On the observability of the quark orbital angular momentum distribution

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 distributionsthat 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 to orbital angular momentum are related to the target-spin asymmetry in deeply virtual Compton scattering, already measured at HERMES.PACS numbers: 13.60.Hb, 13.40.Gp, 24.85.+p 1. Considerable attention has been devoted to the partons' Transverse Momentum Distributions (TMDs), to the Generalized Parton Distributions (GPDs), and to finding a connection between the two [1-3]. TMDs are distributions of different spin configurations of quarks and gluons within the nucleon whose longitudinal and transverse momenta can be accessed in Semi-Inclusive Deep Inelastic Scattering (SIDIS). GPDs are real amplitudes for quarks or gluons being probed in a hard process and then returning to reconstitute a scattered nucleon. They are accessed through exclusive electroproduction of vector bosons along with the nucleon. In each case there is a nucleon matrix element of bilinear, non-local quark or gluon field operators. In principle both TMDs and GPDs are different limits of Wigner distributions, i.e. the phase space distributions in momenta and impact parameters. The purely momentum space form of those are the Generalized TMDs (GTMDs). GTMDs correlate hadronic states with same parton longitudinal momentum, x (assuming zero skewness), different relative transverse distance, z T = b in − b out , between the struck parton's initial and final (out) states, and same average transverse distance, b = (b in + b out )/2, of the struck parton with respect to the center of momentum [4] (Figure 1a).Understanding the angular momentum or spin structure of the nucleon is a major reason for these various distri-FIG. 1: (a) Left: Correlation function for a GTMD; (b) quark-proton scattering in the u-channel.

Parton transverse momentum and orbital angular momentum distributions

“…W U is obtained by Fourier-transforming (2) for Γ = γ + from z − z to the quark intrinsic momentum k (the average of the initial and final quark momenta in the symmetric system of variables [8]), projecting onto (z − z ) + = 0, as well as from the (transverse) momentum transfer ∆ T (the difference between the initial and final quark momenta) to the transverse position b T . If one foregoes the transformation to b T , one can relate L U q to the k 2 T moment of 1 Throughout this paper we consider zero skewness, i.e., the plus component of the momentum transfer vanishes, ∆ + = 0.…”

“…(note that, in [8], E 2T and G 2 were identified as encoding similar twist-three structures, without, however, providing the precise relationship given in (5)).…”

Single and double spin asymmetries for deeply virtual Compton scattering measured with CLAS and a longitudinally polarized proton target

“…Therefore, observing a sizeable sin 2φ component in the target-spin asymmetry would mean having some sensitivity to twist-three CFFs. A recent paper [33] pointed In the highest −t bin of the third (Q 2 -xB) bin, β was set to zero due to the limited φ coverage, while no fit is performed on the first −t bin of the highest (Q 2 -xB) bin, where only one data point is present. The curves show the predictions of the VGG [23] (red-dashed) and KMM12 [26] (green-dotted) models.…”

Recent Developments in Nucleon Spin Decomposition

“…The next big question for the community is, 'Can we measure the canonical OAM in experiments?' This is a very difficult problem as discussed for instance in [29]. However, there is some hope.…”