# Pion-nucleon scattering in the P33channel in the linear sigma model

- Authors
- Journal
- Nuclear Physics A 0375-9474
- Publisher
- Elsevier
- Publication Date
- Volume
- 524
- Issue
- 4
- Identifiers
- DOI: 10.1016/0375-9474(91)90264-7

## Abstract

Abstract A consistent study of the NN interaction requires the investigation of the Δ resonance, as the Δ can affect the properties of the effective light σ meson originating from correlated two-pion exchange and vice versa. We study how the Δ appears as an effective degree of freedom in the linear σ model. Since the field-theoretic scattering amplitudes respect certain analytic properties, it is appropriate to use partial-wave dispersion relations for πN 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 σ meson, we can find a P 33 resonance. For intermediate σ masses, we find a πN bound state. We confirm that the calculated resonance mass depends sensitively on the short-range πN attraction. Nevertheless, the existence of a P 33 resonance is compatible with the existence of an effective light σ meson in this model.

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