reach C₉ ^LQ,μ∼−1, which can explain the R_K and R_K^⁎ anomalies. In addition, in this simple model, the Higgs lepton-flavor violating h→μτ decay can occur at the tree level, and its branching ratio can be as large as the current experimental upper limit.