Spin Structure of the Nucleon in the Asymptotic Limit

Abstract

In analogy to the Altarelli-Parisi equation for the quark and gluon helicity contributions to the nucleon spin, we derive an evolution equation for the quark and gluon orbital angular momenta. The solution of the combined equations yields the asymptotic fractions of the nucleon spin carried by quarks and gluons: 3n f /(16 + 3n f ) and 16/(16 + 3n f ), respectively, where n f is the number of active quark flavors. These are identical to the well-known asymptotic partitions of the nucleon momentum between quark and gluon contributions. We show that the axial-anomaly contribution to the quark helicity is cancelled by a similar contribution to the quark orbital angular momentum, making the total quark contribution to the nucleon spin anomalyfree.

Interplay of Spin and Orbital Angular Momentum in the Proton

“…Nevertheless, the apparent discrepancy is of concern. At this point, we recall the crucial fact that neither the total, nor the orbital angular momentum is renormalization group invariant (RGI) [27]. The lattice QCD values are evaluated at a scale set by the lattice spacing, around 4 GeV 2 .…”

Off-forward matrix elements in light-front Hamiltonian QCD

“…(31) and (32), one also verifies that in perturbation theory the total quark (gluon) momentum contribution is identical to the total quark (gluon) helicity contribution. This result is expected from the fixed point solutions of the leading log evolution equations of J q and J g calculated in [12], which shows that the partition of the nucleon spin between quarks and gluons follows the partition of nucleon momentum.…”

QCD form factors and hadron helicity nonconservation

“…1 OAM can also be re-expressed with generalized parton distributions in a manifestly gauge-invariant formalism [8,9].…”