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how does one explain the theoretical motivation behind the Higgs, given a small number of minutes and a motivated-but-nonexpert audience?
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That's pretty good. It's also close to the impression you get when looking at the standard model's defining formulae: the main thing the Higgs mechanism does is to give mass to the weak gauge bosons themselves (which reduces the range of the associated forces). That you also end up having to hook the matter particles up to it to give them mass terms with the right symmetries is sort of a sidelight.
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