Abstract
Most of the progress in high-energy Quantum Chromodynamics has been obtained within the eikonal approximation and infinite Wilson-line operators. Evolution equations of Wilson lines with respect to the rapidity parameter encode the dynamics of the hadronic processes at high energy. However, even at high energy many interesting aspects of hadron dynamics are not accessible within the eikonal approximation, the spin physics being an obvious example. The higher precision reached by the experiments and the possibility to probe spin dynamics at future Electron Ion Colliders make the study of deviations from eikonal approximation especially timely. In this paper, I derive the sub-eikonal quark and gluon propagators which can serve as a starting point of studies of these effects.
Highlights
It is well known that high-energy behavior of QCD amplitudes can be described by the evolution of relevant Wilson-line operators
The typical example is the deep inelastic scattering (DIS) at low Bjorken xB, where the T-product of two electromagnetic currents can be approximated by a perturbative expansion in terms of coefficient functions and matrix elements of Wilson-line operators evaluated in the proton or nucleus state
The new evolution equations will describe, for example, the high-energy dynamics of scattering processes with spin. These sub-eikonal corrections to high-energy Operator Product Expansion (OPE) are similar to higher-twist corrections to the usual light-ray OPE [40] which are important part of QCD phenomenology [41,42,43,44]
Summary
It is well known that high-energy behavior of QCD amplitudes can be described by the evolution of relevant Wilson-line operators. The evolution equation of the Wilson-line operators with respect to the rapidity parameter provides the energy dependence of the cross section. This procedure takes the name of high-energy Operator Product Expansion (OPE) The subject of this paper is the derivation of these corrections to the quark and gluon propagator in the background of a shock-wave These results represent the first necessary step to include spin dynamics in the high-energy OPE formalism. [26, 27] sub-eikonal corrections to scalar and gluon propagators have been calculated in order to construct a formalism that provides evolution equations of gluon Transverse Momentum Distribution (TMD) from low to moderate xB. In the appendix we include an alternative derivation of the eikonal quark propagator and we calculate the sub-eikonal corrections to the gluon propagator in background-Feynman gauge
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