The Use of Analyticity in the $ππ$ and $K\bar K$ Coupled Channel System

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Studies on the IJ=00 $ππ$ and $K\bar K$ coupled--channel system are made using newly derived dispersion relations between the phase shifts and poles and cuts. It is found that the $σ$ resonance must be introduced to explain the experimental phase shifts, after evaluating the cut contribution. The effects of nearby branch point singularities to the determination of the $f_0(980)$ resonance are also carefully clarified.
Summary of talks given at International Conference on Flavor Physics 2001, Zhangjiajie, Hunan, May 30th, 2001, at BES annual meeting, and at Eurodaphne workshop on Nonperturbative Methods in Chiral Theories, Valencia, Spain, June 28th, 2001. To appear in the proceedings

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