The Schwinger-Dyson equation on Pomeron loop summation and renormalization

Abstract

The solution to the Schwinger-Dyson equation that describes the summation over Pomeron loop diagrams is derived. The solution is a closed expression which splits into two parts. The first leads directly to the renormalization of the BFKL Pomeron, and the second contribution is equivalent to non interacting Pomerons with renormalized vertices. Thus a closed expression is derived for the sum over Pomeron loop diagrams in the perturbative QCD approach, which preserves unitarity.