A new method to study the number of colors in the final-state interactions of hadrons

Based on Chiral Perturbation Theory we introduce the dependence on the number of colors (NC) for the ππ→ππ scattering amplitudes. Those amplitudes are calculated from dispersion relations that respect analyticity and coupled channel unitarity, as well as accurately describing experiment. By varying NC the trajectories of the poles and residues (the couplings to ππ) of the light mesons, the σ/f0(500), f0(980), ρ(770) and f2(1270) are investigated. Our results show that the method proposed is a reliable way to study the NC dependence in hadron-hadron scattering with final-state interactions.