Spin Structure of the Nucleon in the Asymptotic Limit

In analogy with the Altarelli-Parisi equation for quark and gluon helicity contributions to the nucleon spin, we derive an evolution equation for quark and gluon orbital angular momenta. Solution of the combined equations yields asymptotic fractions of the nucleon spin carried by quarks and gluons: $\Delta \Sigma {/2+L}_q{=3n}_f/\left({16+3n}_f\right)$ and $\Delta {g+L}_g=16/\left({16+3n}_f\right)$, respectively, with $n_f$ the number of active quark flavors. These are identical to the well-known asymptotic partitions of the nucleon momentum between quark and gluon contributions. The axial-anomaly contribution to the quark helicity is canceled with a similar contribution to the quark orbital angular momentum, making the total quark contribution to the nucleon spin anomaly free.