Rigorous Parametric Dispersion Representation with Three-Channel Symmetry

Abstract

Starting with an analyticity domain in the two Mandelstam variables which is contained in the domain obtained by Martin, we derive a parametric dispersion representation for scattering amplitudes in the equal-mass case. For pion-pion scattering this representation is a rigorous consequence of the axioms of local field theory; it displays in a symmetric and explicit way the contributions of all three channels, and it has only "physical" absorptive parts. This representation is useful for deriving sum rules involving only absorptive parts and relating all three channels. Some of these sum rules are given in this paper, the most important of which form a set of independent physical relations that lead to necessary and sufficient conditions ensuring full crossing symmetry.