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

We study the gauged $$U(1)_{L_\mu -L_\tau }$$U(1)Lμ-Lτ scotogenic model with emphasis on latest measurement of LHCb $$R_{K^{(*)}}$$RK(∗) anomaly and AMS-02 positron excess. In this model, neutrino masses are induced at one-loop level with $$Z_2$$Z2-odd particles, i.e., right-handed neutrinos $$N_\ell (\ell =e,\mu ,\tau )$$Nℓ(ℓ=e,μ,τ) and inert scalar doublet $$\eta $$η inside the loop. Meanwhile, the gauged $$U(1)_{L_\mu -L_\tau }$$U(1)Lμ-Lτ symmetry is broken spontaneously by the scalar singlet S, resulting to the massive gauge boson $$Z'$$Z′. Provided certain couplings to quarks induced by heavy vector-like quarks, the gauge boson $$Z'$$Z′ would contribute to the transition $$b\rightarrow s \mu ^+\mu ^-$$b→sμ+μ-, hence explain the $$R_{K^{(*)}}$$RK(∗) anomaly. As for the Majorana fermion DM N, the gauge boson $$Z'$$Z′ and the singlet Higgs $$H_0$$H0 will generate various annihilation channels, among which the $$NN\rightarrow Z'Z'$$NN→Z′Z′ and $$NN\rightarrow Z'H_0(\rightarrow Z'Z')$$NN→Z′H0(→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 $$R_{K^{(*)}}$$RK(∗) anomaly and AMS-02 positron excess can be explained simultaneously.