Pion-nucleon scattering inside the Mandelstam triangle

TL;DR

This paper uses heavy baryon chiral perturbation theory and dispersion relations to analyze pion-nucleon scattering within the Mandelstam triangle, determining low-energy constants and the sigma-term with different phase shift analyses.

Contribution

It reconstructs the pion-nucleon amplitude in the unphysical region and compares low-energy constants derived from different phase shift analyses.

Findings

Sigma-term is 40 MeV with Karlsruhe analysis

Sigma-term is larger with VPI analysis

Provides a detailed comparison with phase shift data

Abstract

We study the third order pion-nucleon scattering amplitude obtained from heavy baryon chiral perturbation theory inside the Mandelstam triangle. We reconstruct the pion-nucleon amplitude in the unphysical region by use of dispersion relations and determine the pertinent low-energy constants by a fit to this amplitude. A detailed comparison with values obtained from phase shift analysis is given. Our analysis leads to a pion-nucleon sigma-term of sigma(0) = 40 MeV based on the Karlsruhe partial wave analysis. We have repeated the same procedure using the latest solution of the VPI group and find a much larger value for sigma(0).