AGK cutting rules and perturbative QCD

The purpose of this article is to describe a few features of semihard interactions, in high energy nuclear collisions, that are better understood with the help of the AGK cutting rules, and of the probabilistic picture of the interaction which follows. In the first part of the article the cutting rules are discussed for the simplest component of the forward three-body parton amplitude in the large a fixed t limit. The case considered corresponds to the term - at the lowest order in the coupling constant and with vacuum quantum number exchange in both t channels - of the amplitude which describes the interaction of a high energy quark with the two target quarks. The different leading cuts of the amplitude are shown to be proportional to one another with the same weights of the cutting rules derived in the context of multi-Pomeron exchange. The probabilistic picture of the multiple interactions, which originates from the cutting rules, and the self-shadowing cross sections are then discussed. The second part of the article deals with the semihard interactions. The semihard cross section in high energy nucleus-nucleus collisions is represented as a self-shadowing cross section, and a feature which is pointed out is that the single scattering factorized expression of the perturbative QCD parton model holds at any order in the multiparton correlations, the relation being the analog of the AGK cancellation for the average number of soft interactions in high energy hadron-nucleus collisions. Finally, an infrared problem which finds a solution within the self-shadowing representation of the semihard cross section is discussed.