Quarks at next-to-eikonal accuracy in the CGC: Forward quark-nucleus scattering

We derive Next-to-Eikonal (NEik) corrections to the background quark propagator, which stem from (i) considering a finite longitudinal width target instead of an infinitely thin shockwave and (ii) including the interaction of the quark with the transverse components of the background field. These two different corrections to the eikonal approximation combine together and provides a gauge covariant expression for the quark propagator at NEik accuracy. We then apply our results to quark (or antiquark) scattering on a nucleus at NEik accuracy, considering both unpolarized cross section and helicity asymmetry.