Chiral unitary meson-baryon dynamics in the presence of resonances: Elastic pion-nucleon scattering

Abstract

We develop a novel approach to chiral meson-baryon dynamics incorporating unitarity constraints and explicit resonance fields. It is based on the most general structure of any pion-nucleon partial wave amplitude neglecting the unphysical cuts as derived from the N/D method. This amplitude is then matched to the one-loop heavy baryon chiral perturbation theory result at third order and to tree level exchanges of baryon- and meson states in the s,t and u channels. This generates the left-hand cuts. The unitarization procedure does not involve form factors or regulator functions. The resonance parameters are determined from fits to the S- and P-wave pion-nucleon partial wave amplitudes for energies up to 1.3 GeV. In particular, the $Δ(1232)$ is accurately reproduced whereas scalar and vector meson couplings are less precisely pinned down. We also obtain a satisfactory description of the $π$N threshold parameters. Further extensions of this method to coupled channels and the three-flavor case are briefly discussed.