An extension of Weinberg's approach is applied to the aa-scattering amplitude of the leading order in 1 / N , . The resulting sum rules (SR's) restrict the masses and widths of aa resonances providing dualitylike properties of the aa amplitude and enable us to express constants of chiral Lagrangians in terms of resonance parameters. The numerical verification of SR's displays agreement with present experimental information and consistency with the results of some models.

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We develop the phenomenological amplitude of the πN → ππN reaction describing the exchanges of ∆ and N * along with the OPE mechanism. The contribution of the latter contains 4 independent low energy parameters (up to O(k 4 ) order). The terms of the polynomial background are added to stand for far resonances and for contact terms originating from the off-mass-shell interactions. These terms are introduced with the account of isotopic, crossing, C, P and T symmetries of strong interactions.The data consisting of total cross sections in the energy region 0.300 ≤ P Lab ≤ 500 MeV/c and 1D distributions from the bubble-chamber experiments for three reaction channels were undergoing fittings to determine free parameters of the amplitude. The best solutions are characterized by χ 2 DF = 1.16. At the considered energies the isobar exchanges are found to be more important than OPE. The obtained solutions reveal the need in more precise data and/or in polarization measurements because of large correlations of isobar parameters with the OPE ones.The theoretical solutions were used for modeling the Chew-Low extrapolation and the Olsson-Turner threshold approach. It is shown that the noncritical application of the former results in 100% theoretical errors, the extracted values being in fact the random numbers. The results of the Olsson-Turner method are characterized by significant systematic errors coming from unknown details of isobar physics. Sankt-Petersburg 1997

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