Van Hove Analysis of the Reactions ${\pi }^{-}p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$ and ${\pi }^{+}p\to {\pi }^{+}{\pi }^{+}{\pi }^{-}p$ at 16 GeV/c

Data from the reactions ${\pi }^{-}p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$ and ${\pi }^{+}p\to {\pi }^{+}{\pi }^{+}{\pi }^{-}p$ have been obtained at 16 GeV/c in approximately equal samples from the BNL 80-in. hydrogen bubble chamber. We have studied both reactions for resonance production and compared our results with predictions of the one-pion-exchange model (OPEM) calculated by Wolf. The four-body longitudinal phase-space (LPS) plot suggested by Van Hove was used to analyze the data from both reactions. The events were separated according to distinct regions of the LPS plot in order to study the following classes of quasi-two-body final states: (1) diffractively produced three-pion states, (2) diffractively produced $\pi \pi p$ states, (3) double-resonance production such as ${\rho }^0{\Delta }^{++}$, (4) single-resonance production such as ${\pi }^{-}{\pi }^{-}{\Delta }^{++}$. The Van Hove analysis provided a much cleaner separation of resonances from background effects than the usual techniques. We observe production of the $A_1$ and $A_2$ mesons as well as the $N^{*}\mathrm{}\left(1470\right)\mathrm{}$ and $N^{*}\mathrm{}\left(1700\right)\mathrm{}$ isobars in the ${\pi }^{+}{\pi }^{-}p$ system for both reactions. There is strong formation of the doubly resonant states ${\rho }^0{\Delta }^{++}$ and $f^0{\Delta }^{++}$ and the general features of the nondiffractive events are all in good agreement with one-pion exchange. Detailed comparisons between the data and the OPEM in each LPS plot region show that Van Hove analysis provides a sensitive test for the OPE model.