We report a complete calculation of the quark and glue momenta and angular momenta in the proton. These include the quark contributions from both the connected and disconnected insertions. The quark disconnected insertion loops are computed with Z4 noise, and the signal-to-noise ratio is improved with unbiased subtractions. The glue operator is comprised of gauge-field tensors constructed from the overlap operator. The calculation is carried out on a 163×24 quenched lattice at β=6.0 for Wilson fermions with κ=0.154, 0.155, and 0.1555, which correspond to pion masses at 650, 538, and 478 MeV, respectively. The chirally extrapolated u and d quark momentum/angular momentum fraction is found to be 0.64(5)/0.70(5), the strange momentum/angular momentum fraction is 0.024(6)/0.023(7), and that of the glue is 0.33(6)/0.28(8). The previous study of quark spin on the same lattice revealed that it carries a fraction of 0.25(12) of proton spin. The orbital angular momenta of the quarks are then obtained from subtracting the spin from their corresponding angular momentum components. We find that the quark orbital angular momentum constitutes 0.47(13) of the proton spin with almost all of it coming from the disconnected insertions.
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This work is partially supported by U.S. DOE Grant No. DE-FG05-84ER40154 and the Center for Computational Sciences of the University of Kentucky. The work of M. Deka is partially supported by the Institute of Mathematical Sciences, India. The work of T. Doi is supported in part by MEXT Grant-in-Aid for Young Scientists (B) (Grant No. 24740146).
Deka, M.; Doi, T.; Yang, Y. B.; Chakraborty, B.; Dong, S. J.; Draper, Terrence; Glatzmaier, M.; Gong, M.; Lin, H. W.; Liu, Keh-Fei; Mankame, D.; Mathur, N.; and Streuer, T., "Lattice Study of Quark and Glue Momenta and Angular Momenta in the Nucleon" (2015). Physics and Astronomy Faculty Publications. 309.