Study ofππElastic Scattering Using the Chew-Low Extrapolation Method

The cross sections for ${\pi }^{-}{\pi }^0$ and ${\pi }^{-}{\pi }^{+}$ elastic scattering, and the $I=0\mathrm{}$ $s$-wave and $I=1\mathrm{}$ $p$-wave phase shifts, ${{\delta }_0}^0$ and ${\delta }_1$, are calculated for $400<\mathrm{}{M}_{\pi \pi }<900\mathrm{}$ MeV using a Chew-Low extrapolation. The extrapolation information permits resolving a fourfold ambiguity which has been present in other attempts to determine ${{\delta }_0}^0$ from the reaction ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$. The result for ${{\delta }_0}^0$ is consistent with a curve which increases through 90° around $M_{\pi \pi }=720\mathrm{}$. The $\rho$ width obtained from the extrapolated $p$-wave amplitude is 105 ± 15 MeV.