Gluon moment and parton distribution function of the pion from $N_f=2+1+1$ lattice QCD

Journal Article · 11 June 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.109.114509 · OSTI ID:2474164

Good, William ; Hasan, Kinza; Chevis, Allison ; Lin, Huey-Wen

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 $⟨x{⟩}_g=0.394\left(58{)}_{\mathrm{stat}+\mathrm{NPR}}\right(39{)}_{\text{mixing}}$ in the $\overline{\mathrm{MS}}$ 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. Published by the American Physical Society 2024

• Sponsoring Organization: USDOE
• Grant/Contract Number: AC02-05CH11231; SC0024053
• OSTI ID: 2474164
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 11 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English