Unifying approaches: derivation of Balitsky hierarchy from the Lipatov effective action

TL;DR

This paper derives the Balitsky hierarchy of correlators directly from Lipatov's effective action, clarifying the origin of sub-leading corrections and proposing a versatile calculation scheme.

Contribution

It presents a novel derivation of the Balitsky hierarchy from Lipatov's effective action, including sub-leading eikonal corrections, and suggests broader applications.

Findings

Derived the Balitsky hierarchy from Lipatov's effective action.

Identified the origin of sub-leading eikonal corrections.

Outlined potential applications of the calculation scheme.

Abstract

We consider a derivation of the hierarchy of correlators of ordered exponentials directly from the Lipatov's effective action~\cite{LipatovEff} formulated in terms of interacting ordered exponentials~\cite{OurZub}. The derivation of the Balitsky equation~\cite{Bal} from the hierarchy is discussed as well as the way the sub-leading eikonal corrections to the Balitsky equation arise from the transverse field contribution and sub-leading eikonal corrections to the quark propagator. We outline other possible applications of the proposed calculation scheme.