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The Higgs mechanism gets rid of the mass gap problem, and it's been experimentally proven, so why is there still a problem?

Why are the million dollars still up for grabs?

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  • $\begingroup$ Well it's an objective decision from the people who give out the million dollars. What's their reasoning? $\endgroup$ – user250721 Feb 3 at 3:17
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    $\begingroup$ Have you read this description of the problem? “For example, in the case of G=SU(3)—the strong nuclear interaction—the winner must prove that glueballs have a lower mass bound, and thus cannot be arbitrarily light.” Does that follow from Peter Higgs’ work? I don’t think it does. $\endgroup$ – G. Smith Feb 3 at 4:33
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    $\begingroup$ In what way do you imagine that the Higgs mechanism "gets rid of the mass gap problem"? $\endgroup$ – Martin C. Feb 3 at 16:49
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The standard model Higgs particle has a weak charge, but no color charge. As a result it generates as mass gap in electroweak theory (masses for the W and Z), but not in QCD (no gluon mass). However, we know that QCD (even pure QCD, without fermions) does have a mass gap: Glueballs are heavy. The millenium prize problem asks why that is.

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The mass gap problem specifically asks for a work which succeeds in mathematically defining the QFT in a rigorous fashion:

Prove that for any compact simple gauge group G, a non-trivial quantum Yang–Mills theory exists on $\mathbb{R}^{4}$ and has a mass gap $\Delta > 0$. Existence includes establishing axiomatic properties at least as strong as those cited in Streater & Wightman (1964), Osterwalder & Schrader (1973) and Osterwalder & Schrader (1975).

The work of Higgs does not even attempt to use these rigorous methods of mathematical physics.

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  • $\begingroup$ Higgs' mechanism is not hard to handle rigorously. It was largely done in the early 80s. No prize for that. $\endgroup$ – user1504 May 12 at 19:45

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