The Gluon Moment and Parton Distribution Function of the Pion from $N_f = 2 + 1 + 1$ Lattice QCD

TL;DR

This paper reports the first lattice QCD calculation of the pion gluon moment in the continuum-physical limit, providing a key insight into the pion's internal structure and gluon distribution.

Contribution

It introduces a novel lattice QCD approach to compute the pion gluon moment, including nonperturbative renormalization and continuum extrapolation, with results consistent with global fits and models.

Findings

Pion gluon moment: 0.364(38) in MS scheme at 2 GeV

Results align with global fits and QCD models

First continuum-physical limit calculation of this quantity

Abstract

We present the first calculation of the pion gluon moment from lattice QCD in the continuum-physical limit. 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, using ensembles generated by MILC Collaboration with 2+1+1 flavors of highly improved staggered quarks (HISQ). On the lattice, we nonperturbatively renormalize the gluon operator in RI/MOM scheme using the cluster-decomposition error reduction (CDER) technique to enhance the signal-to-noise ratio of the renormalization constant. We extrapolate the pion gluon moment to the continuum-physical limit and obtain $0.364(38)_{\text{stat}+\text{NPR}}(36)_\text{mixing}$ in the $\overline{\text{MS}}$ scheme at 2 GeV, with first error being the statistical error and uncertainties in nonperturbative renormalization, and the second being a systematic uncertainty estimating the effect of ignoring quark mixing. Our pion gluon momentum fraction has a central value lower than two recent single-ensemble lattice-QCD results near physical pion mass but is consistent with the recent global fits by JAM and xFitter and with most QCD-model estimates.