THE CHIRAL LAGRANGIAN PARAMETERS, (L)OVER-BAR(1), (L)OVER-BAR(2), ARE DETERMINED BY THE RHO-RESONANCE

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