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Register a new userMore on the relation between the two physically inequivalent decompositions of the nucleon spin
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Authors
Masashi Wakamatsu
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The recent controversy on the nucleon spin decomposition problem is critically overviewed. We argue that there exist two and only two physically inequivalent gauge-invariant decompositions of the longitudinal nucleon spin, contrary to the rapidly spreading view in the QCD spin physics community that there are infinitely many decompositions of the nucleon spin.
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We discuss the uniqueness or non-uniqueness problem of the decomposition of the gluon field into the physical and pure-gauge components, which is the basis of the recently proposed two physically inequivalent gauge-invariant decompositions of the nucleon spin. It is crucialy important to recognize the fact that the standard gauge fixing procedure is essentially a process of projecting out the physical components of the massless gauge field. A complexity of the nonabelian gauge theory as compared with the abelian case is that a closed expression for the physical component can be given only with use of the non-local Wilson line, which is generally path-dependent. It is known that, by choosing an infinitely long straight-line path in space and time, the direction of which is characterized by a constant 4-vector $n^mu$, one can cover a class of gauge called the general axial gauge, containing three popular gauges, i.e. the temporal, the light-cone, and the spatial axial gauge. Within this general axial gauge, we have calculated the 1-loop evolution matrix for the quark and gluon longitudinal spins in the nucleon. We found that the final answer is exactly the same independently of the choices of $n^mu$, which amounts to proving the gauge-independence and path-independence simultaneously, although within a restricted class of gauges and paths. By drawing on all of these findings together with well-established knowledge from gauge theories, we argue against the rapidly spreading view in the community that there are infinitely many decompositions of the nucleon spin.
The question whether the total gluon angular momentum in the nucleon can be decomposed into its spin and orbital parts without conflict with the gauge-invariance principle has been an object of long-lasting debate. Despite a remarkable progress achieved through the recent intensive researches, the following two issues still remains to be clarified more transparently. The first issue is to resolve the apparent conflict between the proposed gauge-invariant decomposition of the total gluon angular momentum and the textbook statement that the total angular momentum of the photon cannot be gauge-invariantly decomposed into its spin and orbital parts. We show that this problem is also inseparably connected with the uniqueness or non-uniqueness problem of the nucleon spin decomposition. The second practically more important issue is that, among the two physically inequivalent decompositions of the nucleon spin, i.e. the canonical type decomposition and the mechanical type decomposition, which can we say is more physical or closer to direct observation ? In the present paper, we try to answer both these questions as clearly as possible.
A general consensus now is that there are two physically inequivalent complete decompositions of the nucleon spin, i.e. the decomposition of the canonical type and that of mechanical type. The well-known Jaffe-Manohar decomposition is of the former type. Unfortunately, there is a wide-spread misbelief that this decomposition matches the partonic picture, which states that motion of quarks in the nucleon is approximately free. In the present monograph, we reveal that this understanding is not necessarily correct and that the Jaffe-Manohar decomposition is not such a decomposition, which natively reflects the intrinsic (or static) orbital angular momentum structure of the nucleon.
We argue against the rapidly spreading idea of gauge-invariant-extension (GIE) approach in the nucleon spin decomposition problem, which implies the existence of infinitely many gauge-invariant decomposition of the nucleon spin.
We review the status of our understanding of nucleon structure based on the modelling of different kinds of parton distributions. We use the concept of generalized transverse momentum dependent parton distributions and Wigner distributions, which combine the features of transverse-momentum dependent parton distributions and generalized parton distributions. We revisit various quark models which account for different aspects of these parton distributions. We then identify applications of these distributions to gain a simple interpretation of key properties of the quark and gluon dynamics in the nucleon.
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