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

Alex NieMiera; William Good; Huey-Wen Lin; Fei Yao

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

Alex NieMiera, William Good, Huey-Wen Lin, Fei Yao

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 $M_π\approx 310$~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.

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

Abstract

~GeV are performed at lattice spacings of

~fm, a pion mass of

~MeV, with

quark flavors. We apply gradient flow smearing with

, finding that self-renormalization remains stable. The renormalized gluon matrix elements and PDFs show consistent behavior across lattice spacings, with the

~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

region.

Paper Structure (9 equations, 3 figures, 1 table)

This paper contains 9 equations, 3 figures, 1 table.

Figures (3)

Figure 1: The renormalized matrix elements across each lattice spacing (data points) compared to the perturbative one-loop $\overline{\text{MS}}$ result illustrated by the black curve. We denote the short distance region as $z \in [0.05, 0.36]$ fm as illustrated by the blue band, and the lattice-spacing--independent matrix element $\text{exp}[g(z) - m_0 z]$ by the grey band.
Figure 2: Renormalized lattice matrix elements (colored points) across three ensembles for $P_z \approx 2.0$-$2.2$ GeV compared to the continuous renormalized matrix elements (colored bands) obtained through the large-$\nu$ extrapolations and the continuum-extrapolated renormalized matrix element (gray band) obtained through Eq. \ref{['eq:cont_extrap']}.
Figure 3: (upper) The MSULat unpolarized gluon PDF at $P_z = 2.12$ GeV in the continuum limit, shown alongside results obtained at individual lattice spacings. (lower) The MSULat unpolarized gluon PDF at $P_z = 2.12$ GeV compared to select phenomenological determinations.