Remarks on the complex branch points in pi-N scattering amplitude and the multiple poles structure of resonances

A simple heuristic argument to understand the existence of branch points in the unphysical sheet for pi-N scattering amplitude is presented. It is based on a hypothesis that the singularity structure of the pi-N scattering amplitude is a smooth varying function of the pion mass. We find that, in general, multiple poles structure of a resonance is a direct mathematical consequence when additional Riemann surface is included in the study and the two-pole structure found to correspond to the Roper resonance is a good example.