Abstract
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 z2→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(−z2)-dependence at short distances z2. 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.
Highlights
Lattice calculations of parton distribution functions (PDFs) are a subject of considerable interest and efforts
There is no need to specify the nature of matrix element characteristic of a particular parton distribution. This means that one and the same Feynman diagram calculation may be used both for finding matching conditions for PDFs, and for distribution amplitude (DA)’s and generalized parton distributions (GPDs) corresponding to non-forward ones
We should choose the operators with the sets {μα; λβ} that contain Mpp in their parametrization. Note that it is the density of the momentum G(x) ≡ xf g (x) carried by the gluons rather than their number density f g (x) that is a natural quantity in this definition of the gluon PDF
Summary
Lattice calculations of parton distribution functions (PDFs) are a subject of considerable interest and efforts (see Ref. [1] for a recent review and references to extensive literature). The calculation is complicated by strict requirements of gauge invariance In this situation, a very effective method is provided by the coordinate-representation approach of Ref. The results are obtained in an explicitly gauge-invariant form In this approach, there is no need to specify the nature of matrix element characteristic of a particular parton distribution. There is no need to specify the nature of matrix element characteristic of a particular parton distribution This means that one and the same Feynman diagram calculation may be used both for finding matching conditions for PDFs (given by forward matrix elements), and for DA’s and GPDs corresponding to non-forward ones
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
