We examine the conventional picture that gluons carry about half of the nucleon momentum in the asymptotic limit. We show that this large fraction is due to an unsuitable definition of the gluon momentum in an interacting theory. If defined in a gauge-invariant and consistent way, the asymptotic gluon momentum fraction is computed to be only about one-fifth. This result suggests that the asymptotic limit of the nucleon spin structure should also be reexamined. A possible experimental test of our finding is discussed in terms of novel parton distribution functions.
Parallel to the construction of gauge invariant spin and orbital angular momentum for QED in paper (I) of this series [1], we present here an analogous but non-trivial solution for QCD. Explicitly gauge invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task, and opens a more promising avenue towards the understanding of the nucleon spin structure.PACS numbers: 11.15.-q, 13.88.+e, 14.20.Dh,14.70.DjAs a composite particle, the nucleon naturally gets its spin from the spin and orbital motion of its constituents: quarks and gluons. From a theoretical point of view, the first task in studying the nucleon spin structure is to find out the appropriate operators for the spin and orbital angular momentum of the quark and gluon fields. Given these operators, one can then study their matrix elements in a polarized nucleon state, and investigate how these matrix elements can be related to experimental measurements. Pitifully and surprisingly, after 20 years of extensive discussions of the nucleon spin structure [2,3,4,5], this first task was never done, and even largely eluded the attention of the community.At first thought, it seems an elementary exercise to derive the quark and gluon angular momentum operators. From the QCD Lagrangianone can promptly follow Nöther's theorem to write down the conserved QCD angular momentum:
We analyze the problem of spin decomposition for an interacting system from a
natural perspective of constructing angular momentum eigenstates. We split,
from the total angular momentum operator, a proper part which can be separately
conserved for a stationary state. This part commutes with the total Hamiltonian
and thus specifies the quantum angular momentum. We first show how this can be
done in a gauge-dependent way, by seeking a specific gauge in which part of the
total angular momentum operator vanishes identically. We then construct a
gauge-invariant operator with the desired property. Our analysis clarifies what
is the most pertinent choice among the various proposals for decomposing the
nucleon spin. A similar analysis is performed for extracting a proper part from
the total Hamiltonian to construct energy eigenstates.Comment: 5 pages, no figure; published in Phys.Rev.D (Rapid Communications
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