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

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.

arXiv comment46 pages. This version includes an improved discussion of the power counting used for subeikonal corrections. The derivation of next-to-eikonal effects associated with the dynamics of the target is also significantly improved, and exposed in the new appendix D

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• Small-x Evolution of the Gluon Generalized Parton Distribution Eg of the Nucleon
• Finite width effects on the azimuthal asymmetry in proton-nucleus collisions in the Color Glass Condensate
• Global analysis of polarized DIS & SIDIS data with improved small-$x$ helicity evolution
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• Exclusive photoproduction of $B_c^{\pm }$ and bottomonia pairs
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Quantum simulating multi-particle processes in high energy nuclear physics: dijet production and color (de)coherence