The concept of effective field theory leads in a natural way to a construction principle for phenomenological sensible models known under the name of the Cheshire Cat Principle. We review its formulation in the chiral bag scenario and discuss its realization for the flavor singlet axial charge. Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. The presence of this surface term allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. We show that one can obtain a striking Cheshire-Cat phenomenon with a negligibly small singlet axial charge.
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