New relation between transverse angular momentum and generalized parton distributions

Original · EN

I derive a rigorous relation between the expectation value of the transverse component of the angular momentum <Jₜ> of a quark in a transversely polarized nucleon in terms of the Generalized Parton Distributions H and E, namely <Jₜ(quark)> = 1/2M [P₀ ∫ dx x Eq(x,0,0) + M ∫ dx x Hq(x,0,0)] where P₀ is the energy of the nucleon and where "quark" implies the sum of quark and antiquark of a given flavor. A similar relation holds for gluons. The result is remarkably similar to Ji's relation for the case of longitudinal polarization. In this revised version, I have rectified some misleading statements, introduced a more precise notation and specified mpre clearly the meaning of the terms in both the Ji and the new tranverse relation.