Observables for Quarks and Gluons Orbital Angular Momentum Distributions

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

doi:10.1142/s2010194515600393

Abstract

We discuss the observables that have been recently put forth to describe quarks and gluons orbital angular momentum distributions. Starting from a standard parameterization of the energy momentum tensor in QCD one can single out two forms of angular momentum, a so-called kinetic term – Ji decomposition – or a canonical term – Jaffe-Manohar decomposition. Orbital angular momentum has been connected in each decomposition to a different observable, a Generalized Transverse Momentum Distribution (GTMD), for the canonical term, and a twist three Generalized Parton Distribution (GPD) for the kinetic term. While the latter appears as an azimuthal angular modulation in the longitudinal target spin asymmetry in deeply virtual Compton scattering, due to parity constraints, the GTMD associated with canonical angular momentum cannot be measured in a similar set of experiments.

Highlights

One of the important challenges for QCD is understanding the angular momentum or spin structure of the nucleon where a fundamental question has recently arisen about developing a unique gauge invariant decomposition of the total quark and gluon angular momenta, Jq, and Jg, into their respective spin and orbital components
Notwithstanding the notion that the Generalized Parton Distribution (GPD) that enter Eq (4) can be observed by measuring specific Deeply Virtual Compton Scattering (DVCS) asymmetries and cross sections, to validate this relation it is necessary to identify processes where Orbital Angular Momentum (OAM) can be observed directly through the twist three GPD, G2. This was done in Ref. [17] where, making use of the expressions from an extensive analysis of DVCS at twist three level performed in [9, 10], we were able to single out the helicity amplitudes combinations which contribute to the twist three GPD G2, and to connect this structure function to an observable, namely the sin 2φ modulation in the longitudinal Target Spin Asymmetry (TSA), AsLiUn 2φ [17]
Parity Constraints In Ref. [17] we demonstrated that there was a fundamental reason behind the claim that it was “not known how to extract Wigner distributions or Generalized Transverse Momentum Distribution (GTMD) from experiments” [14], namely we explained how this inherent difficulty was a consequence of parity constraints on the helicity amplitudes which enter the general cross section formulation [21, 22]

Summary

Introduction

One of the important challenges for QCD is understanding the angular momentum or spin structure of the nucleon where a fundamental question has recently arisen about developing a unique gauge invariant decomposition of the total quark and gluon angular momenta, Jq, and Jg, into their respective spin and orbital components (see Refs. [1, 2] for reviews). [17] where, making use of the expressions from an extensive analysis of DVCS at twist three level performed in [9, 10], we were able to single out the helicity amplitudes combinations which contribute to the twist three GPD G2, and to connect this structure function to an observable, namely the sin 2φ modulation in the longitudinal Target Spin Asymmetry (TSA), AsLiUn 2φ [17] This term has already been measured, and found to be quite substantial at HERMES [18] and CLAS [19]. We discuss whether this goal can be met in either case, F14 and G2, and which experimental setup would be required

Parity Constraints

Angular Momentum Distributions

M2 ij T kTi

Conclusions