Next-to-eikonal corrections in the CGC: gluon production and spin asymmetries in pA collisions

TL;DR

The paper develops a systematic next-to-eikonal expansion in the CGC framework by expanding the retarded gluon propagator in a background field and introducing decorated Wilson lines that encode gradients of the background. Applying this to single inclusive gluon production in pA, it shows that unpolarized results retain the standard $k_\\perp$-factorization at leading order, with first corrections vanishing under typical large-target approximations, while spin-dependent observables are governed by next-to-eikonal terms. The work provides explicit operator definitions for the decorated Wilson lines ${\\cal U}^{i}_{(1)}$ and ${\\cal U}_{(2)}$, and demonstrates how these enter both amplitude-level and cross-section calculations, including SSA and helicity asymmetries. This framework paves the way for systematic inclusion of power-suppressed effects in high-energy nuclear collisions and motivates further study of the evolution and phenomenology of the new operators beyond the eikonal limit.

Abstract

We present a new method to systematically include corrections to the eikonal approximation in the background field formalism. Specifically, we calculate the subleading, power-suppressed corrections due to the finite width of the target or the finite energy of the projectile. Such power-suppressed corrections involve Wilson lines decorated by gradients of the background field - thus related to the density - of the target. The method is of generic applicability. As a first example, we study single inclusive gluon production in pA collisions, and various related spin asymmetries, beyond the eikonal accuracy.