Beam-helicity asymmetry in associated electroproduction of real photons $ep to egamma pi N$ in the $Delta$-resonance region

The beam-helicity asymmetry in associated electroproduction of real photons, $epto egamma pi N$, in the $Delta$(1232)-resonance region is measured using the longitudinally polarized HERA positron beam and an unpolarized hydrogen target. Azimuthal Fourier amplitudes of this asymmetry are extracted separately for two channels, $epto egamma pi^0 p$ and $epto egamma pi^+ n$, from a data set collected with a recoil detector. All asymmetry amplitudes are found to be consistent with zero.