Abstract
We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach. The lattice calculation is carried out with pion masses of 340 and 678MeV on a (2+1)-flavor domain-wall fermion configuration with lattice spacing a=0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93GeV. Taking the normalization from similar matrix elements in the rest frame of the nucleon and pion, our results for these matrix elements are consistent with the Fourier transform of the global fit CT14 and PDF4LHC15 NNLO of the gluon PDF, within statistical uncertainty and the systematic one up to power corrections, perturbative O(α_{s}) matching and the mixing from the quark PDFs.
Highlights
We present the first attempt to access the x dependence of the gluon unpolarized parton-distribution function (PDF), based on lattice simulations using the large-momentum effective theory approach
In the large momentum limit, only the leading twist contribution in gðxÞ survives, and gðxÞ can be factorized into the gluon PDF gðyÞ and a perturbative calculable kernel Cðx; yÞ, up to mixing with the quark PDF and the higher-twist corrections Oð1=P2zÞ
For the linear divergence introduced by the Wilson link, an empirical observation in the quark unpolarized quasi-PDF case is that the nonperturbative RI/MOM renormalization constant with pRz 1⁄4 0 can be approximated by the nucleon isovector matrix element with Pz 1⁄4 0 in the z < 0.5 fm region, with ∼10% deviation, while the systematic uncertainties due to the hadron IR structure are hard to estimate [15]
Summary
The lattice calculation is carried out with pion masses of 340 and 678 MeV on a (2 þ 1)-flavor domain-wall fermion configuration with lattice spacing a 1⁄4 0.111 fm, for the gluon quasi-PDF matrix element with the nucleon momentum up to 0.93 GeV. In the large momentum limit, only the leading twist contribution in gðxÞ survives, and gðxÞ can be factorized into the gluon PDF gðyÞ and a perturbative calculable kernel Cðx; yÞ, up to mixing with the quark PDF and the higher-twist corrections Oð1=P2zÞ.
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