n-Particle Cross Sections in Diffraction-Production Models

We show how a simple $t_{min}$ effect can significantly alter the ${\sigma }_n\sim \frac{1}{n^2}$ rule found in most diffractive models of particle production. Data on $\mathrm{pp}$, ${\pi }^{-}p$, and $K^{-}p$ collisions appear consistent with $n^2{\sigma }_n\sim \exp (-\frac{n^4}{s})$, which implies that (1) double diffraction dissociation is the dominant feature, and (2) $〈n〉\sim \ln s$, but correlation functions rise much more slowly than in earlier treatments. Critical comments on diffractive models are given.