Chiral lagrangian calculation of pion-nucleon scattering lengths
196810 pages
Published in:
- Phys.Rev. 176 (1968) 1812-1821
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Abstract: (APS)
We have considered two chiral-invariant Lagrangian models of pion-nucleon scattering: Weinberg's model, which contains a direct pion-nucleon scattering term; and an extension of Schwinger's model in which this direct term is replaced by a ρ-mediated term. These models have been extended by including a πNN*(1236) interaction. This has allowed us to calculate the N* contributions to the S-wave pion-nucleon scattering lengths and to compute the P-wave scattering lengths. The theoretically obtained values for these scattering lengths are found to be in reasonable agreement with experiment, with the possible exception of the a−P12 scattering length, for which only the direct model gives agreement with the present experimental data. For the aS+ scattering length, agreement was obtained only after the introduction of a contact term. The presence of such a term is made more plausible by the study of the asymptotic behavior of the isospin-even amplitudes. We have also compared our analysis with similar current-algebra calculations and obtain over-all agreement, especially with the ρ-exchange model, although we differ from these calculations in various details.- invariance: chiral
- pion-nucleon: interaction
- interaction: pion-nucleon
- scattering: length
- length: scattering
- model: weinberg
- model: schwinger
- current algebra
- model: rho exchange
- rho exchange: model
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