The chiral lagrangian parameters, ℓ1, ℓ2, are determined by the ϱ-resonance

The all-important consequence of Chiral Dynamics for ππ scattering is the Adler zero, which forces ππ amplitudes to grow asymptotically. The continuation of this subthreshold zero into the physical regions requires a P-wave resonance, to be identified with the ϱ. It is a feature of ππ scattering that convergent dispersive integrals for the I = 1 channel are essentially saturated by the ϱ-resonance and are much larger than those with I = 2 quantum numbers. These facts predict the parameters ℓ1, ℓ2 of the Gasser-Leutwyler Chiral Lagrangian, as well as reproducing the well-known KSFR relation and self-consistently generating the ϱ-resonance.