Determination of Chiral Perturbation Theory low energy constants from a precise description of pion-pion scattering threshold parameters

Abstract

We report on our determination of the values of the one and two loop low energy constants appearing in the Chiral Perturbation Theory calculation of the ππ scattering amplitude. For this we use a precise sum rule determination of scattering lengths and slopes that appear in the effective range expansion. In addition we provide new sum rules and the values for these coefficients up to third order in the expansion. Our results when using only the scattering lengths and slopes of the S, P, D and F waves are consistent with previous determinations, but seem to require higher order contributions if they are to accommodate the third order coefficients of the effective range expansion.