Determination ofπ−πCross Sections by the Chew-Low Extrapolation Method

A discussion of the Chew-Low conjecture applied to reactions of the type $\pi +p\to \pi +p+{\pi }^0$ is given. The extrapolation technique and the so-called "physical-region-plot method" are discussed. These methods are then applied to a sample of 1684 interactions of the type ${\pi }^{+}+p\to {\pi }^{+}+p+{\pi }^0$ and 411 interactions of the type ${\pi }^{-}+p\to {\pi }^{-}+p+{\pi }^0$ at 1.25-BeV/c incident pion momentum. In Sec. II, we present details of the way in which this sample was obtained and processed. The ${\sigma }_{{\pi }^{+}{\pi }^0}$ physical-region plots for the ${\pi }^{+}$ data confirm the existence of the now well-established $T=J=1\mathrm{}$ $\pi -\pi$ resonance at 725±25 MeV. On the other hand, the physical-region plot of the ${\pi }^{-}$ data shows strong deviations from the results expected on the basis of this same resonance.