High energy scattering in QCD and cross singularities of Wilson loops

TL;DR

This work connects high-energy quark-quark scattering in QCD to the renormalization of cross singularities of Wilson lines, showing that the amplitude's asymptotics are governed by a 2×2 cross anomalous dimension matrix Γ_cross(γ,g).The authors compute Γ_cross to two-loop order, revealing that its entries can be expressed in terms of the cusp anomalous dimension and a self-energy function, with a consistent large-N structure and potential all-orders generalization.At high energy, the octet exchange exhibits Regge-like behavior after resummation, while the singlet exchange arises from nonleading logarithms; the large-$N$ limit further clarifies the dominance of the cusp contribution in the cross sector.Overall, the paper provides a framework to understand and resum soft-gluon effects in high-energy QCD via Wilson-line cross singularities, offering insights into the interplay between infrared (cusp) and cross (mixing) anomalous dimensions.

Abstract

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft gluon exchanges into Wilson line expectation value we find that there is one-to-one correspondence between high energy asymptotics in QCD and renormalization properties of the so called cross singularities of Wilson lines. Using this relation we show that the asymptotic behavior of the quark-quark scattering amplitude is controlled by a $2\times 2$ matrix of the cross anomalous dimensions. We evaluate the matrix of cross anomalous dimension to two-loop order and study the properties of the obtained expressions to higher loop order.