Gauge Fixing Identity in the Background Field Method of QCD in Pure Gauge

TL;DR

This paper derives a gauge fixing identity in the background field method of QCD, establishing a relation between different generating functionals and applying it to prove factorization theorems in high-energy collider physics.

Contribution

It introduces a new gauge fixing identity in the background field method of QCD and demonstrates its validity across various gauges, enabling proofs of factorization theorems.

Findings

Derived a gauge fixing identity in QCD background field method.

Established a relation between generating functionals in different gauges.

Proved factorization theorems at high-energy colliders.

Abstract

In this paper we derive a gauge fixing identity by varying the covariant gauge fixing term in $Z[A,J,\eta, {\bar \eta}]$ in the background field method of QCD in pure gauge. Using this gauge fixing identity we establish a relation between $Z[J,\eta,{\bar \eta}]$ in QCD and $Z[A,J,\eta, {\bar \eta}]$ in background field method of QCD in pure gauge. We show the validity of this gauge fixing identity in general non-covariant and general Coulomb gauge fixings respectively. This gauge fixing identity is used to prove factorization theorem in QCD at high energy colliders and in non-equilibrium QCD at high energy heavy-ion colliders.