Pion-nucleon amplitude near threshold: the sigma-term and scattering lengths beyond few loops

Abstract

The pion-nucleon amplitude is considered in the vicinity of the elastic scattering threshold within a relativistic dynamical model dressing the pi N N and pi N Delta vertices self-consistently with an infinite number of meson loops. The dressing is formulated as solution of a system of coupled integral equations incorporating unitarity, crossing symmetry and analyticity constraints. The calculated scattering lengths and the sigma-term agree with recent data analyses. The dressing is important in this model both below and at threshold. The contribution of the Delta resonance is discussed, including effects of the consistent dressing of the pi N Delta vertex. A comparison with the approaches of chiral perturbation theory and the Bethe-Salpeter equation is outlined.

28 pages, 3 figures, using REVTeX. The influence of various model ingredients on the near-threshold parameters is discussed in more detail. To be published in Nucl.Phys.A

References in corpus (5)

• Relativistic chiral SU(3) symmetry, large N_c sum rules and meson-baryon scattering
• Low energy analysis of pi N --> pi N
• Compton scattering on the nucleon at intermediate energies and polarizabilities in a microscopic model
• Low-energy Compton scattering on the nucleon and sum rules
• The equivalence theorem and the Bethe-Salpeter equation

Cited by in corpus (3)

• The sigma-term form factor of the nucleon in the large-Nc limit
• The Adler-Weisberger and Goldberger-Miyazawa-Oehme sum rules as probes of constraints from analyticity and chiral symmetry in dynamical models for pion-nucleon scattering
• Ratio of the proton electromagnetic form factors from meson dressing