Comparison between two models for the isospin dependence of many-particle production cross-sections

Abstract

In the present letter we briefly discuss two very simple models for the isotopic-spin dependence of the production amplitudes with the aim of clarifying some general features of production processes. The only experimental data which are sufficiently detailed to permit a choice between these models concern proton-proton interactions. As wc are interested only in qualitative features, we adopt a simplified picture of thcse interactions, assuming that in the final state one finds two protons and a number n of pions with a vanishing total isotopic spin. Taking into account the occurrence of neutrons and other particles in the final state and the possibility tha t the produced pions have a small but nonzero total isotopic spin, one should not get qualitatively different results. The first model is based on the assumption that the production amplitude is symmetric with respect to the permutat ions of the momenta of the produced pions. This assumption is certainly satisfied by an independent jet model (1.2). In fact in this ease the amplitude is given by the product of some factors, each one containing the momentum of one of the produced particles. The isotopic-spin invarianee requires tha t all the factors corresponding to the pions have the same form and the assumed symmetry proper ty follows immediately. We remark that our assumption could be satisfied also by more general models. From the symmetry we are assuming, it follows that the amplitude is also symmetric with respect to the permutat ions of the isotopic spin indices of the produced pions. This symmetry and the assumption that the total isotopic spin is zero determine completely the isotopic-spin wave function of the final pions. A wave function of this kind exists only if the total number n of pions is even and has the form