Peripherality and exchange mechanisms of four-body final states induced by $pi$$sup +$p and anti pp interactions

We define a kinematical variable ${P}_{v}$ which is correlated to the peripherality of a multibody final state. ${P}_{v}=0$ implies that all the final-state particles lie in a plane perpendicular to the incident direction. ${P}_{v}=1$ implies that all the particles in the final state are collinear with the incident direction. ${P}_{v}$ distributions for resonance production are quite different from those for Lorentz-invariant phase space. This property may be used to detect phase-space-like phenomena at high energies in multibody final states ($n\ensuremath{\ge}10$). We compare ${P}_{v}$ distributions for the four-body annihilation and nonannihilation channels of $\overline{p}p$ interactions and the four-body final states of ${\ensuremath{\pi}}^{+}p$ interactions in which the proton goes into the backward and forward hemispheres. We find remarkable kinematic similarities between annihilation and ${\ensuremath{\pi}}^{+}p$ backward-hemisphere channels. We suggest that this is due to the dominance of baryon exchange. There is also a remarkable, but different, similarity between nonannihilation and the ${\ensuremath{\pi}}^{+}p$ forward-hemisphere channels. We suggest that this is due to the dominance of meson exchange.