Extraction of Resonances from Meson-Nucleon Reactions

We present a pedagogical study of the commonly employed Speed-Plot (SP) and Time-delay (TD) methods for extracting the resonance parameters from the data of two particle coupled-channels reactions. Within several exactly solvable models, it is found that these two methods find poles on different Riemann sheets and are not always valid. We then develop an analytical continuation method for extracting the nucleon resonances within a dynamical coupled-channel formulation of the pi-N and gamma-N reactions. The main focus is on resolving the complications due to the coupling with the unstable pi-Delta; rho-N; sigma-N channels which decay into pi-pi-N states. By using the results from the considered exactly solvable models, explicit numerical procedures are presented and verified.