The Gluon Propagator in non-Abelian Weizsäcker-Williams fields

TL;DR

Addresses the problem of computing the gluon propagator in a non-Abelian Weizsäcker–Williams background generated by valence quarks in very large nuclei. The authors solve the small fluctuation equations in a non-singular gauge $A^- = 0$ to obtain a consistent propagator (matching the mv2 result) and then gauge-transform to the Light Cone gauge $A^+ = 0$, using a carefully chosen regularization (Leibbrandt–Mandelstam) for the singularities. The main result is an explicit, causal LC-gauge propagator expressed in terms of the $A^- = 0$ Green's function and background fields, suitable for computing the gluon distribution to $O( ext{ } eta_s^2 ext{)}$ and for subsequent higher-order analyses. This framework clarifies the role of contact terms and self-adjointness in the gluon sector and provides a robust tool for high-energy nuclear phenomenology where gauge-invariant quantities should be regulator-independent.

Abstract

We carefully compute the gluon propagator in the background of a non--Abelian Weizsäcker--Williams field. This background field is generated by the valence quarks in very large nuclei. We find contact terms in the small fluctuation equations of motion which induce corrections to a previously incorrect result for the gluon propagator in such a background field. The well known problem of the Hermiticity of certain operators in Light Cone gauge is resolved for the Weizsäcker--Williams background field. This is achieved by working in a gauge where singular terms in the equations of motion are absent and then gauge transforming the small fluctuation fields to Light Cone gauge.