The Use of Analyticity in the $\pi \pi$ and $K\bar{K}$ Coupled Channel System

Studies on the IJ=00 $\pi \pi$ 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 $\sigma$ 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.