Off-energy-shell continuation of the two-body t-matrix in the presence of resonances

We discuss a situation like pion-nucleon interaction but in the spirit of BGMS-Haftel and hence assuming that all the conditions relevant to the nucleon-nucleon system still hold with the difference that the eigenchannel has a resonances or resonance (in case of π-N, this is expected). We have, undoubtedly, oversimplified the whole problem but having a resonance itself presents some novel (we believe) points which need to be discussed properly and once this is done, the rest follows in a generally straightforward way. In the process, however, we have posed additional questions rather than answer the existing ones. (orig./WL)