We present the first nonperturbatively renormalized determination of the glue momentum fraction ⟨xg in the nucleon, based on lattice-QCD simulations at the physical pion mass using the cluster-decomposition error reduction technique. We provide the first practical strategy to renormalize the gauge energy-momentum tensor nonperturbatively in the regularization-independent momentum-subtraction (RI/MOM) scheme and convert the results to the MS¯ scheme with one-loop matching. The simulation results show that the cluster-decomposition error reduction technique can reduce the statistical uncertainty of its renormalization constant by a factor of O(300) in calculations using a typical state-of-the-art lattice volume, and the nonperturbatively renormalized ⟨xg is shown to be independent of the lattice definitions of the gauge energy-momentum tensor up to discretization errors. We determine the renormalized ⟨xMS¯g(2  GeV) to be 0.47(4)(11) at the physical pion mass, which is consistent with the experimentally determined value.

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Published in Physical Review D, v. 98, issue 7, 074506, p. 1-9.

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

This group of authors is collectively known as the χQCD Collaboration.

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Funded by SCOAP3.

H. L. and Y. Y. are supported by the U.S. National Science Foundation under Grant No. PHY 1653405, “CAREER: Constraining Parton Distribution Functions for New-Physics Searches." This work is partially supported by DOE Grant No. DE-SC0013065 and the DOE TMD topical collaboration. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725. This work used Stampede time under the Extreme Science and Engineering Discovery Environment, which is supported by National Science Foundation Grant No. ACI-1053575. We also thank National Energy Research Scientific Computing Center for providing HPC resources that have contributed to the research results reported within this paper. We acknowledge the facilities of the USQCD Collaboration, which are funded by the Office of Science of the U.S. Department of Energy, used for this research in part. This work is supported in part by the National Science Foundation of China (NSFC) under the project No. 11775229, and by the Youth Innovation Promotion Association of CAS (2015013). Part of this work was performed using computing facilities at the College of William and Mary which were provided by contributions from the National Science Foundation, the Commonwealth of Virginia Equipment Trust Fund and the Office of Naval Research.