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

Abstract

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.