125 GeV Higgs and "Vacuum Instability" So the Higgs has been http://press.web.cern.ch/press/pressreleases/Releases2011/PR25.11E.html [Broken] (maybe). Nothing "beyond the standard model" about that of course; the Higgs is standard model. Except-- in the leadup to the LHC announcement, I repeatedly saw claims that the exact candidate mass of the Higgs, 125 GeV, is a strong sign that something beyond the standard model is going on, because a Higgs at that mass possibly indicates "vacuum instability". Here's a typical example of the claim: So, this is exciting. It seems to me most recent physics theories are solutions looking for a problem and now we have a very large problem to solve. Here are some things I am wondering. Assuming we don't get lucky (and just happen to get the correct top mass and SM parameters to keep the 125-GeV-Higgs universe stable): 1. Where can I read a more precise explanation of this negative Higgs self-coupling -> unstable vacuum idea? 2. Supersymmetry is usually the first theory cited as benefactor if the SM Higgs is found unstable. What other theories can also fix the problem? Can Little Higgs/Composite Higgs/Technicolor do it? Do the "Asymptotic Safety" models which are cited in other threads in this forum currently as producing a ~125 GeV Higgs have a way of solving the vacuum stability issue? Are there any other candidates? 3. Is there any technical reason, out of the gate, to prefer any one of these vacuum-stabilizing candidates over the other? My understanding is SUSY would be strongly preferred in any case due to the many other benefits it brings (solves certain mathematical problems, makes string theory possible, is "beautiful") but are there any known technical advantages of SUSY, or any other candidate, for the specific purpose of solving this particular problem (stabilizing the vacuum with a light Higgs)? 4. Again assuming the problem doesn't go away on its own with more accurate measurements of Higgs, top, etc-- what will be the next steps for discerning which of the vacuum-stabilizing candidate theories is real? Have any of the candidates had their parameter space significantly excluded by the LHC work so far, or do any of the candidates have important parameter space the LHC might be able to detect in future? My very dull impression from blog comment sections is that the next step is to pick a supersymmetry model with a 125 GeV Higgs and start looking for whatever it predicts to be the lightest supersymmetric partner (the word "gluino" keeps getting kicked around)?