Reasonable fits to invariant-mass, momentum-transfer, and Treiman-Yang angle distributions for the reaction pp^A^pir"" at 6.6 GeV/c are obtained from a double-Reggepole model with pion exchange.Results obtained from a detailed analysis of the reaction pp -> A ++ pir~ employing the model of double Regge-pole exchange 1 * 2 are presented in this paper. The data were derived from a sample of four-prong events of the type pp -^ppT&n"' produced by 6.6-GeV/c incident protons. Initial discussion of approximately one quarter of the data presented in this paper has been published. 3 The final state A ++ pir~ is produced peripherally, with predominance of small momentum transfers to the final A ++ and p. Moreover, a plot of the invariant mass of the A ++ 7r*~ system evidences a large enhancement in the range 1.38 to 1.58 GeV.The basic assumption made in this study is that the process/)/? -* A+ + pii~ proceeds primarily via doubly peripheral collisions of the type diagrammed in Fig. 1, in which the exchanged lines represent Regge poles. We wish to remark that, although this model appears to describe the data adequately, we do not interpret our results as necessarily casting doubt on the validity of certain un-Reggeized one-pion-exchange (OPE) calculations. Rather, we wish to emphasize the application of the Regge-pole model of this paper to inelastic three-body scattering processes.The requirement that quantum numbers combine appropriately at the three vertices of Fig. 1 limits the possible pairings of Regge-pole exchanges in the diagram. In this analysis, only those diagrams in which a pion Regge pole couples at the p A ++ vertex are retained. Other diagrams (for example, p coupling at the pA vertex) are eliminated because they are not expected to contribute significantly to the cross section for small irA mass. 4 However, on the left-hand side of the diagram, all Regge poles which participate in ir~~p elastic scattering may be present; and because the cm. energy of the overall reaction is relatively low, all of these are expected to contribute significantly. In summary, therefore, Fig. 1 is to be understood as representing a pion trajectory coupled at the pA ++ vertex and then a sum over all allowed trajectories between the pp and middle iru vertex.Because the initial particles are identical, we must impose the required antisymmetrization of the reaction amplitude. This is properly accomplished by adding to Fig. 1 a diagram in which the initial particle momenta are interchanged. 5 Because cuts are taken in momentum transfer, the interference term is less than 10% of the contribution from one diagram alone and is therefore ignored altogether. The two diagrams are incorporated by taking twice the magnitude of one.The differential cross section for the reaction S 7TA tpA FIG. 1. Basic double-Regge-pole exchange diagram studied here. The pf and qx are four momenta; tp/± 964