Cross-section measurement of two-photon annihilation in-flight of positrons at $\sqrt{s}=20$ MeV with the PADME detector

The inclusive cross-section of annihilation in flight $e^+e^-\rightarrow\gamma\gamma$ of 430 MeV positrons with atomic electrons of a thin diamond target has been measured with the PADME detector at the Laboratori Nazionali di Frascati. The two photons produced in the process were detected by an electromagnetic calorimeter made of BGO crystals. This measurement is the first one based on the direct detection of the photon pair and one of the most precise for positron energies below 1 GeV. This measurement represents a necessary step to search for dark sector particles and mediators weakly coupled to photons and/or electrons with masses ranging from 1 MeV to 20 MeV with PADME. The measurement agrees with the Next to Leading Order QED prediction within the overall 6% uncertainty.