Reconciling dark matter, $R_{K^{(*)}}$ anomalies and $(g-2)_{\mu}$ in an ${L_{\mu}-L_{\tau}}$ scenario

We propose an anomaly free unified scenario by invocation of an extra local ${\rm U(1)}_{L_{\mu}-L_{\tau}}$ gauge symmetry. This scenario simultaneously resolves the $R_{K^{(*)}}$ anomalies, the dark matter puzzle and the long-standing discrepancy in muon's anomalous magnetic moment. A complex scalar ($\eta$) having nonzero ${L_{\mu}-L_{\tau}}$ charge has been introduced to break this new U(1) symmetry spontaneously. Moreover, for the purpose of studying dark matter phenomenology and $R_{K^{(*)}}$ anomalies in a correlated manner, we introduce an inert ${\rm SU(2)}_L$ scalar doublet ($\Phi$), a $\mathbb{Z}_2$-odd real singlet scalar ($S$) and a $\mathbb{Z}_2$-odd coloured fermion ($\chi$) which transforms vectorially under the ${\rm U(1)}_{L_{\mu}-L_{\tau}}$ symmetry. This extra gauge symmetry provides a new gauge boson $Z_{\mu\tau}$ which not only gives additional contribution to both $b\to s \ell\ell$ transition and $(g-2)_{\mu}$ but also provides a crucial annihilation channel for dark matter candidate $\rho_1$ of the present scenario. This $\rho_1$ is an admixture of CP-even neutral component of $\Phi$ and $S$. Our analysis shows that the low mass dark matter regime ($M_{\rho_1}\lesssim 60$ GeV) is still allowed by the experiments like XENON1T, LHC (via Higgs invisible branching) and Fermi-LAT, making the dark matter phenomenology drastically different from the standard Inert Doublet and the Scalar Singlet models. Furthermore, the present model is also fairly consistent with the observed branching ratio of $B\to X_s\gamma$ in $3\sigma$ range and is quite capable of explaining neutrino masses and mixings via Type-I seesaw mechanism if we add three right handed neutrinos in the particle spectrum. Finally, we use the latest ATLAS data of non-observation of a resonant $\ell^+\ell^-$ signal at the 13 TeV LHC to constrain the mass-coupling plane of $Z_{\mu\tau}$.