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.
Highlights
JHEP12(2021)010 may argue that this is an indication for “zero-mode” terms in F (x)
We present results for one-loop corrections to the recently introduced “gluon condensate” PDF F (x)
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
Summary
It is implied that the GG bilocal operator is in a T -product with the S-matrix, i.e. one deals with an “uncut” PDF This means that, in perturbation theory, all the diagram lines correspond to usual propagators. A non-vanishing result may be obtained if one takes off-shell gluons with p2 = 0 This has been done, in particular, by the authors of ref. Dμν (k) = gμν − kμnν + kν nμ n·k in the light-cone gauge Using the latter, and the dimensional regularization (DR) with D = 4 − 2 , a one loop calculation was performed in ref. The term ∼ 1/x, singular for x = 0, comes from the light-cone-gauge denominator factor 1/(kn) which, surprizingly, is not cancelled by numerator factors in this calculation A natural suspect for the origin of the discrepancy between the two results and of their peculiar features is the violation of gauge invariance stemming from using virtual external gluons
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