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 Lz. However, the Jz = 1 2 sum rule includes an angular momentum component and can provide indirect access to properties of Lz. One of the other unknowns in the sum rule is the gluon polarization, ∆G. We can define the gluon spin asymmetry in a proton as A(x,Q2) = ∆G(x,Q ) G(x,Q) . This can be written as a sum of a Q2-invariant piece, A0(x) and a small Q 2-dependent term, ǫ(x,Q2). The x-dependence of A0 can be calculated and a suitable parametrization for ǫ(x,Q2) can be made to estimate this asymmetry. When combined with the measured unpolarized gluon density, G(x,Q2), this provides a model independent prediction for ∆G(x,Q2). 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, Lz.