In the analysis a status and parameters of the scalar, vector, and tensor mesonic resonances are obtained and compared with other results. Possible classification of the resonance states in terms of the SU(3) multiplets is discussed.

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In a combined analysis of the experimental data on the coupled processes ππ → ππ, KK in the channel with I G J P C = 0 + 0 ++ , the various scenarios of these reactions (with different numbers of resonances) are considered. In a model-independent approach, based only on analyticity and unitarity, a resonance is represented by of a pole cluster (poles on the Riemann surface) of the definite type that is defined by the state nature. The best scenario contains the resonances f 0 (665) (with properties of the σ-meson), f 0 (980) (with a dominant ss component), f 0 (1500) (with a dominant flavour-singlet e.g., glueball component) and the f 0 (1710) (with a considerable ss component). If the f 0 (1370) exists, it has a dominant ss component. The coupling constants of observed states with the considered channels and the ππ and KK scattering lengths are obtained. The conclusion on the linear realization of chiral symmetry is drawn.

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The coupled processes -the ππ scattering and ππ → KK in the I G J P C = 0 + 0 ++ channel -are analyzed (both separately and combined) in a model-independent approach based on analyticity and unitarity and using a uniformization procedure. It is shown: 1) a structure of the Riemann surface of the S-matrix for considered coupled processes must be allowed for calculating both amplitudes and resonance parameters, such as the mass and width; 2) the combined analysis of coupled processes is needed as the analysis of only ππ channel does not give correct values of resonance parameters even if the Riemann surface structure is included.The study of scalar mesons is very important for such profound topics in particle physics as the QCD vacuum. However, despite of a big effort devoted to studying various aspects of the problem [1] (for recent reviews see [2-5]) a description of this sector is far from being complete. Parameters of the scalar mesons, their nature and status of some of them are still not well settled [1]. E.g., applying our model-independent method in three-channel analyses of processes ππ → ππ, KK, ηη(ηη ′ ) [6,7] we have obtained parameters of the f 0 (600) and f 0 (1500) which differ considerably from results of analyses utilizing other methods (mainly those based on the dispersion relations and Breit-Wigner approaches). Reasons of this difference should be understood because our method is based only on a demand for analyticity and unitarity of the amplitudes using a uniformization procedure. The construction of amplitudes is practically free from any dynamical (model) assumptions using only the mathematical fact that a local behavior of analytic functions determined on the Riemann surface is governed by the nearest singularities on all corresponding sheets. I.e., the obtained parameters of resonances can be considered as free from theoretical prejudice.First note that in our previous three-channel analyses with the uniformizing variables [6,7] we were enforced to construct a four-sheeted model of the eight-sheeted Riemann surface. This we have achieved neglecting the ππthreshold branch-point which means that we have considered the nearest to the physical region semi-sheets of the initial Riemann surface. This is in the line with our approach of a consistent account of the nearest singularities on all relevant sheets. The two-channel analysis utilizes the full Riemann surface and is, therefore, free of these approximations. To verify a plausibility of our assumptions in the three-channel calculations, we have performed a combined two-channel analysis of data on ππ → ππ, KK to check whether the results of our three-channel analyses [6,7] are also obtained in the two-channel consideration. Moreover, to better understand reasons for the aboveindicated difference in results, we have performed first the analysis only of the ππ scattering data in the two-channel approach.The two-channel S-matrix is determined on the four-sheeted Riemann surface. The matrix elements S ij , where i, j = 1(ππ), 2(KK) denote channel...