An N/D study of the S-11 channel pi N scattering amplitude

Extensive dynamical N/D calculations are conducted in the study of S-11 channel low energy pi N scatterings, based on various phenomenological model inputs of left cuts at the tree level. The subtleties of the singular behavior of the partial wave amplitude, at the origin of the complex s plane, are analysed in detail. Furthermore, it is found that the dispersion representation for the phase shift, delta, must be modified in the case of pi N scatterings. An additional contribution from the dispersion integral exists, which approximately cancels the contribution of the two virtual poles located near the end points of the segment cut, induced by u channel nucleon exchanges. With limited reliance on the details of the dynamical inputs, the subthreshold resonance N* (890) survives.