Multiparticle terms in the 2-body scattering amplitude

Abstract

An attempt is made to relate the Van Hove overlap-function approach with the Glauber multiparticle collision theory. It is then shown that even within strongly interacting particles at high energy and small angle the Glauber relation for the scattering amplitude holds. The derivation is based on the covariant Sudakov method for parametrizing the high-energy kinematics. On the basis of recently predicted oscillations, which seem to be connected with the particular treatment of the many-particle unitarity condition, a simple phenomenological model is proposed having all the common features of other models, plus the oscillations superimposed. The numerical analysis and consequences of the model proposed are not attempted in this paper. It is also shown that the Glauber formula with the complex phase shift identified with a single Regge-pole exchange (Pomeranchukon) in thet-channel is an analytic continuation fromt>0 tot⩽0 (i.e. thes-channel) of the discontinuityδt(n)fj(t) of the amplitudefj(t) at the singularityt=tn(j), wheretn(j) is the threshold for the creation ofn Reggeons, found by Gribovet al. in their analysis of the multiparticle terms in the unitarity condition for thet-channel. The analogy is easily visualized by comparing the corresponding diagrams drawn in both approaches as well as by utilizing the simple relationship that exists between the overlap function and the Glauber complex phase shift.