Effect of the3πResonance on the2πResonance

Abstract

It is shown that the $4\pi$ intermediate state in $\pi -\pi$ scattering plays an important role in determining the position and perhaps even the existence of the $\pi -\pi$ resonance. This large effect occurs by virtue of the $3\pi$ resonance. Quantitative estimates are given. The effect of this result on the nucleon form factors is briefly discussed and a simple model for these functions is proposed. The possibility of higher energy pion resonances is also considered.