We report results on the proton mass decomposition and also on related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of Nf = 2 + 1 domain wall fermion configurations with three lattice spacings and three volumes, and several pion masses including the physical pion mass. With fully nonperturbative renormalization (and universal normalization on both quark and gluon), we find that the quark energy and glue field energy contribute 32(4)(4)% and 36(5)(4)% respectively in the MS¯ (modified minimal substraction) scheme at μ = 2 GeV. A quarter of the trace anomaly gives a 23(1)(1)% contribution to the proton mass based on the sum rule, given 9(2)(1)% contribution from the u, d, and s quark scalar condensates. The u, d, s, and glue momentum fractions in the MS¯ scheme are in good agreement with global analyses at μ = 2 GeV.
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Y. Y. is supported by the US National Science Foundation under Grant No. PHY 1653405 “CAREER: Constraining Parton Distribution Functions for New-Physics Searches." Y. C. and Z. L. acknowledge the support of the National Science Foundation of China under Grants No. 11575196, No. 11575197, and No. 11335001. This work is partially supported by DOE Grant No. DE-SC0013065 and by 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 (XSEDE), which is supported by National Science Foundation Grant No. ACI-1053575. We also thank the National Energy Research Scientific Computing Center (NERSC) for providing HPC resources that have contributed to the research results reported within this Letter. We acknowledge the facilities of the USQCD Collaboration used for this research in part, which are funded by the Office of Science of the U.S. Department of Energy.
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.121.212001 for the details of the calculation and error estimation of the non-perturbative renormalization of the quark and glue energy momentum tensor.
Yang, Yi-Bo; Liang, Jian; Bi, Yu-Jiang; Chen, Ying; Draper, Terrence; Liu, Keh-Fei; and Liu, Zhaofeng, "Proton Mass Decomposition from the QCD Energy Momentum Tensor" (2018). Physics and Astronomy Faculty Publications. 629.