The Balitsky-Kovchegov equation for dipole gluon density in the momentum space

TL;DR

This paper derives the Balitsky-Kovchegov (BK) equation for dipole gluon density directly in momentum space, clarifying its structure and unifying various formulations for proton and nuclear targets.

Contribution

It provides a detailed derivation of the BK equation in momentum space, including resummation and a unified notation, consolidating scattered literature.

Findings

Derivation of the BK equation in momentum space

Explicit structure of the triple-Pomeron vertex

Unified notation for proton and nuclear targets

Abstract

I present derivation the BK equation for the dipole gluon density in momentum space, starting from its standard formulation in coordinate space. I review the equation for both proton and nuclear targets, and I also discuss the resummed BK evolution.The purpose of this paper is to consolidate derivations and formulas scattered across the literature, to show in detail how the structure of the triple-Pomeron vertex emerges in the unfolded form of the nonlinear term, and to establish a consistent notation throughout.