A Numerical Analysis to the π and K Coupled–Channel Scalar Form-factor

A numerical analysis to the scalar form-factor in the ππ and KK coupled–channel system is made by solving the coupled-channel dispersive integral equations, using the iteration method. The solutions are found not unique. Physical application to the ππ central production in the pp → ppππ process is discussed based upon the numerical solutions we found. PACS numbers: 14.40.Aq; 11.55.Fv; 13.75.Lb The I=J=0 channel ππ interactions are of great physical interests. Because the interaction of the I=J=0 channel is very strong, the input bare singularities for a given model can be severely renormalized and distorted by the strong attractive force and extra dynamical singularities may be generated [1]. Therefore the I=J=0 channel affords an ideal test ground for models of strong interactions. Also, the lightest glueball is expected to lie in the I=J=0 channel, as predicted by the lattice QCD calculations. Therefore a detailed study to the dynamics in this channel becomes especially interesting. The low energy I=J=0 ππ system manifests itself in various production processes intensively measured by experiments, i.e., from πN → ππN , γγ → ππ to J/Ψ → φππ, etc., with the center of mass energy, √s, ranging from the ππ threshold to a few GeV. When √ s exceeds the KK̄ threshold, a