Reggeized Double-Peripheral-Model Analysis of Three-Body Final-State Processes: Application to $\mathrm{pp}\to p{\pi }^{-}{\Delta }^{++}$ at 28.5 GeV/c and other Reactions

Use of a double-Regge-pole-exchange model to describe peripheral three-body final-state processes, especially at near-threshold values of the invariant mass of a pair of final-state particles, is described and discussed. The fact is stressed that the model provides an understanding of the entire reaction, yielding distributions in all kinematical variables. As an example, results are presented from a detailed comparison of the predicted model distributions with data from $\mathrm{pp}\to p{\pi }^{-}{\Delta }^{++}$ at 28.5 GeV/c. One simple diagram involving only Pomeranchon and pion exchanges is employed. Good agreement is obtained with the experimental distributions in invariant masses, momentum transfers, and various angles; in particular, the enhancement near 1460 MeV in the (${\pi }^{-}{\Delta }^{++}$) mass spectrum is well fitted. Recent applications of the model to the $A_1$ region in $\pi N\to \pi \rho N$ are reviewed. Also explored is the potential for extracting information on the pion trajectory from three-particle final-state reaction data.