PoS - Proceedings of Science
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
Unpolarized and polarized gluon pseudo-distributions at short distances: Forward case
W. Morris*, I. Balitsky and A. Radyushkin
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Pre-published on: May 16, 2022
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Abstract
We present the results that are necessary in the ongoing lattice calculations of the unpolarized and polarized gluon parton distribution functions (PDFs) within the pseudo-PDF approach. We give a classification of possible two-gluon correlator functions and identify those that contain the invariant amplitude determining the gluon PDF in the light-cone $z^2 \to 0$ limit. One-loop calculations have been performed in the coordinate representation and in an explicitly gauge-invariant form. We made an effort to separate ultraviolet (UV) and infrared (IR) sources of the $\ln\left(-z^2\right)$-dependence at short distances $z^2$. The UV terms cancel in the reduced Ioffe-time distribution (ITD), and we obtain the matching relation between the reduced ITD and the light-cone ITD. Using a kernel form, we get a direct connection between lattice data for the reduced ITD and the normalized gluon PDF.
DOI: https://doi.org/10.22323/1.396.0589
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