Low-energyππscattering in the large-Nclimit of QCD

An extension of Weinberg's approach is applied to the $\pi \pi$-scattering amplitude of the leading order in $\frac{1}{N_c}$. The resulting sum rules (SR's) restrict the masses and widths of $\pi \pi$ resonances providing dualitylike properties of the $\pi \pi$ 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.