ππ→ππcross sections near threshold

An analysis of new data for the reaction ${\pi }^{\pm }\overrightarrow{p}{\pi }^{\pm }{\pi }^{+}n$ at incident energies between 223 and 284 MeV is presented. ${\pi }^{+}{\pi }^{-}$ cross sections are obtained via Goebel-Chew-Low techniques by extrapolation to the pion pole using the pseudoperipheral approximation. A consistency check between the present experimental results and previous experiments at higher energies is made using Roy equations. The isospin 0, S-wave $\pi \pi$ scattering length was obtained using a variety of methods. The result obtained from a threshold expansion is $a_0^0=0.204\mathrm{}\pm 0.014$ (statistical) $\pm 0.008$ (systematic) in inverse pion mass units. It is shown that there are significant differences between the reaction mechanisms for the $\left({\pi }^{-}{\pi }^{+}\right)$ and $\left({\pi }^{+}{\pi }^{+}\right)$ channels.