Dispersion approach to the problem of account for quark-gluon degrees of freedom in hadron-hadron interactions and its application to ππ scattering

On the basis of the theory of generalized R-functions a general representation is presented for partial amplitudes, which is compatible with the requirements of unitarity and analyticity of the S-matrix. The potential scattering model was employed previously in deriving this representation. In the present approach the CDD-poles (Gastillejo, Dalitz, Dyson) which appear in solution of the dispersion relations correspond to the Jaffe-Low P-matrix poles, so one can relate these poles to eigenstate energies of compound quark-gluon bag. The obtained representation results, in particular, in a restriction upon the residue (the vertex constant) of the partial amplitude at the pole, which corresponds to a bound state, with account for the left cut. The method is applied to analysis of s- (I=0.2) and p- (I=1) wave pion-pion scattering in the ππ-mass region below 2 GeV