Pion-Pion Interactions inπ−pReactions at 2.1 BeV/c

An analysis is given of the interactions of two pions as they result from the reactions of negative pions incident upon protons with a momentum of 2.1 BeV/c. A historical background of the motivation for the experiment is given and experimental techniques for dealing with the data are described, from the points of view of both event-by-event analysis and the physical theories which aid in the understanding of the results. Cross sections are given for the various reactions and are inferred by Chew-Low methods for pion-pion scattering. Evidence is presented which indicates that two resonant states in addition to the $\rho$ meson and ${N_{\frac{3}{2}}}^{*}\mathrm{}\left(1238\right)\mathrm{}$ are present in these reactions: (1) the ${N_{\frac{3}{2}}}^{*}\mathrm{}\left(1920\right)\mathrm{}$, whose existence in other reactions is well established, and (2) the $T=0\mathrm{}$, $s$-wave pion-pion interaction, which is still in doubt, known as the ${\epsilon }^0$, the evidence for which stems from an analysis of the decay distribution of the ${\rho }^0$. Finally, corrections to the one-pion-exchange model which involve pion-nucleon scattering vertices are made in an attempt to determine more accurately the low-energy, $T=0\mathrm{}$, $s$-wave pion-pion scattering cross sections, the results suggesting a range of about 10-15 mb in the region below the $\rho$.