Transverse Orbital Angular Momentum in the Proton

Using the equations of motion of QCD and Lorentz invariance relations, we show a new, more direct way of obtaining a sum rule for the proton’s quark transverse angular momentum in terms of contributions identified as spin and orbital components. The new sum rule can be understood as a twist-three relation, with the parton distribution g T encoding the quark transverse spin. We find that the complementary orbital component can be expressed in terms of a moment in the quark transverse momentum, k T , of the generalized transverse momentum-dependent distribution F 12 , or alternatively in terms of the twist-three generalized parton distributions H 2 T and E ˜ 2 T .