A new analysis of scattering from Roy and Steiner type equations
Helmholtz-Institut für Strahlen- und Kernphysik, Universität Bonn, 53115, Bonn, Germany
2 Laboratoire de Physique Théorique (IPN is an unité mixte de recherche du CNRS et de l’Université Paris-Sud (UMR 8608).), Université Paris-Sud, 91406, Orsay, France
3 Institut de Physique Nucléaire(IPN is an unité mixte de recherche du CNRS et de l’Université Paris-Sud (UMR 8608)., Université Paris-Sud, 91406, Orsay, France
With the aim of generating new constraints on the OZI suppressed couplings of chiral perturbation theory a set of six equations of the Roy and Steiner type for the S- and P-waves of the scattering amplitudes is derived. The range of validity and the multiplicity of the solutions are discussed. Precise numerical solutions are obtained in the range GeV which make use as input, for the first time, of the most accurate experimental data available at GeV for both and amplitudes. Our main result is the determination of a narrow allowed region for the two S-wave scattering lengths. Present experimental data below 1 GeV are found to be in generally poor agreement with our results. A set of threshold expansion parameters, as well as sub-threshold parameters are computed. For the latter, a matching with the SU(3) chiral expansion at NLO is performed.
© Springer-Verlag, 2004