Gluon Transverse-Momentum-Dependent Distributions from Large-Momentum Effective Theory

Abstract

We demonstrate that gluon transverse-momentum-dependent parton distribution functions (TMDPDFs) can be extracted from lattice calculations of appropriate Euclidean correlations in large-momentum effective theory (LaMET). Based on perturbative calculations of gluon unpolarized and helicity TMDPDFs, we present a matching formula connecting them and their LaMET counterparts, where the latter are renormalized in a scheme facilitating lattice calculations and converted to the $\overline{\mathrm{MS}}$ scheme. The hard matching kernel is given up to one-loop level. We also show that the perturbative result is independent of the prescription used for the pinch-pole singularity in the relevant correlations. Our results offer a guidance for the extraction of gluon TMDPDFs from lattice simulations, and have the potential to greatly facilitate perturbative calculations of the hard matching kernel.

22 pages, 5 figures. Corrected a few typos. Accepted for publication in JHEP

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• Light Cone Distribution Amplitude for the $\Lambda$ Baryon from Lattice QCD
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Collins-Soper kernel from lattice QCD at the physical pion mass
• Counting linearly polarized gluons with lattice QCD
• Lattice QCD Benchmark of Proton Helicity and Flavor-Dependent Unpolarized Transverse Momentum-Dependent Parton Distribution Functions at Physical Quark Masses