Gluon propagation inside a high-energy nucleus

TL;DR

The paper addresses high-energy semi-hard particle production dominated by small-$x$ partons by deploying the McLerran-Venugopalan / Color Glass Condensate framework and solving the classical Yang-Mills equations in the light-cone gauge $A^+=0$. The authors derive a compact transfer-matrix description, via a Wilson line $U$, for gluon propagation through the nuclear color field and use it to compute gluon production in proton-nucleus collisions. They provide explicit boundary conditions and propagation relations, showing how the proton field is dressed by the nuclear background to yield the standard $pA$ gluon yield, and compare the light-cone and Lorenz gauges, highlighting the simplicity of the $A^+=0$ formulation. This transfer-matrix construction serves as a key building block for higher-order corrections in the CGC approach to high-energy nuclear collisions.

Abstract

We show that, in the light-cone gauge, it is possible to derive in a very simple way the solution of the classical Yang-Mills equations for the collision between a nucleus and a proton. One important step of the calculation is the derivation of a formula that describes the propagation of a gluon in the background color field of the nucleus. This allows us to calculate observables in pA collisions in a more straightforward fashion than already proposed. We discuss also the comparison between light-cone gauge and covariant gauge in view of further investigations involving higher order corrections.

Figures (2)

• Figure 1: Gluon passing through a nucleus. The region shaded in gray is the region where the color source representing the nucleus is non-zero.
• Figure 2: The two contributions to gluon production in pA collisions. Left: the proton source emits the gluon before the collision with the nucleus. Right: the proton source goes through the nucleus before emitting the gluon. The thick solid line represents the proton color current.