THE ASYMPTOTIC RESTRICTIONS FOR THE GAMMA-PI-]PI-PI PROCESS

The method of asymptotic restrictions is applied to the amplitude of gammapi --> pipi reaction. In the leading order of the 1/N(c)-expansion this amplitude is represented as a sum over resonances admissible in the reaction. This sum contains only on-mass-shell parameters of the resonances (masses and widths). Simultaneously we derived sum rules which restrict resonance spectrum and ensure certain dual properties of the gammapi --> pipi amplitude at leading order of the 1/N(c)-expansion. At low energies we find a relation between the axial anomaly and masses and widths of isovector pipi resonances with odd spins and positive normalities. This relation is in excellent agreement with the present experimental data.