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We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-

Parton distribution functions (PDFs) are universal nonperturbative properties of the nucleon which describe the probability densities of quarks and gluons seen by an observer moving at the speed of light relative to the hadron. The unpolarized PDFs can be used as inputs to predict cross sections in high-energy scattering experiments, one of the major successes of QCD. These distributions can be extracted through global analysis using multiple experiments by factorizing the hard-scattering cross sections into the PDFs and short-distance matrix elements that are calculable in perturbation theory. Today, multiple collaborations provide regular updates concerning the phenomenological determination of the PDFs

A new approach for the direct computation of the

Recent renormalized quasi-PDF studies have shown oscillatory behavior

In this paper, we take the CT14 NNLO PDF

The real (top left) and imaginary (top right) pseudonucleon matrix elements derived from CT14 PDFs as functions of

Using the ideal pseudodata

(Left) The quasi-PDFs obtained from the matrix elements shown in Fig.

One solution proposed here is to remove these oscillations by means of a low-pass filter. Note that such a filter should be

(Top left) The filter shapes proposed to apply to

We expect to test the filter function on the known PDFs through similar exercises in this work, then use the same function on lattice data; the mismatch region between the original PDFs and the quasi-PDFs tells us where lattice systematics are present.

Another idea is the “derivative” method; this should not only remove the unphysical oscillation but also allow us to reach smaller

The real (top left) and imaginary (top right) components of

The quasi-PDFs using the derivative method [and a filter

We apply the improved PDF methods to the lattice nucleon matrix elements from clover-on-HISQ lattices

The unpolarized (left) and polarized (right) isovector nucleon PDFs as functions of

In this paper, we propose two ideas to remove the current biggest systematic uncertainty in the LaMET approach to studying

We thank the MILC Collaboration for sharing the lattices used to perform this study. The LQCD calculations were performed using the