We present the first determination of the x-dependent pion gluon distribution from lattice QCD using the pseudo-PDF approach. We use lattice ensembles with 2+1+1 flavors of highly improved staggered ...quarks (HISQ), generated by MILC Collaboration, at two lattice spacings a≈0.12 and 0.15 fm and three pion masses Mπ≈220, 310 and 690 MeV. We use clover fermions for the valence action and momentum smearing to achieve pion boost momentum up to 2.29 GeV. We find that the dependence of the pion gluon parton distribution on lattice spacing and pion mass is mild. We compare our results from the lightest pion mass ensemble with the determination by JAM and xFitter global fits.
Parton distribution functions (PDFs) are important to characterize the structure of the hadrons such as protons and neutrons. The contribution to the structure from quarks has been studied in detail ...during the past few decades. The structure in the gluon sector is also important but less studied. For high-energy hadrons, the gluon contribution dominates at small x, where x is the momentum fraction carried by a quark or gluon. At large x, the uncertainty of the gluon PDF is large, especially compared to that of the quark PDFs at large x. Gluon PDFs for nucleons and pions are mostly extracted from global analysis of experimental data using perturbation theory as a guide. Theoretically, lattice QCD provides an independent non-perturbative theoretical approach to calculate the gluon PDFs. We present the exploratory study of nucleon gluon PDFs from lattice QCD using the quasi-PDF approach. Using valence overlap fermions on the 2 + 1-flavor domain-wall fermion gauge ensemble, the quasi-PDF matrix elements we obtain agree with the Fourier transform of the global-fit PDF within statistical uncertainty. We further study the x-dependent nucleon and pion gluon distributions via the pseudo-PDF approach on lattice ensembles with 2 + 1 + 1 flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration. Using clover fermions for the valence action, and adding momentum smearing, PDFs are found for pion boost momenta up to 2.56 ≈ GeV. Several lattice sizes and spacings (a ≈ 0.9, 0.12 and 0.15 ≈ fm) were evaluated, resulting in three pion masses, Mπ ≈ 220, 310 and 690 ≈ MeV/c2.
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.
We present the key results from the first study of the \(x\)-dependent nucleon gluon distribution from lattice QCD extrapolated to the physical-continuum limit. We use ensembles with \(2+1+1\) ...flavors of highly improved staggered quarks (HISQ) generated by the MILC Collaboration with clover fermions for the valence action on three different lattice spacings and three different pion masses. We took up to \(O(10^6)\) measurements of two-point correlators, obtaining good signal at boost momenta up to 3~GeV. We extrapolated the reduced pseudo-ITD matrix elements to the physical-continuum limit before extracting \(xg(x)/\langle x \rangle_g\). Then using the gluon momentum fraction \(\langle x \rangle_g\) calculated on the same configurations, we determine the unpolarized nucleon gluon PDF \(xg(x)\) and compare results with other lattice and selected global fits.
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 \(a \approx 0.9\), 0.12 and 0.15~fm and three pion masses \(M_\pi \approx 220\), 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-ITD matrix elements obtained from the lattice calculation, then extrapolate them to the continuum-physical limit before extracting \(xg(x)/\langle x \rangle_g\). We use the gluon momentum fraction \(\langle x \rangle_g\) 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.
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