Low Energy Pion--Nucleon Scattering in the Heavy Baryon and Infrared Schemes

Abstract

We study pion--nucleon scattering with a chiral lagrangian of pions, nucleons, and $\Delta$-isobars to order $Q^3$, where $Q$ is a generic small momentum. We compare the results from heavy baryon chiral perturbation theory with those from the infrared regularization scheme. While the former provides a reasonable fit to the data out to a pion c.m. kinetic energy of 100 MeV, the latter is only able to fit up to 40 MeV and even then the parameters obtained are unreasonable. Difficulties with the infrared scheme in the $u$-channel are discussed.

20 pages revtex, minor revisions, to be published in Phys. Rev. C

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• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• Chiral three-nucleon force at N^4LO I: Longest-range contributions
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Nucleon mass: from lattice QCD to the chiral limit
• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
• Meson-Baryon Effective Chiral Lagrangians to O(q^3)
• Infrared regularization with spin-3/2 fields
• Aspects of meson-baryon scattering in three- and two-flavor chiral perturbation theory
• Two-pion exchange nucleon-nucleon potential:O(q^4) relativistic chiral expansion
• $\pi N$ Scattering in the $\Delta (1232)$ Region in an Effective Field Theory
• Infrared and extended on-mass-shell renormalization of two-loop diagrams
• πN scattering in relativistic baryon chiral perturbation theory revisited
• Relativistic $O(q^4)$ two-pion exchange nucleon-nucleon potential: configuration space
• The Role of the Roper in Chiral Perturbation Theory
• Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology
• Relativistic chiral representation of the $\pi N$ scattering amplitude I: The Goldberger-Treiman relation
• Hadron masses: lattice QCD and chiral effective field theory