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

TL;DR

This paper develops a systematic approach to calculate Next-to-Eikonal corrections for quark and scalar propagators in a gluon background, enabling more accurate high-energy scattering predictions including gluon saturation effects.

Contribution

It introduces a general Next-to-Eikonal expansion of the quark propagator and a new method to compute corrections from the background field's $x^-$ dependence, advancing high-energy QCD calculations.

Findings

Derived a general Next-to-Eikonal expansion of the quark propagator.

Developed a systematic method for corrections from background field's $x^-$ dependence.

Enabled study of scattering on dynamically evolving targets.

Abstract

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 non-trivial dynamics instead of on a static one, by going beyond infinite Lorentz time dilation of the target.