Explanation of the 511 keV line: Cascade annihilating dark matter with the $^8$Be anomaly

Abstract

A possible dark matter (DM) explanation about the long-standing issue of the Galactic 511 keV line is explored in this paper. For DM cascade annihilations of concern, a DM pair $\pi_d^{+} \pi_d^{-}$ annihilates into unstable $\pi_d^{0} \pi_d^{0}$, and $\pi_d^{0}$ decays into $e^+ e^-$ with new interactions suggested by the $^8$Be anomaly. Considering the constraints from the effective neutrino number $N_{\mathrm{eff}}$ and the 511 keV gamma-ray emission, a range of DM is obtained, $11.6 \lesssim m_{\pi_d^{\pm}} \lesssim 15$ MeV. The typical DM annihilation cross section today is about 3.3 $\times$ $10^{-29}$ cm$^3$ s$^{-1}$, which can give an explanation about the 511 keV line. The MeV scale DM may be searched by the DM-electron scattering, and the upper limit set by the CMB s-wave annihilation is derived in DM direct detections.