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 interaction with transverse components field. These two different eikonal approximation combine together provide gauge covariant expression for propagator at NEik accuracy. then apply our results (or antiquark) scattering on nucleus accuracy, both unpolarized cross section helicity asymmetry.