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

The study of the $\pi N\to \rho^0 N$ and $\pi N \to \omega N$ 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 $\rho^0$- and $\omega$-mesons produced in $\pi^- p$ and $\pi^+ n$ reactions. We discuss the shape and magnitude of the $\rho^0$-$\omega$ interference in the $\pi^-p \to e^+e^- n$ and $\pi^+n \to e^+e^- p$ 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 $\pi^-p \to e^+e^- n$ cross section but constructive for the $\pi^+n \to e^+e^- p$ 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.