High-energy evolution in planar QCD to three loops: the non-conformal contribution

TL;DR

This paper develops a framework for calculating three-loop corrections to the BK equation in high-energy QCD, verifying the spacelike-timelike correspondence and predicting nonconformal contributions relevant for future collider experiments.

Contribution

It introduces a novel framework based on spacelike-timelike correspondence to compute multi-loop corrections to the BK equation, including the full nonconformal component in the planar limit.

Findings

Verified the spacelike-timelike correspondence at three loops in the large-flavor limit.

Predicted the nonconformal part of the three-loop BK Hamiltonian for a generic gauge theory.

Provided a computational approach relevant for upcoming high-energy collider tests.

Abstract

The Balitsky-Kovchegov (BK) equation offers a tractable description of the high-energy growth of gauge-theory scattering amplitudes and the nonlinear saturation effects that eventually tame it. Motivated by the upcoming Electron-Ion Collider (EIC), whose extended kinematic reach promises more decisive tests of saturation at high energies, we present a framework based on the spacelike-timelike correspondence that streamlines the computation of multi-loop corrections to the BK equation. We explicitly verify the correspondence at three loops in the large-flavor limit and predict the full nonconformal component of the three-loop BK Hamiltonian in the planar limit of a generic gauge theory, treating the numbers of fermions and scalars as free parameters.