The Use of Dispersion Relations in the $ππ$ and $K\bar K$ Coupled-Channel System

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Systematic 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 changed

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