Dark matter contribution to $b\to s{\mu }^{+}{\mu }^{-}$ anomaly in local $U(1{)}_{L_{\mu }-L_{\tau }}$ model

We propose a local $U(1{)}_{L_{\mu }-L_{\tau }}$ model to explain $b \to s \mu^+ \mu^-$ anomaly observed at the LHCb and Belle experiments. The model also has a natural dark matter candidate $N$. We introduce $SU(2{)}_L$-doublet colored scalar $\tilde{q}$ to mediate $b\to s$ transition at one-loop level. The $U(1{)}_{L_{\mu }-L_{\tau }}$ gauge symmetry is broken spontaneously by the scalar $S$. All the new particles are charged under $U(1{)}_{L_{\mu }-L_{\tau }}$. We can obtain $C_9^{\mu ,\mathrm{N}\mathrm{P}}\sim -1$ to solve the $b\to s{\mu }^{+}{\mu }^{-}$ anomaly and can explain the correct dark matter relic density of the universe, ${\mathrm{\Omega }}_{\mathrm{D}\mathrm{M}}{h}^2\approx 0.12$, simultaneously, while evading constraints from electroweak precision tests, neutrino trident experiments and other quark flavor-changing loop processes such as $b\to s\gamma$ and $B_s-{\bar{B}}_s$ mixing. Our model can be tested by searching for $Z^{\mathrm{\prime }}$ and new colored scalar at the LHC and $B \to K^* \nu \overline{\nu}$ process at Belle-II.