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. The disconnected insertion is estimated stochastically which employs the $Z_2$ noise with an unbiased subtraction. This reduced the error by a factor of 4 with negligible overhead. The total quark contribution to the proton spin is found to be $0.30 \pm 0.07$. From this and the quark spin content we deduce the quark orbital angular momentum to be $0.17 \pm 0.06$ which is $\sim 34$% of the proton spin. We further predict that the gluon angular momentum to be $0.20 \pm 0.07$, i. e. $\sim$ 40% of the proton spin is due to the glue.

Figures (7)

• Figure 1: Quark skeleton diagrams for the three-point function $G_{NT_{4 j}N}(t_{2},t_{1},\vec{p},-\vec{q})$. (a) is the connected insertion. (b) is the disconnected insertion.
• Figure 2: Dipole fitting for $T_{CI}(q^2)$ at 4 different $\kappa$ values.
• Figure 3: Chiral extrapolation for $J_{q, CI}$ as a function of the quark mass. The value at the chiral limit is indicated by $\bullet$.
• Figure 4: The summed ratios of Eq.(\ref{['ratio']}) for the DI are plotted for different time slice $t_2$ with and without unbiased subtraction. Ratios without subtraction are shifted slightly towards right.
• Figure 5: The summed ratios of Eq.(\ref{['ratio']}) for the DI are plotted for $|\vec{q}| = 2\pi/La$.