Unpolarized gluon PDF of the nucleon from lattice QCD in the continuum limit

TL;DR

This work delivers a first-principles lattice-QCD determination of the unpolarized nucleon gluon PDF using LaMET, with three lattice spacings $a=\\{0.105,0.0897,0.0775\\}$ fm, $m_\\pi\\approx 300$ MeV, and nucleon momenta up to $P_z\\approx 1.97$ GeV. It employs distillation smearing, a hybrid nonperturbative renormalization, and one-loop perturbative matching, followed by simultaneous extrapolation to the continuum and infinite-momentum limit to obtain the light-cone PDF. The resulting $x g(x)/\\langle x \\rangle$ is consistent with global fits within the enlarged uncertainties, validating the lattice-LaMET program for gluon PDFs while highlighting remaining systematics in large-\\lambda extrapolations and high-momentum data. The paper outlines concrete paths to improve precision, including momentum smearing, finer lattices, chiral extrapolations, and renormalization-group resummations to extend the reliable $x$-range and reduce scale dependence.

Abstract

We report a state-of-the-art lattice QCD calculation of the nucleon gluon parton distribution function employing large-momentum effective theory. The calculation is carried out on the 2+1 flavour CLQCD ensembles with three lattice spacings a={0.105,0.0897,0.0775} fm and pion mass of approximately 300 MeV, covering nulceon momenta up to 1.97 GeV. Distillation technique is applied to improve the signal of two-point correlators. We then apply the state-of-the-art hybrid renormalization and one-loop perturbative matching, and extrapolate the result to the continuum and infinite momentum limit. Our result is in agreement with that from global analysis within errors.

Figures (12)

• Figure 1: Comparison of renormalized matrix elements with the perturbative one-loop $\overline{\text{MS}}$ results (black curve). Error bars represent the renormalized matrix elements of each lattice spacing. $g(z)$ is the residual from the fitting process and $\rm{exp}[g(z)-m_0 z]$ (gray band) indicates the $a$-independent renormalized matrix element.
• Figure 2: The renormalized matrix elements of C24P29 (upper) , E32P29 (middle), and F32p30 (lower) as a function of $z$ at scale $\mu=2$ GeV, with different colors corresponding to different nucleon momenta.
• Figure 3: Results of the light-cone PDF $xg(x)/\langle x \rangle$ of three ensembles. The colored bands illustrate the results obtained at different lattice spacings and different momenta. The gray band, repeated across the three figures, illustrates the result extrapolated to infinite momentum limit and continuum limit. Only statistic uncertainties are considered in the plot.
• Figure 4: LPC prediction of unpolarized gluon PDF in the continuum and infinite-momentum limit $xg(x)/\langle x \rangle$ in comparison with global fit results. The deep blue band indicates statistical uncertainties of our result, while the light blue band represents the combined effects of both statistical and systematic uncertainties. The gray bands denote the regions where LaMET results are considered unreliable.
• Figure 5: Illustration of the three-point correlator of gluon.