Parametrization of Crossing Symmetric Amplitudes

Abstract

The crossing equations of Balachandran and Nuyts are solved to give the most general expansion of the π0‐π0 amplitude consistent with crossing symmetry and in which the partial wave expansion is manifest. We find that crossing symmetry imposes 2L + 1 constraints on the Lth partial wave if the lower waves are known. The simplest such constraint (in the units were 4m π 2 =1 ) is ∫ 0 1 (1−s)(3s−1)f 0 (s) ds=0 ,where f 0(s) is the s‐wave π0‐π0 amplitude.