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 dark matter is $\chi \chi \to \tau \overline{\tau }$ with the dark matter mass $m_{\chi }=9.43{(}_{-0.52}^{+.063}\text{stat})(\pm 1.2\text{sys})\mathrm{GeV}$ 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 $m_a={12}_{-3}^{+7}\mathrm{GeV}$.

Figure 1

The one and two-loop contributions of the pseudoscalar $a$ to the g-2 of muon (black) and electron (dashed red) given in units of the corresponding standard deviation. The contribution to the muon g-2 is negative for $m_a\lesssim 6.7\mathrm{GeV}$ (dotted black). The pink regions quantify the deviation from the SM value of g-2. The blue region denotes the measured value of the muon g-2 ($1\sigma$). The black dots on the muon curves indicate the best fits of the experimental value of g-2, the $3.4\sigma$ excess. The factor $A$ is defined in Eq. (2).

Figure 2

The vertical pink stripe shows the best fit region ($1\sigma$) of the $\gamma$-ray excess via the $\tau$-channel at the Galactic Center. The horizontal pink region denotes the best fit ($1\sigma$) for the muon g-2. The values of the $A$ parameter required by the fit for different masses $m_a$ are shown at the left axis. For the CDM model, the unitary limit, $A_{\max }\simeq 1000$, is very close to the top part of the frame. The gray regions and the dashed black lines show the constraints (both $2\sigma$) from CMB [41, 42, 43] and dwarf galaxies [44, 45] respectively, with the arrows highlighting how these bounds vary depending on whether the most conservative or the most optimistic case is assumed. The allowed region of our model is framed by a purple dot-dashed rectangle.