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Quantum interference of rho0- and omega-mesons in the pi N -> e+e- N reaction

The study of the $πN\to ρ^0 N$ and $πN \to ωN$ amplitudes below and close to the vector meson production threshold ($1.4<\sqrt s <1.8$ GeV)reveals a rich structure arising from the presence of baryon resonances in this energy range. These resonances are reflected in the interference pattern of the $e^+e^-$ decays of the $ρ^0$- and $ω$-mesons produced in $π^- p$ and $π^+ n$ reactions. We discuss the shape and magnitude of the $ρ^0$-$ω$ interference in the $π^-p \to e^+e^- n$ and $π^+n \to e^+e^- p$ reaction cross sections as functions of the total center of mass energy $\sqrt s$. We find contrasted results: the interference is largely destructive for the $π^-p \to e^+e^- n$ cross section but constructive for the $π^+n \to e^+e^- p$ cross section. An experimental study of these reactions would provide significant constraints on the coupling of vector meson-nucleon channels to low-lying baryon resonances.