On the Pomeranchuk singularity in massless vector theories

It is shown that the Pomeron in massless (abelian of nonabelian) vector theories, as derived from a perturbative high energy description which satisfies unitarity, comes as a diffusion problem in the logarithmic scale of transverse momentum. For a realistic theory there are reasons to expect that this diffusion should come to a stop: (a) the long range forces of the massless gluons should be screened, (b) the Pomeranchuk singularity in the j-plane should be t-dependant, and (c) there should not be a discontinuity in the zero mass limit at t = 0 or in the t 0 limit of the massless case. In the third part we outline a scheme for summing all diagrams which are required by unitarity. It uses reggeon field theory in zero transverse dimensions and leads to: (i) the diffusion comes to a stop (zero drift and zero diffusion constant); (ii) the total cross section is constant (up to powers of lns); (iii) in order to give a meaning to the divergent perturbation expansion, one has to add a nonperturbative term of the order exp(-const/g2). (orig.)