Looking for Lights from the Darkness: Signals from MeV-scale Solar Axion-like Particles

The axion-like particles $a$ can be produced in the Sun via the process of $p + D \to {}^3{\rm He} +a$, with mass up to 5.5 MeV. The photons in the subsequent decay $a \to \gamma\gamma$ can deviate significantly from the Sun, or even from roughly the opposite direction of the Sun. The nontrivial angular and spectral distributions of such photons enable us new methods to detect the {\it lights from the darkness}. In this letter, we consider both the space detection and terrestrial experiments at the South Pole. As a result of the two-body decay and the geometric effects, there exists a critical height for the terrestrial experiments, below which there is no photon for some regions of the parameter space. With the sensitivities of $10^{-16}$ ($10^{-17}$) erg cm$^{-2}$ s$^{-1}$ for the MeV-scale photons in future space and terrestrial experiments, the coupling $g_{a\gamma}$ of $a$ to photons can be probed up to $3\times10^{-12}$ ($1\times10^{-12}$) GeV$^{-1}$, well surpassing the current supernova limits.