Light-Cone Parton Distribution Functions from Lattice QCD

We extract parton distribution functions (PDFs) of the nucleon from lattice QCD using an ensemble of gauge field configurations simulated with light quark masses fixed to their physical values. Theoretical and algorithmic improvements that allow such a calculation include momentum smearing to reach large nucleon boosts with reduced statistical errors, nonperturbative renormalization, target mass corrections, and a novel modified matching of lattice QCD results to connect to what is extracted from experimental measurements. We give results on the unpolarized and helicity PDFs in the modified minimal subtraction scheme at a scale of 2 GeV and reproduce the main features of the experimentally determined quantities, showing an overlap for a range of Bjorken-$x$ values. This first direct nonperturbative evaluation opens a most promising path to compute PDFs in an ab initio way on the lattice and provides a framework for investigating also a wider class of similar quantities, which require the evaluation of hadronic matrix elements of nonlocal operators.

Figure 1

Comparison of unpolarized (upper panel) and polarized (lower panel) bare matrix elements for momenta $6\pi /L$ (blue circles), $8\pi /L$ (red diamonds), and $10\pi /L$ (green stars) using five stout steps.

Figure 2

Comparison of unpolarized PDF at momenta $6\pi /L$ (green band), $8\pi /L$ (red band), and $10\pi /L$ (blue band). The results from the phenomenological analysis of ABMP16 [56] (NNLO), NNPDF [57] (NNLO), and CJ15 [55] (NLO) are displayed for illustrative purposes. Logarithmic scale is used in the $x$ axis (down to $|x|=0.035$) for better visibility.

Figure 3

Comparison of polarized PDF at momenta $6\pi /L$ (green band), $8\pi /L$ (red band), and $10\pi /L$ (blue band), DSSV08 [58], NNPDF1.1pol [59], and JAM17 NLO phenomenological data [60]. Logarithmic scale is used in the $x$ axis (down to $|x|=0.035$) for better visibility.

Figure 4

Upper panel: Comparison of unpolarized PDF from the B55 ensemble and phenomenological determinations. Lower panel: Unpolarized PDF using the ensemble of this Letter (blue) and from the B55 ensemble (orange) at momentum $\sim 1.4\mathrm{GeV}$.