A Lattice Study of Quark and Glue Momenta and Angular Momenta in the Nucleon

Abstract

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 $Z_4$ noise, and the signal-to-noise 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 $16^3\times 24$ quenched lattice at $\beta =6.0$ for Wilson fermions with $\kappa =0.154,0.155$, 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.

Renormalization section is expanded to include more details. There are slight changes in the final numbers. A few modification and corrections are made in the rest of the text

References in corpus (15)

• Extraction of Spin-Dependent Parton Densities and Their Uncertainties
• The angular momentum controversy: What's it all about and does it matter?
• Reply to the Comment on "Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited" [PRL 100:232002 (2008)]
• Spin and orbital angular momentum in gauge theories: Nucleon spin structure and multipole radiation revisited
• Measurement of Parton Distributions of Strange Quarks in the Nucleon from Charged-Kaon Production in Deep-Inelastic Scattering on the Deuteron
• The RHIC SPIN Program: Achievements and Future Opportunities
• Disconnected quark loop contributions to nucleon observables in lattice QCD
• Moments of nucleon generalized parton distributions from lattice QCD
• Evidence for the Absence of Gluon Orbital Angular Momentum in the Nucleon
• Generalized form factors, generalized parton distributions and the spin contents of the nucleon
• Gluon contributions to the pion mass and light cone momentum fraction
• Classical Limits of Scalar and Tensor Gauge Operators Based on the Overlap Dirac Matrix
• Perturbative Renormalization and Mixing of Quark and Glue Energy-Momentum Tensors on the Lattice
• Looking at the gluon moment of the nucleon with dynamical twisted mass fermions
• Finite density simulations using a determinant estimator

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