Pomeranchuk singularity in a Reggeon field theory with quartic couplings

Abstract

We employ the methods of the renormalization group to investigate the structure of Pomeron Green's functions near $l=1\mathrm{}$, $t=0\mathrm{}$ in a theory where only four-Pomeron couplings are present. When certain conditions on the renormalized couplings are met, the $l\to 1$, $t\to 0$ behavior of the theory is governed by free effective couplings (the theory is "infrared-free"). In this situation the renormalized Pomeron trajectory is of the form $\alpha \mathrm{}\left(t\right)=1+At+\frac{\mathrm{Bt}}{{\left(\ln Ct\right)}^5}$ for $t>\mathrm{}0\mathrm{}$, where $A$, $B$, and $C$ are constants; the total cross section behaves as ${\sigma }_T\mathrm{}\left(s\right)\mathrm{}\sim {\gamma }_1+\frac{{\gamma }_2}{{\left(\ln \ln s\right)}^5}$, with ${\gamma }_1$ and ${\gamma }_2$ positive.