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Evolution equation for gluon Regge trajectory

I. A. Korchemskaya, G. P. Korchemsky

TL;DR

The paper develops a Wilson-line-based operator-product framework for the Regge limit of QCD, formulating a Reggeon trajectory OPE and deriving a renormalization-group evolution equation governed by a 2×2 cross anomalous-dimension matrix. The leading high-energy behavior is controlled by the cusp anomalous dimension, yielding a Reggeized gluon trajectory whose 1- and 2-loop coefficients align with known results and clarify the connection between Regge dynamics and Wilson-line renormalization. The approach provides a universal description of Reggeon exchange, links to unitarity corrections, and hints at nonperturbative effects via IR renormalons, establishing a structured path to incorporate higher-order and nonperturbative corrections in high-energy QCD. Overall, the work bridges Regge theory and field-theoretic renormalization of nonlocal gauge-invariant operators, offering a robust, universal description of the Reggeon trajectory across processes.

Abstract

Analysing the asymptotic behaviour of the quark-quark elastic scattering amplitude at high energy and fixed transferred momentum and assuming that gluon is reggeized, we obtain the evolution equation for the gluon Regge trajectory in QCD. It is closely related to the renormalization properties of the Wilson lines and it is in a complete agreement with the recent results of two-loop calculations.

Evolution equation for gluon Regge trajectory

TL;DR

The paper develops a Wilson-line-based operator-product framework for the Regge limit of QCD, formulating a Reggeon trajectory OPE and deriving a renormalization-group evolution equation governed by a 2×2 cross anomalous-dimension matrix. The leading high-energy behavior is controlled by the cusp anomalous dimension, yielding a Reggeized gluon trajectory whose 1- and 2-loop coefficients align with known results and clarify the connection between Regge dynamics and Wilson-line renormalization. The approach provides a universal description of Reggeon exchange, links to unitarity corrections, and hints at nonperturbative effects via IR renormalons, establishing a structured path to incorporate higher-order and nonperturbative corrections in high-energy QCD. Overall, the work bridges Regge theory and field-theoretic renormalization of nonlocal gauge-invariant operators, offering a robust, universal description of the Reggeon trajectory across processes.

Abstract

Analysing the asymptotic behaviour of the quark-quark elastic scattering amplitude at high energy and fixed transferred momentum and assuming that gluon is reggeized, we obtain the evolution equation for the gluon Regge trajectory in QCD. It is closely related to the renormalization properties of the Wilson lines and it is in a complete agreement with the recent results of two-loop calculations.

Paper Structure

This paper contains 4 sections, 43 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Operator production expansion
  3. Cross singularities of Wilson lines
  4. Evolution equation

Figures (2)

  • Figure 1: The general structure of the Feynman diagrams for the scattering of two Wilson lines at short transverse distances $z_\perp$. The soft gluons are factorized into two Wilson lines with a cross point at the origin. The coefficient functions $C_1$ and $C_2$ represent the hard gluons contribution.
  • Figure :