Quark and scalar propagators at next-to-eikonal accuracy in the CGC through a dynamical background gluon field

We revisit the calculation of quark and scalar propagators in a gluon background field at next-to-eikonal accuracy, which will provide the first power correction to scattering processes in the high-energy limit, including gluon saturation effects. The two main results of our study are as follows. First, we derive a very general next-to-eikonal expansion of the quark propagator in terms of the scalar propagator, which allows us to isolate spinor-specific next-to-eikonal corrections from the universal ones. Second, we present a new method allowing, for the first time, a systematic calculation of the next-to-eikonal corrections coming from the x- dependence of the background field. This opens the possibility to study high-energy scattering processes on a target with nontrivial dynamics instead of on a static one, by going beyond infinite Lorentz time dilation of the target.

Automated summary

We revisit the calculation of quark and scalar propagators in a gluon background field and provide the first power correction method. The main results include deriving a next-to-eikonal expansion of the quark propagator, isolating spinor-specific next-to-eikonal corrections from universal ones, and presenting a new method to calculate next-to-eikonal corrections from the x-dependence of the background field.