MULTICHANNEL RESONANCES IN THE COUPLED-CHANNELS OF MESON SCATTERING -A SCALAR SECTOR

A method is formulated for determining model-independent values of the parameters of multichannel resonances with the aim of establishing th e QCD nature of these resonances. The approach is based on direct appl ication of such general principles as analyticity and unitarity to the analysis of experimental data on coupled processes of particle scatte ring. The representation of resonances by pairs of complex conjugate c lusters of poles and zeros on the Riemann surfaces of two- and three-c hannel S matrices is discussed. The multisheet structure of the Rieman n surfaces is taken into account by choosing proper uniformizing a var iables. In this approach, the analysis of data on one process makes it possible to predict the amplitudes of other coupled processes. This c an be done by constructing analytic continuations of the S matrix to a ll unphysical sheets of the Riemann surface or with the aid of formula s of the Le Couteur-Newton type. The role of closed channels in the fo rmation of resonances is investigated in the K- and S-matrix approache s. The method is applied to the isoscalar s-wave channel of the couple d processes pi pi --> pi pi, K (K) over bar, eta eta and of scalar res onances.