Pion-Pion Scattering in theϕ4Theory

Abstract

Pion-pion scattering has been calculated using the determinantal method, assuming that a relativistic $\left(\frac{\lambda }{4}\right){\left({\varphi }_i{\varphi }_i\right)}^2$ coupling is responsible for the interaction. The scattering amplitude for the individual partial waves is expressed as a ratio of two power series and terms through ${\lambda }^3$ have been kept in each series. Numerical results for the $S$ and $P$ waves have been obtained. $\lambda$ is adjusted by attempting to fit the electromagnetic structure of nucleons. The best value of $\lambda$ obtained by this fit is unfortunately so large that the validity of the determinantal approximation is doubtful.