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