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

Understand

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.