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The Gluon Moment and Parton Distribution Function of the Pion from Lattice QCD
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
in the
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.Comment: 13 pages, 5 figure