On the anomalous dimensions of the multiple pomeron exchanges

TL;DR

This paper computes explicit multi-pomeron exchange amplitudes in the QCD dipole model, proposes a general formula for their anomalous dimensions, and discusses their variation due to DGLAP evolution, comparing with reggeon field theory.

Contribution

It introduces a general formula for the anomalous dimensions of multi-pomeron exchanges in the dipole model, advancing understanding of high-energy scattering.

Findings

Explicit calculations of single, double, and triple BFKL pomeron exchange amplitudes.

Proposal of a general formula for anomalous dimensions of $1\Rightarrow k$ amplitudes.

Observation of anomalous dimension variation due to DGLAP evolution.

Abstract

High energy hard scattering in large $N_{c}$ limit can be described by the QCD dipole model. In this paper, single, double and triple BFKL pomeron exchange amplitudes are computed explicitly within the dipole model. Based on the calculation, the general formula $\gamma^{(k)*}_{0}=\chi^{-1}(k\chi({1/2}))$ which governs the anomalous dimension of $1\Rightarrow k$ amplitude is conjectured. As far as the unitarity problem is concerned, we find that the anomalous dimension $\gamma$ varies from graph to graph due to the DGLAP evolution. In the end, a comparison between this computation and reggeon field theory is provided.