Quantum interference in the e^+e^- decays of rho⁰ and omega-mesons produced in pi^- p reactions

The study of the pi^- p -> rho^0 n and pi^- p -> omega n amplitudes close and below the vector meson production threshold (1.2< sqrt(s) <1.8 GeV) reveals a rich dynamics arising from the presence of specific baryon resonances in this energy range. The interference pattern of the e^+e^- decays of the rho^0 and omega mesons produced in pi^- p reactions reflects directly this dynamics. We discuss this interference pattern in the pi^- p -> e^+e^- n reaction as function of the total center of mass energy sqrt(s). We emphasize the importance of an experimental study of this reaction, which could be made with the HADES detector and the available pion beam at GSI.