A calculation of the [1,1] padé approximant for pion-nucleon phase-shifts

Abstract

Low-energy pion-nucleon phase-shifts have been computed using, (i) once subtracted fixed hyperbola dispersion relations and (ii) elastic unitarity, in the [1, 1] Padé approximation. A t-channel s-wave pole (σ-meson) has been introduced, the residue of which is determined from Adler's self-consistency condition. It is found that although the inclusion of the Adler condition gives results which are considerably closer to experimental phase-shifts as compared to earlier calculations of this kind with fixed momentum transfer dispersion relations, the agreement with data is still far from satisfactory.