Abstract
It is shown that the confinement effect that is significant at great distances from the nucleon center is capable of inducing the appreciable quark helicity flip. A simultaneous change in projections of the orbital angular momentum of quarks on the direction of their motion, which follows from the Dirac equation, ensures the conservation of the total angular momentum of the system. Thus, a part of the proton spin, measured in experiments with deep inelastic scattering of leptons, may be hidden in the orbital angular momentum of quarks.
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Notes
Expressions for \(\gamma \)-matrices in cylindrical coordinates can be found using the vector form of their transformations, \({{\gamma }^{s}} = \,\,{{{{\gamma }^{i}}\partial {{x}^{s}}} \mathord{\left/ {\vphantom {{{{\gamma }^{i}}\partial {{x}^{s}}} {\partial {{x}^{i}}}}} \right. \kern-0em} {\partial {{x}^{i}}}}\), accompanying the substitution of variables \({{x}^{i}} \to {{x}^{s}}\) [4].
Here and after the solutions to the Dirac equation do not undergo the secondary quantization. They have the usual probabilistic interpretation, accepted in relativistic quantum mechanics [5].
It is interesting to note that noninteracting gluons, having a certain orbital angular momentum, are described by fields, well localized in the finite spatial region [6].
This description is valid, strictly speaking, only in the infinite momentum frame, when all partons are concentrated in the plane, perpendicular to the direction of the proton motion.
Here, the names and notation for special functions are used which are accepted in the MAPLE system.
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Translated by M. Samokhina
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Kostenko, B.F. Proton Spin Puzzle and Confinement of Quarks. Phys. Part. Nuclei 49, 552–556 (2018). https://doi.org/10.1134/S1063779618040366
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DOI: https://doi.org/10.1134/S1063779618040366