The proton spin in the chiral bag model: Casimir contributions and Cheshire Cat Principle

The flavor singlet axial charge has been a source of study in the last year s due to its relation to the so-called Proton Spin Problem. The relevant fl avor singlet axial current is anomalous, i.e., its divergence contains a pi ece which is the celebrated U-A(1) anomaly. This anomaly is intimately asso ciated with the eta' meson, which gets its mass from it. When the gauge deg rees of freedom of QCD are confined within a volume as is presently underst ood, the UA(1) anomaly is known to induce color anomaly leading to "leakage " of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This "color bou ndary term" inherits part or most of the dynamics of the volume (i.e., QCD) . In this paper, we exploit this mapping of the volume to the surface via t he color boundary condition to perform a complete analysis of the flavor si nglet axial charge in the chiral bag model using the Cheshire Cat Principle . This enables us to obtain the hitherto missing piece in the axial charge associated with the gluon Casimir energies. The result is that the flavor s inglet axial charge is small independent of the confinement (bag) size rang ing from the skyrmion picture to the MIT bag picture, thereby confirming th e (albeit approximate) Cheshire Cat phenomenon. (C) 1999 Elsevier Science B .V. All rights reserved.