A method is given which leads to a wide class of models with strong CP invariance. These models contain a spontaneously broken U(1) symmetry. If this symmetry were global, its breaking would lead to a massless scalar. Because the U(1) is anomaly free, it can be gauged, leading by the Higgs mechanism to a massive gauge boson, the aspon, which might be detectable.
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Frampton et al. (1991) studied this question.
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