Next-to-next-to-eikonal corrections in the CGC

TL;DR

This paper extends the theoretical understanding of gluon production in proton-nucleus collisions by calculating next-to-next-to-eikonal corrections, revealing their impact on cross sections and helicity asymmetries beyond the eikonal approximation.

Contribution

It introduces the calculation of gluon propagator corrections at next-to-next-to-eikonal order and applies these to analyze observables in pA collisions beyond the eikonal limit.

Findings

Next-to-next-to-eikonal corrections modify the unpolarized cross section.

Eikonal and next-to-next-to-eikonal contributions to helicity asymmetry vanish.

Next-to-eikonal corrections are non-zero for helicity asymmetry.

Abstract

We extend the study of corrections to the eikonal approximation that was initiated in Ref. \cite{Altinoluk:2014oxa} to higher orders. These corrections associated with the finite width of the target are investigated and the gluon propagator in background field is calculated at next-to-next-to-eikonal accuracy. The result is then applied to the single inclusive gluon production cross section at central rapidities and the light-front helicity asymmetry, in pA collisions, in order to analyse these observables beyond the eikonal limit. The next-to-next-to-eikonal corrections to the unpolarized cross section are non-zero and provide the first corrections to the usual $k_\perp$-factorized expression. In contrast, the eikonal and next-to-next-to-eikonal contributions to the helicity asymmetry vanish, while the next-to-eikonal ones are non-zero.