Controversy concerning the definition of quark and gluon angular momentum

Journal Article · Sun May 01 00:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.096012· OSTI ID:21541661

Leader, Elliot ^[1]

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1. Blackett laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ (United Kingdom)

A major controversy has arisen in QCD as to how to split the total angular momentum into separate quark and gluon contributions, and as to whether the gluon angular momentum can itself be split, in a gauge-invariant way, into a spin and orbital part. Several authors have proposed various answers to these questions and offered a variety of different expressions for the relevant operators. I argue that none of these is acceptable and suggest that the canonical expression for the momentum and angular momentum operators is the correct and physically meaningful one. It is then an inescapable fact that the gluon angular momentum operator cannot, in general, be split in a gauge-invariant way into a spin and orbital part. However, the projection of the gluon spin onto its direction of motion, i.e. its helicity is gauge invariant and is measured in deep inelastic scattering on nucleons. The Ji sum rule, relating the quark angular momentum to generalized parton distributions, though not based on the canonical operators, is shown to be correct, if interpreted with due care. I also draw attention to several interesting aspects of QED and QCD, which, to the best of my knowledge, are not commented upon in the standard textbooks on field theory.

• OSTI ID: 21541661
• Journal Information: Physical Review. D, Particles Fields, Vol. 83, Issue 9; Other Information: DOI: 10.1103/PhysRevD.83.096012; (c) 2011 American Institute of Physics; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM OPERATORS
DEEP INELASTIC SCATTERING
DISTRIBUTION
FIELD THEORIES
GAUGE INVARIANCE
GLUONS
HELICITY
QUANTUM CHROMODYNAMICS
QUANTUM ELECTRODYNAMICS
QUARKS
SPIN
SUM RULES
ANGULAR MOMENTUM
BOSONS
ELECTRODYNAMICS
EQUATIONS
FERMIONS
INELASTIC SCATTERING
INTERACTIONS
INVARIANCE PRINCIPLES
LEPTON-BARYON INTERACTIONS
LEPTON-HADRON INTERACTIONS
LEPTON-NUCLEON INTERACTIONS
MATHEMATICAL OPERATORS
PARTICLE INTERACTIONS
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SCATTERING