On the observability of the quark orbital angular momentum distribution

Aurore Courtoy,Gary R Goldstein,J Osvaldo Gonzalez Hernandez,Simonetta Liuti,Abha Rajan

doi:10.1016/j.physletb.2014.02.017

Abstract

We argue that due to parity constraints, the helicity combination of the purely momentum space counterparts of the Wigner distributions – the generalized transverse momentum distributions – that describes the configuration of an unpolarized quark in a longitudinally polarized nucleon can enter the deeply virtual Compton scattering amplitude only through matrix elements involving a final state interaction. The relevant matrix elements in turn involve light-cone operators projections in the transverse direction, or they appear in the deeply virtual Compton scattering amplitude at twist three. Orbital angular momentum or the spin structure of the nucleon was a major reason for these various distributions and amplitudes to have been introduced. We show that the twist three contributions associated with orbital angular momentum are related to the target-spin asymmetry in deeply virtual Compton scattering, already measured at HERMES.

Highlights

Understanding the angular momentum or spin structure of the nucleon is a major reason for these various distri
ITALY, Italy 4University of Virginia - Physics Department, 382 McCormick Rd., Charlottesville, Virginia 22904 - USA and Laboratori Nazionali di Frascati, INFN, Frascati, Italy. 5University of Virginia - Physics Department, 382 McCormick Rd., Charlottesville, Virginia 22904 - USA We argue that due to Parity constraints, the helicity combination of the purely momentum space counterparts of the Wigner distributions – the generalized transverse momentum distributions – that describes the configuration of an unpolarized quark in a longitudinally polarized nucleon, can enter the deeply virtual Compton scattering amplitude only through matrix elements involving a final state interaction
We show that the twist three contributions associated to orbital angular momentum are related to the target-spin asymmetry in deeply virtual Compton scattering, already measured at HERMES

Summary

On the Observability of the Quark Orbital Angular Momentum Distribution

The twist three correlator does not map directly onto a 2-body process For this reason there are twice as many vector and axial vector twist three GPDs and TMDs. As we have noted, for the non flip quark-proton helicity amplitudes at twist three one finds that the chiral even structures correspond to what would be chiral odd at twist two, AtΛw±3 ,Λ± → AtΛw±2 ,Λ∓. In Ref.[32] the quarks and gluons angular momentum components were identified with observables obtained from Deeply Virtual Compton Scattering (DVCS) type experiments Both Jq(g) and Lq can be measured owing to the well known relation involving twist two GPDs, dx x(Hq(g)(x, 0, 0) + Eq(g)(x, 0, 0)) = Jq(g) →.

Sum Rule Integrand

AULsin q