[Paper Review] Identification of Observables for Quark and Gluon Orbital Angular Momentum

Aurore Courtoy, Gary R. Goldstein+3 more|arXiv (Cornell University)|Dec 1, 2014

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This paper resolves a key debate on the observability of quark and gluon orbital angular momentum (OAM) in QCD by distinguishing between kinetic OAM—directly observable via twist-3 generalized parton distributions (GPDs) like $G_2$—and canonical OAM, which is not accessible in single-hadronic-plane scattering due to parity constraints. The authors show that while kinetic OAM is measurable through the $\sin 2\phi$ modulation in target-spin asymmetries, canonical OAM, linked to the GTMD $F_{14}$, lacks a known experimental probe despite theoretical consistency.

ABSTRACT

A new debate has recently arisen on the subject of orbital angular momentum in QCD, in particular on its observability and on its partonic interpretation. Orbital momentum can be defined in QCD using two different decomposition schemes that yield a kinetic and a canonical definition, respectively. We argue that kinetic orbital angular momentum is intrinsically associated with twist three generalized parton distributions, and it is therefore more readily observable, while, due to parity constraints, canonical angular momentum, if defined as suggested in the literature in terms of generalized transverse momentum distributions, cannot be observed in scattering processes involving a single hadronic reaction plane.

Motivation & Objective

• To clarify the physical observability of quark and gluon orbital angular momentum (OAM) in QCD, particularly distinguishing between kinetic and canonical definitions.
• To resolve the debate on whether canonical OAM, defined via GTMDs like $F_{14}$, can be measured in exclusive scattering processes.
• To establish that kinetic OAM, linked to the twist-3 GPD $G_2$, is observable through measurable asymmetries like $A_{LU}^{\sin 2\phi}$ in deep virtual Compton scattering (DVCS).
• To explain why $F_{14}$, associated with canonical OAM, cannot be accessed experimentally despite non-zero model results, due to parity constraints on helicity amplitude combinations.
• To provide a physical, parity-based explanation for the lack of observable connection to $F_{14}$, beyond formal definitions, grounding it in transformation properties of the correlator under parity.

Proposed method

• The authors analyze the matrix element of the quark orbital angular momentum operator in the light-front formalism, distinguishing between kinetic and canonical OAM via different decomposition schemes.
• They link kinetic OAM to the second moment of the twist-3 GPD $G_2^q$, which appears in the parametrization of the quark-quark correlation function and is connected to the $\sin 2\phi$ modulation in the longitudinal target-spin asymmetry $A_{LU}^{\sin 2\phi}$.
• For canonical OAM, they examine the GTMD $F_{14}$, derived from the unintegrated quark-quark correlation function, which is formally related to the second moment in transverse momentum $k_T$ of the orbital angular momentum distribution.
• They apply parity transformation analysis to the helicity amplitudes contributing to $F_{14}$, showing that no single-hadronic-plane process can isolate this combination due to parity-odd structure.
• They use model calculations (e.g., reggeized quark-diquark model) to compute spatial distributions of $\widetilde{E}_{2T}$ and $F_{14}$, demonstrating their distinct partonic configurations.
• They compare results from models with and without confinement (e.g., quark-target model), showing that only confining models yield non-zero $F_{14}$, suggesting its gauge-link structure is essential.

Experimental results

Research questions

• RQ1 Can the kinetic orbital angular momentum of quarks and gluons be directly observed in deep inelastic scattering experiments?
• RQ2 Why is the canonical orbital angular momentum, defined via GTMD $F_{14}$, not observable in single-hadronic-plane exclusive processes despite theoretical consistency?
• RQ3 What is the role of final-state interactions and gauge links in distinguishing between kinetic and canonical OAM in QCD?
• RQ4 How do parity transformation properties of helicity amplitudes constrain the observability of GTMDs like $F_{14}$?
• RQ5 Can model calculations that yield non-zero $F_{14}$ be trusted as evidence of physical observability, or is a direct experimental probe still required?

Key findings

• The kinetic orbital angular momentum $L^q$ is directly observable through the $\sin 2\phi$ modulation in the longitudinal target-spin asymmetry $A_{LU}^{\sin 2\phi}$, which has been measured at HERMES and CLAS with substantial signal strength.
• The canonical orbital angular momentum $L_{\text{can}}^q$ is formally related to the second moment of the GTMD $F_{14}$, but this quantity cannot be accessed in any single-hadronic-plane scattering process due to parity constraints on the helicity amplitude combinations.
• The matrix element associated with $F_{14}$ transforms correctly under parity, confirming its physical consistency as a representation of OAM, but its observability is blocked by the lack of a suitable probe for its specific helicity structure.
• Model calculations show that $F_{14}$ is non-zero only in confining models (e.g., reggeized quark-diquark), while it vanishes in non-confining models like the quark-target model, indicating the gauge link structure is essential for its physical content.
• The twist-3 GPD $G_2^q$ (identified as $\widetilde{E}_{2T}$) is physically distinct from $F_{14}$, as confirmed by their different spatial distributions in the transverse plane and by the fact that $F_{14}$ integrates to zero over $k_T$.
• The authors conclude that while both $G_2^q$ and $F_{14}$ represent OAM, only the former is accessible via current experimental techniques, necessitating an extension of the master formula to describe processes sensitive to $F_{14}$.