Probing the Orbital Angular Momentum through the Polarized Gluon Asymmetry

The orbital angular momentum is one of the least understood of the spin characteristics of a proton. There are no direct ways to model the orbital angular momentum. However, the Jz=1/2 sum rule includes an angular momentum component and can provide indirect access to its properties. One of the other unknowns in the sum rule is the gluon polarization. We can define the gluon spin asymmetry in a proton as the ratio of the polarized to unpolarized gluon distributions. This can be written as a sum of a scale-invariant piece and a small scale-dependent term. The x-dependence of the asymmetry can be calculated and a suitable parametrization for scale-dependent term can be made to estimate this asymmetry. When combined with the measured unpolarized gluon density, this provides a model independent prediction for the polarized gluon distribution. This eliminates one unknown in the Jz=1/2 sum rule and allows a reasonable estimate for the size and evolution of the orbital angular momentum of the constituents.