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As a preliminary we consider the phenomenology of the European Muon Collaboration experimental result without assuming SU(3) invariance. The most reliable conclusion is that the singlet axial-vector current matrix element is rather small. We calculate this matrix element in a variety of chiral-soliton models in which the axial anomaly equation is satisfied. There are a number of subtleties which we explore. It turns out that reasonable chiral models including only pseudoscalar fields give a zero matrix element. Taking "short-distance" effects consistently into account via the inclusion of vector mesons or explicit quarks does give a small nonzero result. The situation is closely analogous to the prediction of a nonzero result for the nonelectromagnetic part of the neutron-proton mass difference in these chiral models.

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