What would a Higgs at 125 GeV tell us?

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.

51 Responses to What would a Higgs at 125 GeV tell us?

  1. Vladimir Kalitvianski says:

    Apart from SUSY, there may be other theoretical constructions to “stabilize” vacuum and other features. I believe the current way of theoretical description must be redone. We cannot patch our theories every time, we must have a better theoretical concepts free from catastrophes.

  2. Ervin Goldfain says:

    Among many cross-checks that will be required to close the loop, the “would-be” 125 GeV signal has to be confirmed in each decay channel and has to fair well against precision EW tests. It may also turn out that adding more (fb)^(-1) to the current LHC data may reduce rather than amplify the signal. Is background subtraction under solid control?

    I agree that theorists have their work cut out for them, but there is still a long way on the experimental side to reach definitive conclusions.

    • Paul Hoiland says:

      In essence that is true of a lot of things if we keep honest to the scientific method. None of this even if the rumors turn out true is a settled issue. In fact, while if true they could say they think they have found the God-particle, to actually say they have it without further cross check and refinement would be just wrong.

      • Paul Hoiland says:

        A Higgs boson with mass above the present experimental bound may only be obtained for relatively heavy third generation squarks, requiring a precise, somewhat unnatural balance between different contributions to the effective Higgs mass parameter. Basically, enhanced SU(2) D-terms. A light neutral CP-even Higgs boson of the MSSM which couples to the weak gauge bosons with a strength close to the standard model one would play a relevant role in the mechanism of electroweak symmetry breaking. But it is also a metastable model that requires fine tuning to account for a lack of major decay of the vacuum. There is Perturbative and weakly coupled, Strongly coupled, the list goes on and on.

  3. Ervin Goldfain says:

    “Fair” = fare.

    Sorry for this misspelling in my previous reply.

  4. Paul Hoiland says:

    Some of the Higg’s as a composite ideas would be a meta-stable vacuum solution in that there either is a stablizing mechanism that accounts for the forced stablized state or they can decay eventually over time and become energy dependent. When I was looking at Fernando’s RS modeled hyperdrive idea in essence you end up with a forced false vacuum state for the Higg’s. I had tended to ignore the implication for decay in favor of a mechanism that renormalizes to keep the state constant. But in honest relook, it could be more of a meta-stable situation involved and decay is possible.

  5. Paul Hoiland says:

    My choice went back into Fernando’s PV ideas on the Dutch equation and how RS models tend to suggest some stablizing mechanism is involved. But that was a choice of keeping it simple, not anything the model has to demand.

  6. Paul Hoiland says:

    Let’s assume for a moment there are higher Higg’s states that decay, anythiong show up yet in all the graphs around 250 GeV?

    • Philip Gibbs says:

      The summer data had a one sigma excess at 250 GeV. That is very insignificant but we will see what the new data brings.

      • Paul Hoiland says:

        I was aksing because I went back to some of that PV derived model Fernando once used and thought about the composite idea. There should be two possible modes for a primary 250 GeV Higg’s one would be the resulant at 125 GeV. The other would be a meta-stable decay mode at 62.5 GeV. That one would be mostly buried in the noise though even though a lot of Dark Matter research has suggested it’s mass above 40 GeV.

      • You are listing the traditional deviations, 62.5 took a lot of time to be filled, because of some events compatible with charged higgs (yep, susy!). Then 246 GeV is sqrt(2) times top, the Fermi vaccum, and has some excess there, as Phillip remembers.

  7. Is there any work about the possibility that the vacuum is converted into a little bit of negative energy, that is, the cosmological constant instead of propagating in a fast and destructive wave?

  8. Paul Hoiland says:

    You are close to what I was after. It was mentioned in another posting how the Higg’s is weird with it’s zero spin. Sopme would question if it actually moves. Our detection methods in general rely upon light of one form or another. If the thing in a decay mode retains its zero spin nature all one might get is a gravity signature it exists. It is already known Dark Matter had little influence on the cosmos in early times. I started thinking what if it is a decay mode for the Higg’s. It would show a very slow decay of the meta-stable state over time.

  9. Paul Hoiland says:

    That should be some, not sopme. Sorry for the typo.

    • Paul Hoiland says:

      In essence, in another 15 or 16 billion years the cosmos could become almost fully dark matter which could result in collapse and eventually a recycle mode or it could results in a rapid big rip.

  10. What this would tell us, around that value of 124, 125, 128 is that we have indeed seen the frontier of supersymmetry theory and it is not as simple as the string formulation. But these charts are neat and their explanations. Not bad for progress in engineering and experiment but why so slow and uncertain in theory?

    Why indeed has there not been a cosmic catastrophe as mentioned in the initial post here and overview? This is a very insightful question which also speaks of more understanding of the concept of symmetry involved than apparently our maths offered. For I can imagine principles that modify things and keeps the balance on all scales. The Higgs idea, and say its deep idea of relations to the number of such “particles” is useful in pointing out a higher form of space and physics- and applies elsewhere beyond our simple ideas of lower dimensions and lower energy and masses.

    The PeSla

    • Paul Hoiland says:

      It has been proposed before that vacuum decay can exist and you still not have a doomsday event.

      As for theory, well part of it goes back to the nearly infinite set of possible mechanisms and outcomes. Theory awaits being brought in line with observation.

  11. Kea says:

    LOL, if only it was simpler! If only we were born with the complicated zombie brains, then we could eat steak every day …

  12. Nick says:

    I believe the vaccuum will be unstable in a way to allow travel between other universes and realities, but not unstable so the universe can collapse if you pierce it.

    • Paul Hoiland says:

      I rather suspect something akin to that myself.

    • Schmoo says:

      What has lead you to this belief?

      • Paul Hoiland says:

        A lot of physics has been telling us we do not have the whole picture. As for time travel I rather agree with Hawkin on that one and such is prevented. Universe jumping can take place under Brane models and given the current Higgs state may be in that range one could argue it is possible.

  13. JollyJoker says:

    On the half-life of a metastable vacuum, wouldn’t anthropic reasoning completely ruin the assumption it needs to have a half-life of 13+ billion years? I mean, if we can have fine tuning of the cosmological constant to one in 10^120, a similarly unlikely event (2^400?) would be that our vacuum has survived this long even though its half-life is only tens of millions of years.

    Could this be a way to find evidence for anthropic selection?

    • Paul Hoiland says:

      Perhaps, fine tuning is also involved in a lot of M-Thyeory, Brane Theory, supersymmetry, etc.

    • Matt Simmons says:

      Even without anthropic selection, our light cone is only so large. Who’s to say the vacuum instability hasn’t already begun elsewhere?

      • Bill says:

        Good point. Also, would the red shifting in anyway stop the wave of collapsing energy state space? e.g. The argument that eventually galaxies would become invisible is the light coming from all other galaxies would eventually be red shifted to wavelengths larger than the visible universe. Perhaps a wave of collapsing space would still be a way to still communicate between galaxies. e.g. We were here, and you are now going to be toast…

  14. Paul Hoiland says:

    It actually is more a matter of how the actual Higg’s mass effects the parameters of the theory itself and what the eventual theory needs in the way of fine tuning. In general finding the Higg’s mass is only step one on the path to that point.

  15. Paul Hoiland says:

    The ultimate goal is one theory accounting for everything. However, since our knowledge is always limited by our local perspective I would doub’t we will ever know everything.

  16. Albert Z says:

    (1) “I believe the vaccuum will be unstable in a way to allow travel between other universes and realities, but not unstable so the universe can collapse if you pierce it.”

    (2) “I rather suspect something akin to that myself.”

    Clearly some people have already found their way to alternative realities.

    Love the untestable pseudo-physics.

    A big fat plus for science, right?

    Albert Z

  17. Bill says:

    Hmmm. At what point can we say the Higgs would be massive enough to violate the Anthropic principle? e.g. At what energy would we have predicted the universe to already have exploded? It seems if there is an upper limit, and we are right at it, then there is also a lower limit that pushes there. Sort of like the balance between open and closed universe. Speaking of which, if the universe is accelerating in the expansion, presumably then the explosions of the vacuum would be confined to a finite volume of the universe. In which case if the universe is designed, I might expect to find a Higgs mass slightly above the stable limit, but low enough so the accelerating expansion is just enough to protect us beyond the predicted half life from exploding parts of the universe.

  18. vacuum_cleaner says:

    So if the vacuum is unstable, the catastrophe may have happened already in parts of our universe. Then, we are lucky because nobody will ever know… 😉

  19. Joe Butler says:

    Im a total newbie to all this deep physics theory, i love watching programmes on TV about this stuff and im a Biologist by nature so i think i chose the wrong field lol.

    However what is really exciting is to learn for the first time today about vacuum instability etc. Based on the assumption that any HB particle we find is 125 GeV it could theoretically mean the end of all life as we know it at any given time given waht was said above;

    “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.”

    I find this all rather exciting and im not worried for my life yet.

    I just think it is mind blowing to think if the spike on a graph corrisponds to 120Gev were in trouble, if its 130GeV were ok.

    I know i am making an extreme oversimplification of this but it just excites me and this blog is fantastic 😀

    After all this is why we all love physics, is it not?

  20. Paul Hoiland says:

    You also could have a very slow roll decay that is not some brief flash of distruction and it could be stablized by other mechanisms.

  21. Tony Smith says:

    Jester says (at Resonaances):
    “… ATLAS …[has]… an excess of events … around 125 GeV … driven by … H to gamma-gamma … and supported by 3 events … in H to ZZ to 4l …
    CMS has a smaller excess at 125 GeV, mainly in … H to gamma-gamma, but their excess in H to ZZ to 4l is shifted to … 119 GeV (where they also have a small excess in H to gamma-gamma) … All in all, the significance of 125 GeV in CMS is only around 2 sigma

    other 2-sigmaish bumps in the gamma-gamma channel, notably around 140 GeV … cannot be the Standard Model Higgs … but could well be due to Higgs-like … extensions of the Standard Model …
    the Standard Model Higgs is excluded down to approximately 130 GeV …”.

    Is the 140 GeV bump ruled out as Standard Model Higgs only because its cross section is less than 100 per cent of that expected for the Standard Model ?

    If there is a 3-state Higgs in which the Standard Model cross section is split up among the 3 states, one being at 140 GeV,
    the other two in the range up to 240 GeV,
    so that all of them have cross sections substantially less than 100 per cent of that expected for the Standard Model,
    would that be consistent with the 5/fb data analysis
    (which only excludes above 130 GeV for full single Standard Model Higgs) ?

    Do either ATLAS or CMS see bumps (less than full Stanrd Model Higgs cross section) in the Higgs to ZZ to 4l channel in the range 140 GeV to 240 GeV ?


    • Paul Hoiland says:

      In general, the whole picture rules out the SM and does support new physics in the works.

    • Bill says:

      Really, two and three sigma events are interesting but not enough to get excited about. In LEP1, CERN had some very interesting 4 sigma events that did not occur again as we collected more data. Until you have enough data to start measuring interaction rates, it is hard to know if this is the predicted Higgs, or just events with a similar signature. However, so far this is precisely what we would expect to see if it is the Higgs, which is an encouraging sign.

  22. Paul Hoiland says:

    Everything in baby steps is how life works.

  23. Frederick says:

    Too many snowflakes. Couldn’t read.

  24. Mitchell Porter says:

    There have been many false alarms, but this one has enormous hype surrounding it. It seems advisable, if one can make the mental space for it, for purveyors of alternative theories of mass to think about how something might arise in the vicinity of 125 GeV.

    I have run across two interesting ways to arrive at this value, and neither of them is especially tied to the idea that fermion mass results from a Yukawa interaction with a Higgs scalar.

    First is the relationship appearing in that “four-color theorem” paper, arXiv:0912.5189. The paper itself does not make sense, but the formula is simply m_H = 1/2 (m_W+ + m_W- + m_Z).

    Second is the argument that this value has something to do with vacuum stability. The discussion in today’s arXiv:1112.2415 looks interesting: Requiring that the Higgs self-interaction and its beta-function should both vanish at the Planck scale gives 126 GeV. Also see discussions on page 7 about the top quark mass conspiring to balance out loop corrections which would make the “Higgs mass” heavier, and that “the Higgs self-interaction at the electroweak scale is entirely generated by radiative corrections of the RGE evolution from a vanishing coupling at the Planck scale.”

    What I want to suggest is that these relationships may still have a meaning in physical frameworks extremely different to standard renormalizable field theory. As posted above, the VEV of the Higgs field is 246 GeV. If, in your alternative theory of the origin of mass, you can find something analogous to this ubiquitous energy density, you may be halfway to reconstituting these arguments within your own framework.

  25. Fantastic!

    I myself had long since known of the 125 GeV Higgs, but those ivory-tower academics rejected the expirements I submitted.

    I’m quite pleased to see my results begin to attract attention- I’m sure I’ll be mentioned, probably given a coauthorship when the paper comes out.

    For all those budding particle physicists: pay attention! You can make a pretty-workable collider with some aluminum foil, a standard microwave oven, some plumbing supplies, and photographic film for detection. (for those with more cash, you can jerry-rig a standard TN LCD display, sans polarizers, to make a better detector that works in real time, though the detection range is pretty limited and you have to implement your own monitoring software/input device- I used a modified videocard driver hooked up to the monitor to stream results to the program I wrote for this purpose.)

    • Bill says:

      @John – too funny. Seriously though, if you read Analog magazines there is a series of articles that describe how do your own fusion generator at home. The principles are sound, and some people have actually constructed them. You aren’t going to be able to study anything we consider “high energy” physics such as Higgs particles with it, but there is still some interesting science that can be done on those lower energy ranges.

      If you want to do something with higher energy at home, your best bet is a cosmic ray telescope. For the most part though what most people do with those is simply work on designing better particle detectors.

  26. Soap_Bubbles says:

    If the Higgs boson does exist between 115 GeV and 125 GeV and two W bosons weigh in at 80 GeV, then where does the extra 35 – 45 GeV mass come from?

    • Philip Gibbs says:

      The question does not really make sense. the Higgs boson is not a W plus something else. The standard model has a spectrum of particles including the W at 80 GeV, The Z at 90 geV, the Higgs at perhaps 125 GeV and the top at 173 GeV plus many lighter ones. The standard model does not provide any answer to why these are the right masses. That may come eventually from a more advanced model, or they could just be free parameters that can only be determined by experiment.

    • Soap_Bubbles says:

      Could the extra 35-45 GeV indicate that the bosons have structure and hence are composed of even smaller particles?

      We can only use the Heisenberg uncertainty principle to a certain degree and I do not believe it explains the imbalance.

      • Bill says:

        According to the theory, the mass of particles is determined both by the mass of the Higgs and there interaction rate (coupling) to the Higgs. So there is no reason to expect that the mass of any other particle will equal to the mass of the Higgs, unless you pick a theory that requires specific coupling constants. Some particles such as the top quark can have a mass heavier than the Higgs, while others have a mass less than the Higgs. I would be inclined to say it is just chance if the equation M_H + M_H = M_W+ + M_W- + M_Z works.

  27. The Higgs mass (125 GeV) was calculated, along other parameters of the Universe, based on the model of Expansive Nondecelerative Universe, see our paper published in Pacific Journal of Science and Technology
    12(1),214-236 (2011)and included reference.(Exact value is 125.39 GeV).

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