Determination of pion-nucleon S-wave scattering lengths by the N/D method

Abstract

The pion-nucleon S-wave scattering lengths are calculated using the method originally developed by Balazs, wherein an effective-range two-pole approximation is made for the numerator function. The residues of the effective-range poles are determined by matching the amplitude and its derivative with those calculated with a fixed energy dispersion relation. In calculating the latter the contribution of only the N^∗ and ρ, together with those of appropriate nucleon-pole terms, are retained. The calculated scattering length in the T=3/2 state is in excellent agreement with experimental result, while for the T=1/2 state, the calculated value, though of the right sign, is about twice the experimental scattering length.