<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>-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 $\ensuremath{-}0.46&lt;\ensuremath{\lambda}\ensuremath{\lesssim}0.3$. Results are given for various values of $\ensuremath{\lambda}$ within this interval.