Toward Complete Pion Nucleon Amplitudes

TL;DR

This paper bridges low-energy pion-nucleon scattering data with high-energy Regge theory using finite energy sum rules, constructing a comprehensive set of amplitudes through dispersion relations.

Contribution

It introduces a novel method of matching low-energy partial wave analyses with high-energy Regge parametrizations to improve amplitude reconstruction.

Findings

Consistent amplitudes across energy ranges achieved.

Validation of finite energy sum rules in pion-nucleon scattering.

Enhanced understanding of scattering amplitude behavior at different energies.

Abstract

We compare the low-energy partial wave analyses $\pi N$ scattering with a high-energy data via finite energy sum rules. We construct a new set of amplitudes by matching the imaginary part from the low-energy analysis with the high-energy, Regge parametrization and reconstruct the real parts using dispersion relations.