SMatrix Calculations of the PionNucleon PWave Scattering Length a_{13} by the ND Method
Abstract
The Smatrix calculations for the Pwave scattering process of pions on nucleons are carried out with the help of the ND method. According to the Balázs method the numerator function N is considered in the threepole effectiverange approximation. We choose one of the poles in the nucleon pole, where the residue is known. The remaining two residues (b_{i},i=1,2) are to be calculated. We use the following input values: the ρmeson and pionnucleon (3,3) isobar N^{*} discontinuities and the highenergy contributions in the crossed channels, and the nucleon pole in the direct channel. The matching procedure is the usual one: The righthand side of one of the determining equations for the effectiverange parameters b_{i} is analytically established by the projections of the invariant amplitudes with the aid of the fixeds dispersion relations in a regular point s_{R} in the unphysical region. Then the complete determining equations are obtained by comparing these projections and their derivatives, respectively, in the matching point s_{R}. Having thus determined the parameters b_{i} and the effectiverange ND amplitude of the state J=32, I=12, we compute the scattering length a_{13} on the basis of the noncorrelated physical parameters (g^{2},m,W_{R}^{33},μ). Its magnitude a_{13}=0.019 is in excellent agreement with the experimental value of Barnes et al.
 Publication:

Physical Review D
 Pub Date:
 May 1971
 DOI:
 10.1103/PhysRevD.3.2065
 Bibcode:
 1971PhRvD...3.2065S