Crossing symmetry and phenomenological widths in effective Lagrangian   models of the pion photoproduction process
  We investigate the importance of crossing symmetry in effective field models and the effects of phenomenological nucleon resonance widths on the paradigmatic case of pion photoproduction. We use reaction models containing four star resonances up to 1.8 Gev ($\Delta$(1232), N(1440), N(1520), N(1535), $\Delta$(1620), N(1650), $\Delta$(1700), and N(1720)) with different prescriptions for crossed terms and widths, to fit the latest world database on pion photoproduction. We compare $\chi^2$ results from selected multipoles and fits. The $\chi^2$ is highly dependent on the fulfillment of crossing symmetry and the inclusion of $u$ channels. 
C. Fernandez-Ramirez, E. Moya de Guerra, J.M. Udias