Absorption Model Applied toπ−πScattering

A study of the possibility of using an absorption model to obtain a unique $s$-wave $I=0\mathrm{}$ $\pi \pi$ phase shift from the reaction ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ was made. Applying the model to combined data from several latoratories, we obtained a set of reasonable (but twofold ambiguous) values for the isospin-zero $s$-wave phase shift ${{\delta }_0}^0$, using the isotropic moment of the dipion decay distribution. Values for ${{\delta }_0}^0$ deduced by using the $s-p$ wave interference term in the dipion decay cross section agreed well with previous (twofold ambiguous) results obtained by extrapolation procedures. Comparing the two sets of twofold ambiguous solutions for ${{\delta }_0}^0$, the lower or "down" branch was preferred marginally in the dipion mass region below the $\rho$ meson. No unique conclusion could be drawn in the higher-mass region. We emphasize the model dependence of these results, but we believe that similar studies with improved statistics for $-t>\mathrm{}{\mu }^2$ would yield similar results. Good data for $-t<\mathrm{}{\mu }^2$ are required to do definitive model-independent analyses.