Deck-model calculation ofπ−p→π−π+π−p

Abstract

We formulate and study a Deck-type model for the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}p$. The model differs from previous Deck calculations in two respects: (i) Experimental data are used for both $\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}N$ scattering, and (ii) the amplitude has proper Bose symmetry. Feature (i) allows us to examine any desired region of $3\ensuremath{\pi}$ mass (the ${A}_{3}$ is treated on the same footing as the ${A}_{1}$); features (i) and (ii) allow us to examine all the angular dependence in the final state and to compare with partial-wave analyses of experimental data. In this paper we present the results of a study in which events generated from the model by a Monte Carlo method are plotted and fitted in the same way as experimental events. Many of the features of the data are qualitatively reproduced, including certain important properties obtained from the partial-wave analysis in the ${A}_{1}$ region. The ${A}_{3}$ region is not accurately represented by the model. Results of an analytic partial-wave analysis of this model, and the use of it to check the assumptions of the fitting program, are presented in an associated paper.