The Schwinger-Dyson equation on Pomeron loop summation and renormalization

TL;DR

This paper derives a closed-form solution to the Schwinger-Dyson equation for Pomeron loop summation in perturbative QCD, leading to Pomeron renormalization and unitarity preservation.

Contribution

It provides the first closed expression for summing Pomeron loops, incorporating renormalization and non-interacting Pomerons with renormalized vertices.

Findings

Renormalization of the BFKL Pomeron achieved.

Sum over Pomeron loops expressed in closed form.

Unitarity preserved in the perturbative QCD approach.

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.