Dark photon production through positron annihilation in beam-dump experiments

High energy positron annihilation is a viable mechanism to produce dark photons ($A^\prime$). This reaction plays a significant role in beam-dump experiments using experiments using multi-GeV electron-beams on thick targets by enhancing the sensitivity to $A^\prime$ production. The positrons produced by the electromagnetic shower can produce an $A^\prime$ via non-resonant ($e^+ + e^- \to \gamma + A^\prime$) and resonant ($e^+ + e^- \to A^\prime$) annihilation on atomic electrons. For visible decays, the contribution of resonant annihilation results in a larger sensitivity with respect to limits derived by the commonly used $A^\prime$-strahlung in certain kinematic regions. When included in the evaluation of the E137 beam-dump experiment reach, positron annihilation pushes the current limit on $\varepsilon$ downwards by a factor of two in the range 33 MeV/c$^2<m_{A^\prime}<120$ MeV/c$^2$.