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.
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