Unitarized finite energy sum rules and their application to π N-charge exchange

Abstract

The problem of ‘unitarizing’ finite energy sum rules (FESR) by the inclusion of Regge cuts is investigated. Instead of considering Regge cuts in FESR for the full scattering amplitude T fi, new FESR are proposed for that part of T fi, which has just pure Regge pole asymptotic behavior if the Regge cuts are included in T fi. The Regge cuts in the high-energy region are evaluated according to the ‘weak-cut’ version of the Reggeized K-matrix model. The new FESR then look like the conventional ones, however, with T fi replaced by the corresponding two-particle K-matrix element. With these K-matrix FESR the serious difficulties arising in conventional approaches to the problem disappear. With the new K-matrix FESR a detailed analysis of πN-charge exchange is performed. The K-matrix FESR turn out to be satisfied with only the ϱ pole on the high energy side much better and more locally than the corresponding conventional FESR. The ϱ residues in the K-matrix are predicted to choose ‘nonsense’ at α ϱ = 0. If reduced ϱ residues are defined as in the Regge limit of a πN-Veneziano formula, they are found to be practically constant between t = m ϱ 2 and t ≈ −0.4 (GeV/ c) 2. The values agree well with those known at t = m ϱ 2 and with results from high-energy fits.