Application of a Crossing-Symmetric Model Satisfying the Mandelstam Representation to π-π and K-π Scattering

A model for meson-meson scattering satisfying the Mandelstam representation, crossing symmetry, and Regge behavior and including a Pomeranchukon amplitude is applied to π-π and K-π scattering. Solutions are found for the K-π partial waves that satisfy unitarity approximately at low energies, give a satisfactory fit to the on-mass-shell data, and predict scattering lengths consistent with current algebra. Apart from a change in the coupling constant, effectively the same parameters are then used to predict the low-energy π-π scattering, and the solutions are found to satisfy unitarity approximately up to 900 MeV. The predicted on-mass-shell results agree well with the available data. The general conditions below threshold for π-π scattering that follow from crossing symmetry and positivity are well satisfied. The extrapolated π-π and K-π amplitudes off the mass shell are found to agree satisfactorily with the data for πN→ππN and KN→KπN when a phenomenological form factor is used in the extrapolation. The total and differential cross sections at high energy are found to have characteristic Regge behavior. The Pomeranchukon amplitude produces total π-π and K-π cross sections consistent with factorization in the asymptotic region.