Gluon pseudo-distributions at short distances: Forward case

• DOI: 10.1016/j.physletb.2020.135621
• Publication Date: 2020-07-15T12:27:10Z
• Authors: Ian Balitsky; Wayne Morris; Anatoly Radyushkin
• Keywords: Quantum Physics; Physics; QC1-999; High Energy Physics - Lattice (hep-lat); FOS: Physical sciences; Gluon parton distribution functions; 530; 01 natural sciences; Elementary Particles and Fields and String Theory; High Energy Physics - Phenomenology; High Energy Physics - Lattice; High Energy Physics - Phenomenology (hep-ph); Lattice calculations; 0103 physical sciences; Gluon quark mixing

We present the results that are necessary in the ongoing lattice calculations of the 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 $\ln (-z^2)$-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. We also show that our results may be used for a rather straightforward calculation of the one-loop matching relations for quasi-PDFs.<br/>8 pages, 5 figures. Gluon-quark term added<br/>