Systematic effects in the low-energy behavior of the current SAID solution for the pion-nucleon system

TL;DR

This paper examines the low-energy pion-nucleon scattering data using the SAID WI08 solution, revealing systematic effects that challenge key assumptions about data reliability, electromagnetic corrections, and isospin invariance.

Contribution

The study identifies systematic issues in the WI08 solution at low energies, questioning the validity of underlying assumptions in the analysis.

Findings

Scale factors are energy-independent and close to 1.

Systematic effects suggest some assumptions may not hold.

Challenges to data reliability, electromagnetic corrections, or isospin invariance.

Abstract

We investigate the description of the pion-nucleon experimental data at low energy (i.e., below pion laboratory kinetic energy of $100$ MeV) on the basis of the current SAID solution (WI08). We demonstrate that, in a self-consistent analysis scheme, the scale factors of the fits based on the Arndt-Roper formula come out independent of the beam energy and `cluster' around the expectation value of $1$. We report systematic effects in the low-energy behavior of the WI08 solution. These effects indicate that at least one of the three following assumptions, underlying the WI08 analysis, does \emph{not} hold, namely that: a) the bulk of the data is reliable, b) the electromagnetic effects are correctly accounted for, and c) the isospin invariance in the strong interactions of the $\pi N$ system is valid.