Structure of the Pomeranchuk singularity in Reggeon field theory

Using the methods of the renormalization group we study the structure of Pomeranchukon Green's functions in a Reggeon calculus or a Reggeon-field-theory model. We are able to determine the behavior of all Green's functions in the "infrared" limit of small Reggeon momenta and small Reggeon energy ($-E$ = angular momentum minus one). This behavior is governed by a zero of the classic Gell-Mann-Low variety which arises when the triple-Pomeranchukon coupling is pure imaginary as suggested by Gribov's analysis of Feynman graphs in ordinary field theory. The form of the Pomeranchukon propagator dictates that the trajectory function be singular at $t=0\mathrm{}$ and that a variety of scaling laws for the Green's functions be obeyed. By coupling particles into the theory, we find that total cross sections are predicted to rise as a small power of lns, which in the model is approximately ${\sigma }_T\mathrm{}\left(s\right)\mathrm{}\sim {\left(\ln s\right)}^{\frac{1}{6}}$.