Measurement ofT=2ElasticππCross Sections

Experimental differential cross sections from data on the reaction ${\pi }^{-}p\to \left({\pi }^{-}{\pi }^{-}\right){\Delta }^{++}$ at beam momenta of 2.7, 3.0, 3.2, 3.9, and 4.2 $\frac{\mathrm{GeV}}{c}$ have been extrapolated to the one-pion-exchange pole to obtain the ${\pi }^{-}{\pi }^{-}$ elastic scattering cross section. An attempt is made to correct for background due to kinematic overlap with the competing one-pion-exchange process ${\pi }^{-}p\to {\rho }^0\left({\pi }^{-}p\right)$. Analyses done independently on the data in two beam-momentum groupings at ∼3.0 and ∼4.0 $\frac{\mathrm{GeV}}{c}$ give consistent results of a roughly constant 7-11-mb cross section for ${\pi }^{-}{\pi }^{-}\to {\pi }^{-}{\pi }^{-}$ over the dipion mass range 440-750 MeV. Our results are compared with available results from other analyses and with several theoretical predictions for the $T=2\mathrm{}$ $s$-wave phase shift ${{\delta }_0}^2$.