Critique of the angular momentum sum rules and a new angular momentum sum rule
- Department of Physics and Astronomy, Vrije Universiteit, Amsterdam (Netherlands)
- Imperial College London, SW7 2BW (United Kingdom)
- Physics Department, Brookhaven National Laboratory, Upton, New York 11973 (United States)
We present a study of the tensorial structure of the hadronic matrix elements of the angular momentum operators J. Well known results in the literature are shown to be incorrect, and we have taken pains to derive the correct expressions in three different ways, two involving explicit physical wave packets and the third, totally independent, based upon the rotational properties of the state vectors. Surprisingly it turns out that the results are very sensitive to the type of relativistic spin state used to describe the motion of the particle, i.e., whether a canonical (i.e., boost) state or a helicity state is utilized. We present results for the matrix elements of the angular momentum operators, valid in an arbitrary Lorentz frame, for both helicity states and canonical states. These results are relevant for the construction of angular momentum sum rules, relating the angular momentum of a nucleon to the spin and orbital angular momentum of its constituents. It turns out that it is necessary to distinguish carefully whether the motion of the partons is characterized via canonical or helicity spin states. Fortunately, for the simple parton model interpretation, when the proton moves along OZ, our results for the sum rule based upon the matrix elements of J{sub z} agree with the often used sum rule found in the literature. But for the components J{sub x},J{sub y} the results are different and lead to a new and very intuitive sum rule for transverse polarization.
- OSTI ID:
- 20698112
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 70, Issue 11; Other Information: DOI: 10.1103/PhysRevD.70.114001; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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