Gluon parton distribution of the nucleon from (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>)-flavor lattice QCD in the physical-continuum limit
Zhouyou Fan, William Good, Huey-Wen Lin
Abstract
We present the first physical-continuum limit $x$-dependent nucleon gluon distribution from lattice QCD using the pseudo-PDF approach, on lattice ensembles with $2+1+1$ flavors of highly improved staggered quarks (HISQ), generated by MILC Collaboration. We use clover fermions for the valence action on three lattice spacings $a\ensuremath{\approx}0.9$, 0.12 and 0.15 fm and three pion masses ${M}_{\ensuremath{\pi}}\ensuremath{\approx}220$, 310 and 690 MeV, with nucleon two-point measurements numbering up to $O({10}^{6})$ and nucleon boost momenta up to 3 GeV. We study the lattice-spacing and pion-mass dependence of the reduced pseudo--Ioffe-time distribution matrix elements obtained from the lattice calculation, then extrapolate them to the continuum-physical limit before extracting $xg(x)/⟨x{⟩}_{g}$. We use the gluon momentum fraction $⟨x{⟩}_{g}$ calculated from the same ensembles to determine the nucleon gluon unpolarized PDF $xg(x)$ for the first time entirely through lattice-QCD simulation. We compare our results with previous single-ensemble lattice calculations, as well as selected global fits.