The gluon spin in the chiral bag model

We study the gluon polarization contribution at the quark model renormalization scale to the proton spin, Γ, in the chiral bag model. It is evaluated by taking the expectation value of the forward matrix element of a local gluon operator in the axial gauge A+=0. It is shown that the confining boundary condition for the color electric field plays an important role. When a solution satisfying the boundary condition for the color electric field, which is not the conventionally used but which we favor, is used, the Γ has a positive value for all bag radii and its magnitude is comparable to the quark spin polarization. This results in a significant reduction in the relative fraction of the proton spin carried by the quark spin, which is consistent with the small flavor singlet axial current measured in the EMC experiments.