Summary
An effective Lagrangian model of pion-nucleon scattering up to a laboratory pion kinetic energy of 250 MeV is presented, which includesN(939),N(1440) and Δ(1232) exchange andt-channel exchanges. Unitarity is enforced on our amplitudes using three different methods, and for the Δ(1232) resonance we use both the standard propagator and a proposed alternative one. We also consider the effect of imposing constraints from dispersion theory on our model. Although it is possible to obtain a reasonably good description of pion-nucleon scattering in this manner, we find that the ambiguity in the choice of unitarization technique makes it impossible to accurately determine the important parameters which are needed for the modelling of other processes.
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Bofinger, D., Woolcock, W.S. A critical study of effective Lagrangian models for low-energy pion-nucleon scattering. Nuov Cim A 104, 1489–1502 (1991). https://doi.org/10.1007/BF02817432
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DOI: https://doi.org/10.1007/BF02817432