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I will say right away that I don't mean standard-model sphalerons, I mean the sphalerons of some extension of the standard model.

The reason to even think about this is last year's paper by Frampton and Hung (discussion), which proposes that the Higgs mass might be 126 GeV "because" the timescales for vacuum decay and for instanton-induced proton decay are the same. More precisely: the timescale of vacuum decay is unknown, but if it were the same as the timescale for the spontaneous occurrence of a sphaleron in a proton, that would indicate a Higgs mass near the observed mass. (This is not as remarkable as it may sound: the Higgs mass is right on the edge of making the vacuum genuinely stable, so any extremely long lifetime for the vacuum corresponds to a Higgs mass near the value that we see.)

They don't have a coherent causal model. But one way for it to work, would be if proton decay caused vacuum decay. This ought to make for problems with early-universe cosmology, but put that to one side for now, maybe there's a way around that.

What I would like to know is whether the idea of proton decay causing vacuum decay even makes sense. What I envisage is a standard model extension with new scalars that appear in the sphaleron action and in an extended Higgs-sector potential. Perhaps the new scalar has a VEV of its own, the proton-destroying sphaleron action is minimized when that VEV changes, but the new VEV will in turn destabilize the existing Higgs VEV and drive it into a new, true minimum.

The effect of an extra scalar on electroweak vacuum stability is a current topic of research, and section 4 of this paper shows sneutrinos nominally contributing to the sphaleron action in an extension of the MSSM (though here their contribution is negligible).

  • Wow, this is very interesting stuff and such a nice question :-). Can you shortly explain what a spaleron exactly is in technical terms? What is their action and motivation in BSM extendet theories? I will probably ask this on Quora as soon as my WLAN is stable enough, so watch out ... ;-) – Dilaton Jan 28 '14 at 09:05
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    @Dilaton http://en.wikipedia.org/wiki/Sphaleron – anna v Jan 28 '14 at 09:57
  • Questions like these make me want to spend more time studying the standard model. – Kyle Kanos Jan 28 '14 at 14:07
  • @annav yes thanks ;-). BTW I and 3 other people think this is a legitimate technical question too, it has already 4 reopwen votes, so maybe you or Mitchell could help with the 5th reopen vote? Both of you knowleadgeable folks could do much good in the review queues by preventing legitimate questions from getting closed, help reopen nide questions ones, etc ... ;-) – Dilaton Jan 29 '14 at 06:40

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