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I have seen in popular media, claims that Hawking does not believe the Higgs boson exists due to microscopic black holes and even made a bet against it. This is based on something published in journal Physical Review D.

I don't have access to journal Physical Review D, and I can't find a clear detailed explanation what his claim is, and what his proposed alternative is. Can someone explain it for this curious layman?

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Please include precise Physical Review D reference. –  Qmechanic Mar 31 '11 at 23:22
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The news article didn't say. I'll google scholar search for it. EDIT: Got it (or at least this was the only good Hawking + Higgs hit) "Virtual black holes" Hawking, SW, PHYSICAL REVIEW D, Volume: 53, Issue: 6, Pages: 3099-3107, Published: 1996 –  Ginsberg Mar 31 '11 at 23:29
    
The paper is here: arxiv.org/abs/hep-th/9510029 –  Ben Crowell Aug 14 '13 at 15:04
    
So in summary, Hawking wrote a paper claiming that the Higgs didn't exist, and Motl wrote a blog entry claiming that the Hawking paper didn't exist. –  Ben Crowell Aug 14 '13 at 15:28
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I would like to explain Hawking's reasoning here, because it wasn't so completely silly back then as it sounds today. The paper is based on the incorrect idea that there is coherence loss in virtual gravity states. This idea is due to Hawking's black hole radiation, which seems to require miraculous nonlocal conspiracy between incoming matter and outgoing radiation to avoid wrecking quantum mechanics. Thanks to 't Hooft, Susskind, and all the many people working on AdS/CFT, it is now certain that the miracle happens, so that quantum mechanics is fine. But although most people suspected this back then, it wasn't demonstrated in any scientifically convincing way until at least BFSS that same year.

Hawking's paper is basically noting the naturalness problem for scalar fields, nothing more. It is using an unusual high energy phenomenon to illustrate the naturalness problem, namely gravitational fluctuations with weird topology: fluctuations which are not certainly necessary. (Witten has argued that the naive notion of a path integral over topology is not required by any principle, since you can't cancel out topology locally using anti-topology. So a path integral can be consistently restricted in terms of the topology it allows.) It is also claiming that the loss of coherence will be observable in some way with scalar fields at low energy, a question which is moot now, because there is no loss of coherence. But the basic conclusion is just: naturalness forbids scalars.

Fundamental scalars are unstable to quadratic and quartic interactions which blow up the mass generically to the Planck mass. We already knew that from general principles of renormalization theory, and the detailed calculations in the paper are basically irrelevant. This is the hierarchy problem.

The solutions to the hierarchy problem which actually work (i.e., not counting large extra dimensions), solve Hawking's version of the problem just as well. If you have supersymmetry, the supergravity in a SUSY background will not generate SUSY breaking through fluctuations whatever the microscopic completion, because the SUSY is defined as a long distances symmetry. It would be just as silly as saying that the black hole loops would break Lorentz invariance. So the Higgs would be protected.

Similarly, for composite Higgs ideas, like technicolor, the argument fails. But the LHC would still see some sort of composite scalars in this model.

I think the charitable thing to say about Hawking's paper is that it is the last gasp of qualitative path-integral methods in quantum gravity, before string theory became precise enough to replace this ad-hoc way of thinking.

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There is a book review which mentions this:

Famously, Stephen Hawking made his bet for $100 with Gordy Kane that neither LEP nor any other particle collider would ever see the Higgs boson because of virtual black holes. Perhaps unsurprisingly, Peter Higgs was very doubtful of the calculations that lead Hawking to this conclusion (and Peter certainly wasn’t alone) and this lead to a little public drama between the two scientists in the media.

Maybe the book has details.

See also Lubos Motl's blog on the subject where also the reference to the paper of Hawking is discussed, rather unfavorably. :;

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