Observable effects of poles and shadow poles in coupled-channel systems

Using separable potentials in a coupled-channel Lippmann-Schwinger equation, we investigate the motion of poles on the different Riemann sheets and their observable effects as the coupling strength is varied. Only in the weak-coupling limit can one determine in which uncoupled channel the pole originated by the sheet on which it lies. Cusp structure versus resonance peak as one crosses a threshold is found to depend on the distance of the pole from the physical sheet. Resonance poles in each uncoupled channel can produce double-loop Argand plots similar to those seen in πN $P_{11}$ amplitude analysis.