Roy’s equations and the ππ experimental data

Abstract

Roy's equations are used to check if the scalar-isoscalar ππ scattering amplitudes fitted to experimental data fulfill crossing symmetry conditions. It is shown that the amplitudes describing the "down-flat" phase shift solution satisfy crossing symmetry below 1 GeV while the amplitudes fitted to the "up-flat" data do not. In this way the long standing "up-down" ambiguity in the phenomenological determination of the scalar-isoscalar ππ amplitudes has been resolved confirming the independent result of the recent joint analysis of the π + π − and π 0 π 0 data. IntroductionIn 1997 a new analysis of the π − p ↑ → π + π − n reaction on a polarized target was performed in the m ππ effective mass range from 600 to 1600 MeV [1]. For the first time the pseudoscalar (π-exchange) amplitude was separated from the pseudovector (a 1 -exchange) amplitude in the region of the the four-momentum transfer squared from −0.005 to −0.2 (GeV/c) 2 . Below 1000 MeV, where the S-and P -waves strongly interfere, the partial wave analysis of the π + π − data provided us with two scalarisoscalar solutions, called "up" and "down", which differ by their intensities. Lack of information on a sign difference between the phases of the S-and P -waves near the position of the ρ resonance led us to other two branches of the "up" and "down" amplitudes named "steep" and "flat". It was shown in [2] that both "up-steep" and "down-steep" S-wave isoscalar amplitudes significantly violate unitarity below 1 GeV * Unité de Recherche des Universités Paris 6 et Paris 7, associée au CNRS † This work has been performed in the framework of the IN2P3-Polish Laboratories Convention (project number 99-97).