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There are a number of approximate relations among elementary particle masses. In conventional theories, these are explained by assuming a hierarchy of interactions with the property that the stronger interactions have the more extensive symmetry. In renormalizable theories based on spontaneously broken gauge symmetry, this view is untenable. Manifest breaking of the gauge symmetry would destroy the renormalizability. We explore the possible origin of approximate mass formulas in theories of this kind.
Georgi et al. (1972) studied this question.