2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/223726Systematic and careful studies are made on the properties of the IJ=00 $ππ$ and $K\bar K$ coupled-channel system, using newly derived dispersion relations between the phase shifts and poles and cuts. The effects of nearby branch point singularities to the determination of the $f_0(980)$ resonance are estimated and and discussed.22 pages with 5 eps figures. A numerical bug in previous version is fixed, discussions slightly expanded. No major conclusion is changedHigh Energy Physics - Phenomenologytext