Nonperturbatively Renormalized Nucleon Gluon Momentum Fraction in the Continuum Limit of $N_f=2+1+1$ Lattice QCD

TL;DR

This paper reports a nonperturbative lattice QCD calculation of the nucleon gluon momentum fraction, achieving continuum limit extrapolation with improved signal techniques, and provides results consistent with recent studies.

Contribution

It introduces a nonperturbative renormalization method for the nucleon gluon momentum fraction using $2+1+1$ flavor ensembles and demonstrates the effectiveness of the CDER technique for signal enhancement.

Findings

Gluon momentum fraction in the nucleon is approximately 0.492 at 2 GeV.

The CDER technique significantly improves the signal at finer lattice spacings.

Results are consistent with other recent lattice QCD calculations at physical pion mass.

Abstract

We present the nonperturbatively renormalized nucleon gluon momentum fraction using ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. The calculation is done using clover fermions for the valence action with three pion masses, $220$, $310$ and $690$ MeV and three lattice spacings, 0.09, 0.12, and 0.15 fm. The renormalization is done using RI/MOM nonperturbative renormalization and using cluster-decomposition error reduction (CDER) to enhance the signal-to-noise ratio of the renormalization constant. We find the CDER technique is particularly important to improve the signal at the finer lattice ensembles where the lattice volume is larger. We extrapolate the gluon momentum fraction to the continuum-physical limit and obtain $\langle x \rangle_g = 0.492(52)_\text{stat.+NPR}(49)_\text{mixing}$ in the $\bar{\text{MS}}$ scheme at 2 GeV, where first error includes the statistical error and uncertainties in nonperturbative renormalization, while the latter systematic accounts for ignoring quark mixing. Our gluon momentum fraction is consistent with other recent lattice-QCD results at physical pion mass.