Forward analysis of $\pi$N scattering with an expansion method

TL;DR

This paper introduces an expansion method for analyzing $$N forward scattering data, incorporating experimental errors via covariance matrices, and computes subthreshold expansion coefficients with associated uncertainties.

Contribution

The paper presents a novel expansion approach that satisfies forward dispersion relations and includes a detailed error analysis for $$N scattering data.

Findings

Calculated subthreshold expansion coefficients with error bars

Validated the expansion method against experimental data

Provided a framework for error-aware scattering analysis

Abstract

The $\pi$N forward scattering data are analyzed using an expansion method, where the invariant amplitudes are represented by expansions satisfying the forward dispersion relations. The experimental errors of the data are taken into account through the covariance matrix of the coefficients of the expansions in a careful error analysis. From the results, some coefficients, $c_{n0}^\pm$, of the subthreshold expansions have been calculated with proper error bars.