On near forward high energy scattering in QCD

TL;DR

Korchemsky presents a framework to analyze near-forward high-energy parton scattering in QCD by factorizing soft gluon exchanges into Wilson lines along eikonal trajectories. The energy dependence is controlled by the renormalization of cross singularities of these Wilson lines, captured by a $2×2$ anomalous-dimension matrix Γ_cross that governs the RG evolution. At one loop, this structure produces a Regge-like high-energy behavior with a trajectory α(t) = - (α_s/2π) N log(-t/λ^2), with the singlet exchange dominating at large s. The method extends to quark–antiquark and gluon–gluon scattering and links infrared soft-gluon dynamics to ultraviolet cross singularities, offering a route to higher-order resummations and deeper insight into high-energy QCD.

Abstract

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft gluon exchanges into Wilson lines vacuum expectation values and studying their properties, we find that the asymptotics of the scattering amplitude is controlled by the renormalization properties of the so called cross singularities of Wilson loops. Using this fact, we evaluate the scattering amplitude and show that its asymptotics is determined by the properties of the $2\times 2$ matrix of anomalous dimensions which appears after one renormalizes the cross singularities of Wilson loops. A generalization to the case of quark-antiquark and gluon-gluon elastic scattering is discussed.