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We review the large-[ital N][sub [ital c]] approach to meson-baryon scattering, including recent interesting developments. We then study [pi][ital N] 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 [ital I]=[ital J] baryond (including the [Delta]) as dictated by large-[ital N][sub [ital c]] group theory. We sum the complete set of multiloop meson-exchange [pi][ital N][r arrow][pi][ital N] and [pi][ital N][r arrow][sigma][ital n] Feynman diagrams, to leading order in 1/[ital N][sub [ital c]]. The key idea, reviewed in detail, is that large [ital N][sub [ital c]] allows the approximation of [ital loop] graphs by [ital 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 [ital S] matrix and the rich nucleon and [Delta] resonance spectrum of this simple model, comparing not only to experiment but also to [pi][ital N] scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-baryon [ital S] matrix which hitherto has been uncovered only with Skyrmionmore » methods can also be described by models with explicit baryon fields, thanks to the 1/[ital N][sub [ital c]] expansion.« less |
