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

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.

Comments: The revised arXiv version incorporates minor updates to the figures and includes a preprint number