Coy Dark Matter and the anomalous magnetic moment

Coy Dark Matter removes the tension between the traditional WIMP paradigm of Dark Matter and the latest exclusion bounds from direct detection experiments. In this paper we present a leptophilic Coy Dark Matter model that, on top of explaining the spatially extended 1-5 GeV $\gamma$-ray excess detected at the Galactic Center, reconciles the measured anomalous magnetic moment of muon with the corresponding Standard Model prediction. The annihilation channel of DM is $\chi \chi \to \tau \bar{\tau }$ with the DM mass $m_\chi = 9.43,(^{+.063}_{-0.52},{\rm stat.}),(\pm 1.2 ,{\rm sys.})$ GeV given by best-fit of the $\gamma$-ray excess. Fitting the measured anomalous magnetic moment of the muon requires instead a pseudoscalar mediator with a minimal mass $m_a=12_{-3}^{+7}$ GeV.