On-Shell Approach to Pion-Nucleon Physics

Abstract

We discuss an on-shell approach to pion-nucleon physics that is consistent order by order in a $1/f_{\pi }$ expansion with the chiral reduction formula, crossing, and relativistic unitarity. A number of constraints between the on-shell low-energy parameters are derived at tree level in the presence of the pion-nucleon sigma term, and found to be in fair agreement with experiment. We analyze the nucleon form factors, and the $\pi N\to \pi N$ scattering amplitude to one-loop, as well as $\pi N\to \pi \pi N$ to tree level. We use the latter to derive a new constraint for the pion-nucleon sigma term at threshold. We compare our results to both relativistic and non-relativistic chiral perturbation theory, and discuss the convergence character of the expansion in light of experiment.

14 pages, 4 figures

References in corpus (10)

• Chiral Dynamics in Nucleons and Nuclei
• Aspects of chiral pion-nucleon physics
• What $\pi -\pi$ Scattering Tells Us About Chiral Perturbation Theory
• The reaction $\pi N\to \pi \pi N$ at threshold in chiral perturbation theory
• Chiral Corrections to the S-Wave Pion-Nucleon Scattering Lengths
• Chiral invariant renormalization of the pion--nucleon interaction
• A MASTER FORMULA FOR CHIRAL SYMMETRY BREAKING
• Nucleons at Finite Temperature
• Dilepton bremsstrahlung from pion-pion scattering in a relativistic OBE model
• Master Formula Approach to Chiral Symmetry Breaking: Pi-Pi scattering

Cited by in corpus (3)

• Delta(1232) in piN -> pipiN reaction
• The pi N -> pi pi N reaction around the N(1440) energy
• Master formula approach to broken chiral U(3)xU(3) symmetry