The $\pi N \to e^+e^- N$ reaction close to the vector meson production threshold
The $\pi^-p \to e^+e^- n$ and $\pi^+n \to e^+e^- p$ reaction cross sections are calculated below and in the vicinity of the vector meson ($\rho^0$, $\omega$) production threshold. These processes are largely responsible for the emission of $e^+e^-$ pairs in pion-nucleus reactions and contribute to the dilepton spectra observed in relativistic heavy ion collisions. They are dominated by the decay of low-lying baryon resonances into vector meson-nucleon channels. The vector mesons materialize subsequently into $e^+e^-$ pairs. Using $\pi N\to \rho^0 N$ and $\pi N \to \omega N$ amplitudes calculated in the center of mass energy interval $1.4<\sqrt s <1.8$ GeV, we compute the $\pi^-p \to e^+e^- n$ and $\pi^+n \to e^+e^- p$ reaction cross sections in these kinematics. Below the vector meson production threshold, the $\rho^0 - \omega$ interference in the $e^+e^-$ channel appears largely destructive for the $\pi^-p \to e^+e^- n$ cross section and constructive for the $\pi^+n \to e^+e^- p$ cross section. The pion beam and the HADES detector at GSI offer a unique possibility to measure these effects. Such data would provide strong constraints on the coupling of vector meson-nucleon channels to low-lying baryon resonances.