First Self-Renormalized Gluon PDF of Nucleon from Large-Momentum Effective Theory in the Continuum Limit

TL;DR

This paper reports the first lattice-QCD calculation of the nucleon gluon PDF using LaMET with self-renormalization, continuum extrapolation, and high-statistics data, providing results consistent with some global fits.

Contribution

It introduces a self-renormalized LaMET approach for gluon PDFs in the continuum limit, with high-statistics lattice data and stability analysis across lattice spacings.

Findings

Gluon PDFs are stable across lattice spacings.

Results are compatible with continuum limit within errors.

Final PDFs favor near-zero gluonic density at high x.

Abstract

We present the first lattice-QCD determination of the nucleon gluon parton distribution function (PDF) within the large-momentum effective theory (LaMET) framework, employing the hybrid scheme with self renormalization, in the continuum limit. High statistics calculations with boost momentum $P_z \approx 2.0$-$2.2$~GeV are performed at lattice spacings of $a \approx \{ 0.15, 0.12, 0.09 \}$~fm, a pion mass of $M_\pi \approx 310$~MeV, with $N_f=2+1+1$ quark flavors. We apply gradient flow smearing with $\mathcal{T}_\text{W} = 3a^2$, finding that self-renormalization remains stable. The renormalized gluon matrix elements and PDFs show consistent behavior across lattice spacings, with the $a \approx 0.09$~fm results statistically compatible with the continuum limit. Our final LaMET gluon PDF compares reasonably with select global-fit determinations, specifically preferring analyses which have near-zero gluonic density in the $x \gtrsim 0.6$ region.