  Constraints on the parameters in the one- and two-loop pion-pion scattering
amplitudes of standard chiral perturbation theory are obtained from explicitly
crossing-symmetric sum rules. These constraints are based on a matching of the
chiral amplitudes and the physical amplitudes at the symmetry point of the
Mandelstam plane. The integrals over absorptive parts appearing in the sum
rules are decomposed into crossing-symmetric low- and high-energy components
and the chiral parameters are finally related to high-energy absorptive parts.
A first application uses a simple model of these absorptive parts. The
sensitivity of the results to the choice of the energy separating high and low
energies is examined with care. Weak dependence on this energy is obtained as
long as it stays below ~560 MeV. Reliable predictions are obtained for three
two-loop parameters.
