PION-NUCLEON SCATTERING IN THE P-33 CHANNEL IN THE LINEAR SIGMA MODEL

A consistent study of the NN interaction requires the investigation of the DELTA-resonance, as the DELTA can affect the properties of the effective light sigma-meson originating from correlated two-pion exchange and vice versa. We study how the DELTA appears as an effective degree of freedom in the linear sigma-model. Since the field-theoretic scattering amplitudes respect certain analytic properties, it is appropriate to use partial-wave dispersion relations for pi-N scattering, which produce non-linear integral equations that are solved by the N/D method. We choose an amplitude that guarantees the correct threshold behavior and that gives a P-33 resonance with a driving term from one-nucleon exchange. Then we investigate the effect of adding the one-sigma-exchange force. With either a very heavy or a light sigma-meson, we can find a P-33 resonance. For intermediate sigma-masses, we find a pi-N bound state. We confirm that the calculated resonance mass depends sensitively on the short-range pi-N attraction. Nevertheless, the existence of a P-33 resonance is compatible with the existence of an effective light sigma-meson in this model.