Can parameters of f_0-mesons be determined correctly analyzing only pion-pion scattering?

TL;DR

This paper investigates whether analyzing only pion-pion scattering suffices to accurately determine f_0-meson parameters, emphasizing the importance of coupled-channel analysis for correct resonance characterization.

Contribution

It demonstrates that a coupled-channel analysis of pion-pion and pi pi --> K antiK processes is essential for accurate f_0-meson parameter extraction, highlighting the role of Riemann surface structure.

Findings

Single-channel analysis yields incorrect resonance parameters.

Coupled-channel analysis provides correct mass and width estimates.

Riemann surface structure is crucial for amplitude calculations.

Abstract

The coupled processes -- the pion-pion scattering and pi pi --> K antiK in the I^GJ^{PC}=0^+0^{++} channel -- are analyzed (both separately and combined) in a model-independent approach based on analyticity and unitarity and using a uniformization procedure. It is shown: 1) a structure of the Riemann surface of the S-matrix for considered coupled processes must be allowed for calculating both amplitudes and resonance parameters, such as the mass and width; 2) the combined analysis of coupled processes is needed as the analysis of only pi-pi channel does not give correct values of resonance parameters even if the Riemann surface structure is included.