Correlations of $\boldsymbol{\pi N}$ Partial Waves for Multi-Reaction Analyses

TL;DR

This paper provides covariance matrices for $oldsymbol{\pi N}$ partial waves, enabling more accurate correlated fits in multi-reaction analyses to better identify baryonic resonances and assess uncertainties.

Contribution

It supplies the necessary covariance matrices for $oldsymbol{\pi N}$ partial waves, facilitating improved correlated $oldsymbol{\chi^2}$ fits in baryon resonance studies.

Findings

Covariance matrices enable precise correlated fits.

Systematic errors are incorporated into the analysis.

Enhanced assessment of resonance signals and uncertainties.

Abstract

In the search for missing baryonic resonances, many analyses include data from a variety of pion- and photon-induced reactions. For elastic $\pi N$ scattering, however, usually the partial waves of the SAID or other groups are fitted, instead of data. We provide the partial-wave covariance matrices needed to perform correlated $\chi^2$ fits, in which the obtained $\chi^2$ equals the actual $\chi^2$ up non-linear and normalization corrections. For any analysis relying on partial waves extracted from elastic pion scattering, this is a prerequisite to assess the significance of resonance signals and to assign any uncertainty on results. The influence of systematic errors is also considered.