Small-x Evolution in the Next-to-Leading Order

TL;DR

This paper discusses the next-to-leading order corrections to the Balitsky-Kovchegov equation in QCD and ${ m N}=4$ SYM, crucial for understanding high-energy scattering processes in future collider experiments.

Contribution

It provides the NLO kernel for the BK equation in QCD and ${ m N}=4$ SYM, including conformal and non-conformal parts, advancing the theoretical understanding of small-x evolution.

Findings

Derivation of the NLO BK kernel in QCD.

Separation of conformal and non-conformal contributions.

Implications for future deep inelastic scattering experiments.

Abstract

After a brief introduction to Deep Inelastic Scattering in the Bjorken limit and in the Regge Limit we discuss the operator product expansion in terms of non local string operator and in terms of Wilson lines. We will show how the high-energy behavior of amplitudes in gauge theories can be reformulated in terms of the evolution of Wilson-line operators. In the leading order this evolution is governed by the non-linear Balitsky- Kovchegov (BK) equation. In order to see if this equation is relevant for existing or future deep inelastic scattering (DIS) accelerators (like Electron Ion Collider (EIC) or Large Hadron electron Collider (LHeC)) one needs to know the next-to-leading order (NLO) corrections. In addition, the NLO corrections define the scale of the running-coupling constant in the BK equation and therefore determine the magnitude of the leading-order cross sections. In Quantum Chromodynamics (QCD), the next-to-leading order BK equation has both conformal and non-conformal parts. The NLO kernel for the composite operators resolves in a sum of the conformal part and the running-coupling part. The QCD and ${\cal N}=4$ SYM kernel of the BK equation is presented.