Determination of theS-Waveπ−πAmplitude near theϱPeak from the Reactionπ−+p→π++π−+n

A fit to recent extensive data for the reaction ${\pi }^{-}+p\to {\pi }^{+}+{\pi }^{-}+n$ at incident ${\pi }^{-}$ momentum ∼4 $\frac{\mathrm{BeV}}{c}$ and final two-pion center-of-mass energy $m_{\pi \pi }\sim m_{\rho }$ was made. The peripheral model with absorption was used in the fit. The asymmetry in the final two-pion distribution ${\theta }_{\pi }$ gives a quantitative determination of the $\pi -\pi$, $S$-wave, $I=0\mathrm{}$ scattering amplitude. A constant phase shift of ∼+60° gives as good a fit the to data as a resonance ${\epsilon }^0$ (at 730 MeV with a width of 90 MeV), proposed by Durand and Chiu. A negative phase shift of ∼-60° is ruled out by examining the distribution in ${\theta }_{\pi }$ as a function of $m_{\pi \pi }$.