13 December: please follow the live blog for up-to-date news
The rumours tell us that next week ATLAS and CMS will announce a strong but inconclusive signal for the Higgs boson at about 125 GeV. This may be wrong and even if it is right there may be other candidate signals to think about, and it will take much more data to verify that the signal is indeed correct for the Higgs, but if it is right, what then are the implications of the Higgs at this mass?
This question will be the subject of much discussion in the coming months and I can only touch on it here. Certainly the central topic of the debate will be the stability of the vacuum and whether it implies new physics, and if so, at what scale?
It has been known for about twenty years that for a low Higgs mass relative to the top quark mass, the quartic Higgs self-coupling runs at high energy towards lower values. At some point it would turn negative indicating that the vacuum is unstable. In other words the universe could in theory spontaneously explode at some point releasing huge amounts of energy as it fell into a more stable lower energy vacuum state. This catastrophe would spread across the universe at the speed of light in an unstoppable wave of heat that would destroy everything in its path. Happily the universe has survived a very long time without such mishaps so this can’t be part of reality, or can it?
As it turns out a Higgs mass of 125 GeV is quite a borderline case. The situation was analysed taking into account the best recent valued for the top mass and weak coupling constants by Ellis et al in 2009. Here is their most relevant graphic with a line running across at 125 GeV (plus or minus 1 GeV) added by me. The horizontal axis tells us the energy at which the coupling constant goes negative. The yellow band indicates the limit for vacuum stability. Because of uncertainty in the top mass and the weak coupling, and also due to some theoretical unknowns, the exact point at which this limit is reached is not known exactly. The yellow band covers the range of possibilities.
The second plot taken from Quiros shows the scale of instability as a function of Top and Higgs mass. I have added a green spot where we now seem to live.
At 126 GeV the vacuum might remain stable up to Plank energies (see e.g. Shaposhnikov and Wetterich). If this is the case then there is nothing to worry about, but depending on the precise values of the standard model parameters, instability could also set in at energies around a million TeV. This is well above anything we can explore at the LHC but such energies are found in the more extreme parts of the universe and nothing bad has happened. The most likely explanation would be that some new unknown physics changes the running of the coupling to avert it from going negative. Examples of something that could do this include the existence of a Higgsino or a stop as predicted by supersymmetry, but there are other possibilities.
It is also possible that some amount of vacuum instability could really be present. If there is meta-stability the vacuum could remain in its normal state. There would be the possibility of disaster at any moment but the half-life for the decay of the vacuum would have to be more than about the 13 billion years that it has survived so far. In the plot above the blue band indicates the region where a more immediately unstable vacuum is reached. It is unlikely that this case is realised in nature.
As the plot shows, if the mass of the Higgs turns out to be 120 GeV despite present rumours to the contrary then the stability problem would be a big deal. This would be a big boost for SUSY models that stabilize the vacuum amd mostly prefer the light Higgs mass. If on the other hand the Higgs mass was found at 130 GeV or more, then the stability problem would be no issue. 125 GeV leaves us in the uncertain region where more research and better measurements of the top mass will be required. It will still encourage the SUSY theorists as work such as that of Kane shows, but the door will still be open to a range of possibilities.
There are other things apart from the stability of the vacuum that theorists will look at. What is the nature of the electro-weak phase transition implied by this Higgs mass? Can it play some role in inflation or other phenomenology of the early universe? How does the result fit with electro-weak precision measurements and what else would be required to reconcile theory with experiment in such tests, especially the muon magnetic anomaly? 2011 has been a great year for the experimenalists but next year the theorists will also have a lot of work to do.