Unitary and causal dynamics based on the chiral Lagrangian

TL;DR

This paper develops a scheme based on the chiral Lagrangian to analyze pion-nucleon interactions, employing analytic extrapolation constrained by fundamental principles to match experimental data up to 1300 MeV.

Contribution

It introduces a novel method combining chiral perturbation theory with analytic extrapolation constrained by gauge invariance, causality, and unitarity for scattering analysis.

Findings

Reproduces experimental data up to 1300 MeV

Provides partial-wave amplitudes via analytic extrapolation

Discusses a longstanding puzzle in photon asymmetry measurements

Abstract

Pion-nucleon scattering, pion photoproduction, and nucleon Compton scattering are analyzed within a scheme based on the chiral Lagrangian. Partial-wave amplitudes 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. Experimental data are reproduced up to energies $\sqrt{s}\simeq 1300$ MeV in terms of the parameters relevant at order $Q^3$. A striking puzzle caused by an old photon asymmetry measurement close to the pion production threshold is discussed.