New relation between transverse angular momentum and generalized parton distributions

I derive a rigorous relation between the expectation value of the transverse component of the Belinfante version of the angular momentum ⟨JTᵇᵉˡ⟩ of a quark in a transversely polarized nucleon in terms of the generalized parton distributions H and E, namely ⟨JTᵇᵉˡ(quark)⟩=[1/2M][P₀∫_-1¹dxxEq(x,0,0)+M∫_-1¹dxxHq(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, whose content I spell out precisely, and which has proved extremely interesting in testing models, in comparing different definitions of quark and gluon angular momentum, and in comparing with lattice calculations. The transverse relation can offer additional insights into all of these, by extending them to the new domain of transversely polarized and moving nucleons.