Sum rules for π scattering in the backward direction

Abstract

We write finite-energy sum rules (FESR) at fixedu forthe π scattering amplitudesAiu,DIu, ,Iu=1/2, 3/2 (Iu isospin exchanged in theu-channel) and we verify the consistency between the Regge terms, as obtained by high-energy data, and the integrals over the low-energy region. We use then our FESR to obtain a better determination of the Regge parameters for Δδ-trajectory exchange. We find, in particular, a negative sign for the residue nearu=0. Finally our results are employed to discuss the validity of the «mean-value principle», developed by Dolen, Horn and Schmid for the Regge boson exchange, in the case of fermion exchange (u≃0); we find that the generalization of this principle does not seem possible for the amplitudes we studied, at least if one tries to represent the amplitude of a single channel with the fermion Regge term alone.