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We study the gauged \(U(1)_{L_\mu -L_\tau }\) scotogenic model with emphasis on latest measurement of LHCb \(R_{K^{(*)}}\) anomaly and AMS-02 positron excess. In this model, neutrino masses are induced at one-loop level with \(Z_2\)-odd particles, i.e., right-handed neutrinos \(N_\ell (\ell =e,\mu ,\tau )\) and inert scalar doublet \(\eta \) inside the loop. Meanwhile, the gauged \(U(1)_{L_\mu -L_\tau }\) symmetry is broken spontaneously by the scalar singlet S, resulting to the massive gauge boson \(Z'\). Provided certain couplings to quarks induced by heavy vector-like quarks, the gauge boson \(Z'\) would contribute to the transition \(b\rightarrow s \mu ^+\mu ^-\), hence explain the \(R_{K^{(*)}}\) anomaly. As for the Majorana fermion DM N, the gauge boson \(Z'\) and the singlet Higgs \(H_0\) will generate various annihilation channels, among which the \(NN\rightarrow Z'Z'\) and \(NN\rightarrow Z'H_0(\rightarrow Z'Z')\) channel could be used to interpret the AMS-02 positron excess. We give a comprehensive analysis on model parameter space with consider various current constraints. The combined analysis shows that the \(R_{K^{(*)}}\) anomaly and AMS-02 positron excess can be explained simultaneously.

Gauged $$U(1)_{L_\mu -L_\tau }$$ scotogenic model in light of $$R_{K^{(*)}}$$ anomaly and AMS-02 positron excess