Abstract
There have been rapid developments in the direct calculation of the Bjorken-$x$ dependence of parton distribution functions (PDFs) using lattice QCD, and the technique shows promising results. Among various new methods, large-momentum effective theory (LaMET), which calculates boosted hadron matrix elements of multiple spatial displacements on the lattice, shows promising PDFs at physical pion mass by both ${\mathrm{LP}}^{3}$ and ETMC Collaborations. However, the finite-volume systematics have not yet been studied, and it has been suggested that such systematics can be more significant for LaMET-type operators than the traditional bilinear quark operators in charges and form factors. In this work, we present the first study of the finite-volume systematic for both isovector nucleon unpolarized and helicity matrix elements on three lattice volumes (2.88, 3.84, 4.8 fm) with lattice spacing 0.12 fm and 220-MeV pion mass. We perform two-state simultaneous fits using multiple source-sink separations to remove excited-state contamination and obtain reliable ground-state matrix elements. We then implement nonperturbative renormalization and Fourier transform the matrix elements to momentum-space quasi-PDFs. Overall, we do not see significant finite-volume systematics at the studied boost momenta of ${P}_{z}=1.3$ and 2.6 GeV.
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