Contribution of J<=32 Resonances to the uChannel Exchange Potential in πN Scattering
Abstract
We calculate the contribution of recently found, highly inelastic πN resonances in the S_{31}, S_{11}, P_{11}, and D_{13} partial waves to the exchange uchannel generalized potential for πN scattering. We use the results of the complex phaseshift analyses for incident pion energies <=1 BeV joined to smooth asymptotic functions to obtain the absorptive parts of the amplitudes. Dispersion integrals are performed over these amplitudes in the physical u region and then related to the direct s channel by crossing. Finally, partialwave projections in the direct s channel give the partialwave generalizedexchange uchannel potential input to the ND equations, which are solved for the phase shifts in the direct channel. The results are as follows: (i) Compared to the exchange of the nucleon and the N^{*}_{33} (1238 MeV), the S_{11}, S_{31}, and P_{11} uchannel continua have relatively small contributions to the schannel unphysical cut. (ii) As for the P_{33} partial wave, the D_{13} contribution to the uchannel exchange potential is divergent at large s. Thus a cutoff is needed to solve the ND equations. The effect of including D_{13} exchange is to make it harder to obtain agreement with experiment. (iii) The detailed shape of the P_{33} resonance reduces its contribution to the exchange potential by a factor of 0.75 as compared with the narrowwidth approximation.
 Publication:

Physical Review
 Pub Date:
 January 1967
 DOI:
 10.1103/PhysRev.153.1591
 Bibcode:
 1967PhRv..153.1591C