Scalar dark matter behind $b \to s \mu \mu$ anomaly

We construct a scalar dark matter model with $U(1)_{L_\mu-L_\tau}$ symmetry in which the dark matter interacts with the quark flavours, allowing lepton non-universal $b \to s \ell \bar{\ell}$ decays. The model can solve $b \to s \mu \mu$ ($R_{K^{(*)}}$) anomaly and accommodate the relic abundance of dark matter simultaneously while satisfying the constraints from other low energy flavour experiments and direct detection experiments of dark matter. The new fields include vector-like heavy quarks $U$ and $D$, $U(1)_{L_\mu-L_\tau}$ breaking scalar $S$, as well as the dark matter candidate $X_I$ and its heavy partner $X_R$. To explain both $b \to s \mu \mu$ anomaly and the dark matter, {\it i)} large mass difference between $X_R$ and $X_I$ is required, {\it ii)} electroweak scale dark matter and heavy quarks are favoured, {\it iii)} not only electroweak scale but ${\cal O}(10)$ TeV dark gauge boson $Z'$ and $X_R$ are allowed.