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: $L_q(x)=<M_L(x)>\hat{I}”q_{QM}(x)$. The quark orbital angular momentum $L_q(x)$ and the quark helicity distribution $\hat{I}”q(x)$ are connected to the quark model spin distribution $\hat{I}”q_{QM}(x)$ by a relation: $\frac{1}{2}\hat{I}”q(x)+L_q(x)=\frac{1}{2}\hat{I}”q_{QM}(x)$, which means that one can decompose the quark model spin contribution $\hat{I}”q_{QM}(x)$ by a quark helicity term $\hat{I}”q(x)$ {\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 ($\hat{I}´q(x)$): $\hat{I}”q(x)+L_q(x)=\hat{I}´q(x)$, from which we may have new sum rules connecting the quark orbital angular momentum with the nucleon axial and tensor charges.

20 latex pages, including an eps figure, to appear in Phys. Rev. D