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 slightly amend 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, finding 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.

• Received 11 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.074014