Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian

TL;DR

This paper introduces a new method for analyzing photon- and pion-nucleon scattering using chiral perturbation theory, ensuring physical constraints like gauge invariance, causality, and unitarity, and successfully reproduces empirical amplitudes up to 1300 MeV.

Contribution

A novel analytic extrapolation scheme for scattering amplitudes that incorporates fundamental physical constraints within a chiral effective field theory framework.

Findings

Successfully reproduces empirical s- and p-wave amplitudes up to 1300 MeV.

Ensures gauge invariance, causality, and unitarity in the extrapolation process.

Provides a stable and physically consistent method for analyzing nucleon scattering data.

Abstract

We present and apply a novel scheme for studying photon- and pion-nucleon scattering beyond the threshold region. Partial-wave amplitudes for the $\gamma\, N$ and $\pi N$ states are obtained by an analytic extrapolation of subthreshold reaction amplitudes computed in chiral perturbation theory, where the constraints set by electromagnetic-gauge invariance, causality and unitarity are used to stabilize the extrapolation. Based on the chiral Lagrangian we recover the empirical s- and p-wave amplitudes up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$.