Slope of the Forward Peak: Ans-Channel Analysis

Starting from the exact multiparticle unitarity relation, we derive the derivative extension of the optical theorem. The slope of the forward peak is then related in a model-independent way to the rotational properties of production amplitudes. A sequential representation is developed for treating an $n$-particle state. The formalism is then applied to the multiperipheral and diffractive models. The analysis makes clear the mechanisms in which the forward slope is built up in those models. In the case of the multiperipheral model the slope is proportional to the number of links in the multiperipheral chain. Quantitatively, the slope of the Pomeranchuk trajectory at $t=0\mathrm{}$ is too large. In an oversimplified version of the diffractive model, the predicted slope of the elastic forward peak is one-half the mean slope, the average being taken over all two-cluster production processes; consequently, it is too small. The realistic high-energy model is somewhere between the two extremes considered.