S-Wave Dominant Solutions of the Pion-Pion Integral Equations

Abstract

The integral equations for pion-pion scattering formulated by Chew and Mandelstam are put into a form suitable for numerical solution. An iteration procedure is described that is applicable when the $S$-wave amplitude dominates the equations, all higher partial waves being small; this paper considers only solutions for which such is the case. The requirement that the equations have consistent solutions without bound states turns out to limit the pion-pion coupling constant to the range $-0.46<\lambda \lesssim 0.3$. Results are given for various values of $\lambda$ within this interval.