Elimination of ambiguities in ππ amplitudes using Roy ’ s equations ∗

Roy’s equations are used to check if scalar-isoscalar π − π amplitudes fitted to the “up-flat” and “down-flat” phase shift solutions fulfill crossing symmetry below 1 GeV. It is shown that the amplitude fitted to the “down-flat” solution satisfies crossing symmetry while the “up-flat” one does not. In such a way the “up-down” ambiguity in the scalar-isoscalar phase shifts is resolved in favour of the “down-flat” solution. PACS 11.55.Fv, 11.80.Gw, 13.75.Lb Direct study of the ππ scattering is beyond present experimental possibilities. However, phenomenological phase shifts can be obtained through partial wave analyses of final states of reactions in which pions are produced. These analyses are often model dependent and can lead to ambiguous results. In 1997 a study of the π−p ↑→ ππn reaction on a polarized target was performed for the m ππ effective mass between 600 and 1600 MeV leading to four solutions for the ππ scalar-isoscalar phase shifts below 1 GeV [1]. Using the unitarity constraint two “steep” solutions were rejected while the two remaining ones, called “down-flat” and “up-flat”, passed this test [2]. ∗Presented at the Meson 2002, Seventh International Workshop on Production, Properties and Interactions of Mesons, Cracow, Poland, 24-28 May 2002.