Determination of two-loop ππ scattering amplitude parameters Original Research Article

The chiral expansion of the ππ amplitude to the order of two loops was expressed in terms of six independent parameters in a previous paper: four of these are shown here to satisfy sum rules. Their derivation, where crossing symmetry plays a key role, is explained. Their convergence properties are studied and their practical evaluation, in terms of the available data on ππ phase shifts above 0.5 GeV, is discussed. Below 0.5 GeV the chiral amplitude itself is employed, such that the parameters are determined in a self-consistent way. Some care is devoted to the estimate of the errors.