S-Waveπ−πScattering Phase Shifts

Using an absorptive one-pion exchange mechanism for the reaction ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$, a fit is made to experimental data at 4 $\frac{\mathrm{GeV}}{c}$ in order to extract the $\pi -\pi$ scattering phase shifts. The analysis was carried out up to $D$ waves in the $\pi -\pi$ amplitude. The best results indicate a very broad $I=0\mathrm{}$ $S$-wave resonance with $M_R=820\mathrm{}$ MeV and $\Gamma =600\mathrm{}$ MeV.