Abstract
Extensive dynamical calculations are conducted in the study of channel low energy 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 plane, are analysed in detail. Furthermore, it is found that the dispersion representation for the phase shift, , must be modified in the case of 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 channel nucleon exchanges. With limited reliance on the details of the dynamical inputs, the subthreshold resonance survives.
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