Vacuum singularities in a dual multiperipheral model

We set up an explicit dual multiperipheral model, which is similar to the models of Huan Lee, Veneziano, and Chan and Paton, but explicitly takes into account the deferred thresholds arising from the production of resonance clusters. We assume that there are two such clusters, one with (mass)² 0.5 GeV² (ρ,ω,ε,...) and the other with (mass)² 1.5 GeV² (f,B,D,A₂,...). At lower energies only the first plays any role, and we find that the total vacuum-state cross section σ∝ on the average, where α_^P0.85. For s50 GeV², on the other hand, the second cluster also comes in, and σ flattens out. This behavior has all the features of the experimental data and is thus a completely satisfactory alternative to the conventional description in terms of the P and f. In addition, all of the parameters describing our vacuum singularities can be calculated a priori in our model, and are in reasonably good agreement with the data.