We present results for one-loop corrections to the recently introduced "gluon condensate" PDF F(x). In particular, we give expression for the gg-part of its evolution kernel. To enforce strict compliance with the gauge invariance requirements, we have used on-shell states for external gluons, and have obtained identical results both in Feynman and light-cone gauges. No "zero mode" δ(x) terms were found for the twist-4 gluon PDF F(x). However a q2δ(x) term was found for the ξ=0 GPD F(x,q2) at nonzero momentum transfer q. Overall, our results do not agree with the original attempt of one-loop calculations of F(x) for gluon states, which sets alarm warning for calculations that use matrix elements with virtual external gluons and for lattice renormalization procedures based on their results.
@article{arxiv.2111.00887,
title = {One-loop structure of parton distribution for the gluon condensate and "zero modes"},
author = {Anatoly Radyushkin and Shuai Zhao},
journal= {arXiv preprint arXiv:2111.00887},
year = {2021}
}