Pion-Nucleon Scattering in a Large-N Sigma Model

Abstract

We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi mesons to the nucleon are echoed by couplings to the entire tower of I=J baryons (including the Delta) as dictated by large-N_c group theory. We sum the complete set of multi-loop meson-exchange πN --> πN and πN --> σN Feynman diagrams, to leading order in 1/N_c. The key idea, reviewed in detail, is that large-N_c allows the approximation of LOOP graphs by TREE graphs, so long as the loops contain at least one baryon leg; trees, in turn, can be summed by solving classical equations of motion. We exhibit the resulting partial-wave S-matrix and the rich nucleon and Delta resonance spectrum of this simple model, comparing not only to experiment but also to pion-nucleon scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-baryon S-matrix which hitherto has been uncovered only with skyrmion methods, can also be described by models with explicit baryon fields, thanks to the 1/N_c expansion.

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Cited by in corpus (5)

• Large-N_c Baryons
• Factorization and Non-Factorization of In-Medium Four-Quark Condensates
• Consistency of the Baryon-Multimeson Amplitudes for Large-N_c QCD
• A Multiple Commutator Formula for the Sum of Feynman Diagrams
• From Effective Lagrangians, to Chiral Bags, to Skyrmions with the Large-N_c Renormalization Group