Comment on "Scrutinizing pion-pion scattering in light of recent lattice phase shifts"

TL;DR

This paper critiques a recent lattice-QCD analysis of pion-pion scattering, emphasizing the importance of including the $Kar{K}$ channel for reliable conclusions about the $\sigma$-meson state.

Contribution

It highlights the neglect of the $Kar{K}$ channel in previous analysis and discusses how including it can alter the interpretation of scattering phase shifts.

Findings

Neglecting the $Kar{K}$ channel can lead to misleading conclusions.

Including coupled channels is crucial for accurate scattering analysis.

Model comparisons suggest different interpretations when channels are considered.

Abstract

In a recent paper by Xiu-Li Gao, Zhi-Hui Guo, Zhiguang Xiao, and Zhi-Yong Zhou, Phys. Rev. D 105, 094002 (2022), here referred to as I, $S$-wave $\pi\pi$ scattering phase shifts obtained in a lattice-QCD calculation are analyzed using dispersive $S$-matrix methods. We question the reliability of the conclusion from this analysis that, for a pion mass of 391 MeV, the lattice phases favor the presence of both a $\sigma$-meson bound state and a nearby virtual state. Our main criticism concerns the neglect of the $S$-wave $K\bar{K}$ channel, which was considered alongside additional $s\bar{s}$ interpolating fields in the lattice computation used by the authors of I and also in typical coupled-channel models. As an illustration, some results from such a recent model are presented as well. Concluding remarks concern possible improvements of the analysis in I as well as further model tests.