Two-Particle Approximation for the Three-Pion Amplitude

Abstract

A two-particle approximation is suggested for the $3\pi \to 3\pi$ amplitude: The amplitude is replaced by a $\rho +\pi \to \rho +\pi$ amplitude multiplied by $2\pi$ resonance factors. An approximate calculation of the $J=1-$, $T=0\mathrm{}$ partial wave for the $\rho -\pi$ amplitude is made, including only the "elastic" and one-pion-exchange cuts, but it seems to give no hint of a $3\pi$ resonance.