The Quark Orbital Angular Momentum in a Light-Cone Representation

Abstract

We perform an analysis of the quark angular momentum in a light-cone representation by taking into account the effect due to the Melosh-Wigner rotation and find that there is a relativistic correction factor connecting the quark orbital angular momentum with the quark model spin distribution: $L_q(x)={<M_L(x)>}\Delta q_{QM}(x)$. The quark orbital angular momentum $L_q(x)$ and the quark helicity distribution $\Delta q(x)$ are connected to the quark model spin distribution $\Delta q_{QM}(x)$ by a relation: $\frac{1}{2}\Delta q(x)+ L_q(x)=\frac{1}{2}\Delta q_{QM}(x)$, which means that one can decompose the quark model spin contribution $\Delta q_{QM}(x)$ by a quark helicity term $\Delta q(x)$ {\it plus} an orbital angular momentum term $L_q(x)$. There is also a new relation connecting the quark orbital angular momentum with the measurable quark helicity distribution and transversity distribution ($\delta q(x)$): $\Delta q(x)+L_q(x)=\delta q(x)$, from which we may have new sum rules connecting the quark orbital angular momentum with the nucleon axial and tensor charges.