Secondary trajectories in Reggeon field theories

Abstract

We study the corrections to any secondary Regge trajectory arising from repeated exchange of the Pomeranchuk singularity. Using renormalization-group methods we are able to determine the form of all Pomeron, Reggeon Green's functions in the neighborhood of $J=\alpha \mathrm{}\left(0\right)=1\mathrm{}$ for the Pomerons and $J={\alpha }_R\mathrm{}\left(0\right)\mathrm{}\approx \frac{1}{2}$ for the Reggeons. Starting with bare linear trajectories for both Pomerons and Reggeons we establish how these are modified by a triple-Pomeron and a two-Reggeon-Pomeron coupling. In an expansion of the theory around $D=4\mathrm{}$ space dimensions $D=2\mathrm{}$ is where physics takes place), we find three allowed stable points of the renormalization-group equations in the infrared [$J\to 1 or {\alpha }_R\mathrm{}\left(0\right)\mathrm{}$] limit. For each of these we study the renormalized Reggeon trajectories and the structure of the Green's functions.