GeV Dark Matter in $U(1)_{L_{\mu}-L_{\tau}}$: Role of $(g-2)_{\mu}$ Anomaly

In this work, we investigate the connection of the detection possibility of a light GeV scale fermionic dark matter (DM) with recent anomalous $(g-2)_{\mu}$ measurement with $\sim 4 \sigma$ deviation from the SM. The $U(1)_{L_{\mu}-L_{\tau}}$ scenario readily explains $(g-2)_{\mu}$ anomaly, allowing only a portion of hitherto allowed parameter space, and restricts the $Z^{\prime}$ mass in the range of $20-200$~MeV. This constraint impacts the enhancement of the neutrino floor, the neutrino background in the DM direct detection experiments. Neutrino floor is enhanced for a lighter $Z^{\prime}$ of the $(g-2)_{\mu}$ allowed spectrum, whereas for a heavier $Z^{\prime}$, the modification is not significant. %The GeV scale DM is severely constrained by the $(g-2)_{\mu}$ result as it restricts For the GeV scale DM, $(g-2)_{\mu}$ restriction results in insignificance of s-channel resonant annihilation in DM annihilation, therefore resulting in t-channel dependence to produce the observed DM relic. A t-channel annihilation aided by large couplings can bring the relic density in the observed range, direct detection cross section of the GeV DM shoots up. Consequently, super-GeV (with mass $1-10$~GeV) DM gets almost gets ruled out except for a small parameter region for heavier $Z^{\prime}$, where as sub-GeV (with mass $0.1-1$~GeV) DM detection possibility remains bright with more detection possibility for heavier $Z^{\prime}$. Direct detection constraints when aided by $(g-2)_{\mu}$, constrains the GeV DM compared to DM indirect detection measurements.