Quark orbital angular momentum from lattice QCD

Abstract

We calculate the quark orbital angular momentum of the nucleon from the quark energy-momentum tensor form factors on the lattice with the quenched approximation. The disconnected insertion is estimated stochastically which employs the Z 2 noise with an unbiased subtraction. This reduced the error by a factor of 3-4 with negligible overhead. The total quark contribution to the proton spin is found to be 0.30Ϯ0.07. From this and the quark spin content we deduce the quark orbital angular momentum to be 0.17Ϯ0.06 which is ϳ34% of the proton spin. We further predict that the gluon angular momentum is 0.20Ϯ0.07; i.e., ϳ40% of the proton spin is due to the glue.

Chiral structure of nucleon gravitational form factors

“…A pragmatic application of our present results consists of their use for extrapolation of experimental measurements of the angular momentum sum rule (6) to zero momentum transfer [5] and as a fit formula for lattice simulations of the parton angular momentum by means of the nucleon gravitational form factors [9]. Our considerations can be extended to other single-nucleon observables such as parity-odd generalized parton distributions as well as off-forward quark transversity and tensor gluon form factors.…”

“…Carlo simulations [9,10] were done with lattices 16 2 × 32 where ∆ 2 min ∼ 0.4 GeV 2 . Thus in order to enter the regime of validity of χPT one needs repeat the simulations with bigger lattices.…”

Interplay of Spin and Orbital Angular Momentum in the Proton

“…One should observe that these calculations were performed at fairly large quark mass and omit disconnected terms, which may carry significant orbital angular momentum [26] and are certainly needed to account for the U(1) axial anomaly. Nevertheless, the apparent discrepancy is of concern.…”

Energy–momentum tensor form factors of the nucleon within a π–ρ–ω soliton model

“…The EMT form factors of the nucleon have been investigated in various approaches, for example, in lattice QCD [12,13,14,15,16,17,18,19], in chiral perturbation theory [20,21,22,23,24], in the chiral quark-soliton model (χQSM) [25,26,27,28,29,30,31,32] as well as in the Skyrme model [33]. Those of nuclei have also been studied [10,34,35,36].…”