Pole Extrapolation of the Reactionsπ−p→π−π+nandπ+p→π+π−Δ++(1238)

Experimental differential cross sections from data on the reactions ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ and ${\pi }^{+}p\to {\pi }^{+}{\pi }^{-}{\Delta }^{++}\mathrm{}\left(1238\right)\mathrm{}$ have been extrapolated to the one-pion-exchange pole to obtain the ${\pi }^{+}{\pi }^{-}$ elastic scattering cross section from threshold to 1.4 GeV. Consistent results are obtained in three c.m. energy ranges for both reactions. The data have been fitted to several $t$-dependent extrapolation functions, and the results of the fits are tabulated and plotted as a function of ${\pi }^{+}{\pi }^{-}$ effective mass. In particular, we find cross sections of approximately 25 and 125 mb, respectively, at the $K$ and central ${\rho }^0\mathrm{}\left(765\right)\mathrm{}$ mass positions.