Self-consistent statistical error analysis of $\pi\pi$ scattering

TL;DR

This paper evaluates the statistical validity of $\pi\pi$ scattering data analysis, showing that current methods mostly satisfy normality conditions and that slight data adjustments can improve analysis robustness without significantly altering key resonance parameters.

Contribution

It demonstrates the conditions for valid statistical error analysis in $\pi\pi$ scattering and proposes minor data selection modifications to enhance residual normality and analysis reliability.

Findings

Current analyses show minimal violations of residual normality.

Adjusted data selection improves normality without affecting resonance parameters.

Resonance pole parameters remain stable despite data selection changes.

Abstract

We analyze the conditions under which a statistical error analysis can be carried out in the case of $\pi\pi$ scattering, namely the normality of residuals in the conventional $\chi^2$-fit method. Here we check that the current and benchmarking analyses only present very small violations of the normality requirements. In particular, we show how it is possible to amend slightly the selection of the experimental data, and improve the normality of residuals. As an example, we discuss the $0^{++}$ channel and the implications for the $f_0(500)$ and $f_0(980)$ resonances, obtaining that the new selection of data provides very similar and compatible results. In addition, the effect on the $f_0(500)$ and $f_0(980)$ resonance pole parameters is almost negligible, which reinforces the central results and the uncertainty analysis performed in these benchmarking determinations.