Fixing two chiral perturbation theory parameters by fitting pion-pion phase shifts

In this paper, we fix the parameters ℓ1 and ℓ2 of the one loop corrected chiral perturbation theory by fitting the low energy pion-pion S- and P- experimental phase-shifts. The corresponding values of the scattering lengths are calculated. Related approaches for data fitting, in particular the unitarization program of current algebra, are also discussed.