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Quantum interferences in the $γN \to e^+e^- N$ reaction close to the vector meson production threshold

The exclusive photoproduction of $e^+e^-$ pairs from nucleons close to the vector meson production threshold ($1.4<\sqrt s <1.8$ GeV) results from two main processes: the emission of Bethe-Heitler pairs and the photoproduction of $ρ^0$- and $ω$-mesons decaying into $e^+e^-$ pairs. The Bethe-Heitler amplitudes are purely electromagnetic and reflect mostly the nucleon magnetic structure. The $γN\to e^+e^- N$ amplitudes arising from vector meson production and decay are derived from $γN\to ρ^0 N$ and $γN \to ωN$ amplitudes supplemented by the Vector Meson Dominance assumption. The vector meson photoproduction amplitudes are calculated using a relativistic and unitary coupled-channel approach to meson-nucleon scattering. They depend sensitively on the coupling of vector fields to baryon resonances. The $γN \to e^+e^- N$ differential cross sections display interference patterns. The interference of Bethe-Heitler pair production with vector meson $e^+e^-$ decay is quite small in the domain of validity of our model for all angles of the emitted $e^+e^-$ pair. The interference of $ρ^0$- and $ω$-mesons in the $e^+e^-$ channel can be large. It is constructive for the $γp \to e^+e^- p$ reaction and destructive for the $γn \to e^+e^- n$ reaction. We discuss the shape and magnitude of the $e^+e^-$ pair spectra produced in the $γp \to e^+e^- p$ and $γn \to e^+e^- n$ reactions as functions of the pair emission angle and of the total center of mass energy $\sqrt s$.