Abstract
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.
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Radyushkin, A., Zhao, S. One-loop structure of parton distribution for the gluon condensate and “zero modes”. J. High Energ. Phys. 2021, 10 (2021). https://doi.org/10.1007/JHEP12(2021)010
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DOI: https://doi.org/10.1007/JHEP12(2021)010