Can and does the pomeron occur more than once in a single process?

Abstract

A study of high energy diffractive amplitudes (the elastic amplitude being a special case), has revealed the following regularities at small momentum transfers: (a) they all tend to be almost purely imaginary, and (b) they all have the same energy dependence, leading to universal, constant (modulo logarithms) cross sections at high energies. In this paper, it is assumed that these regularities are produced by an underlying, common mechanism, which is defined as the pomeron. The question then addressed is whether the pomeron, so defined, can and does occur more than once in a single process. It is demonstrated that various models for the pomeron (involving Regge poles, Regge cuts, geometric ideas like diffraction, etc.) lead to different answers to this question, none of them quantitative. By contrast, the introduction of the pion-pole dominance (PPD) hypothesis is shown to lead to a model-independent quantitative answer. Assuming just the above definition of the pomeron, the PPD hypothesis predicts certain processes that must be termed multi-pomeron by the advocates of all models, and provides estimates for their cross sections. The predictions of this hypothesis are compared with experiment. It is shown that PPD leads to, and sets lower bounds for, inclusive triple-pomeron cross sections assuming no more than our general definition of the pomeron. It is pointed out that the repetition of the pomeron, guaranteed by PPD, may be used to set upper bounds on asymptotic total cross sections. The crucial property of the result, that total cross sections must eventually die away, is that it does not rely on any model-dependent property of the pomeron, such as factorization.