Global Fit Kills (or at least wounds) The Standard Model

A few days ago I showed how to combine the Higgs confidence level plots by adding in inverse square. At the time I did not understand why this worked (I am a bit slow at statistics.) Since then I have looked again at the work on electroweak precision tests and the global fit where you can find the same calculation being done. The inverse square of the 95% confidence level limits is just one-quarter of the Δχ2 estimator. For independent variables these can be directly added to give an overall Δχ2 which can then be mapped back to an overall confidence level limit. This is exactly what I was doing in my combinations. So now I know that these combo plots are essentially correct, neglecting any correlations which should be zero.

The latest update to the Global Electroweak Fit was submitted to arXiv earlier this month. There is a good plot showing the Δχcombination of the results from LEP, CMS, ATLAS and the Tevatron.

The global fit also takes into account the measurements of parameters such as the masses and widths of the W,Z and top particles. These can be fitted to the standard model to get another Δχ plot for the Higgs mass which looks like this

This can be combined with the direct searches to give an overall estimator plot

The way you read these plots is to look at the limits allowed below the horizontal dotted lines. The line at Δχ2= 1 tells us the one standard deviation points so we estimate a value for the Higgs mass,

MH = 120+12-5 GeV.    (pre-EPS best fit)

The region below  Δχ2= 4 tells us what is allowed at 95% confidence level. Already this plot limits the Higgs mass to between 114 GeV and 143 GeV assuming that the standard model is correct.

These results were derived before the recent results of direct searches for Higgs announced at EPS HEP Now we just have to wait for the Gfitter group to update their charts using the new data. Of course you know that I am impatient and want to see this now so here is my unofficial reconstruction of the global fit using the recent direct searches and the electroweak fit from gfitter.

As you can see there is nothing in the gray region that survives at 1 sigma level. At 95% confidence everything is excluded except a small window between 115 GeV and 122 GeV. In this region the Standard Model vacuum is unstable.

In conclusion, the Standard Model is dead (or at least badly wounded 🙂 ).

This does not kill the Higgs variants in other models such as MSSM but other fits can and will be made for these, not by me though.

50 Responses to Global Fit Kills (or at least wounds) The Standard Model

  1. Mitchell Porter says:

    So if the standard model with a single Higgs doublet is dead, what is the leading candidate to replace it? i.e. what is the next simplest and most plausible quantum field theory that is consistent with all the evidence?

    At Physics Stack Exchange, I asked: Might the LHC see nothing at all? Not just, no Higgs, but no detectable deviation from standard model predictions (apart from the existence of Higgs). This is something I’m still unclear about. Everybody says, you need a Higgs (or something else, like W’ bosons) to preserve unitarity in W-W scattering. OK, fine. And maybe we now know that it can’t be an (ex) standard model Higgs. But is there any LHC experiment which is *guaranteed* to give us any further information beyond the standard model? Like W-W scattering data which would tell us something about how unitarity is preserved? Or could we end up with a situation in which the data coming out of the LHC is *entirely* consistent with the ex standard model, except for the absence of a Higgs? And if so (this is my original question), what should be the “next standard model” in that situation?

    • Philip Gibbs says:

      I don’t know what the next best model is. At this early stage the model based searches work well because they combine several channels of information to give better statistics in a search such as the Higgs search. If those searches don’t give positive answers I think they will have to get much more data so that they can look at each individual channel and compare it with the standard model only. Any deviation can then be considered to work out what type of new particle or process it implies. there is a long way to go.

    • Lawrence B. Crowell says:

      I think there may be something very different going on from the sort of QFT we have been working with. The absence of the Higgs field and paucity of data for SUSY might mean there is some sort of “horizon” in the momentum scale. This horizon might be associated with the break down of conformal QFT at higher energy scales and the onset of masses in our low energy world where we observe mass.


    • Mitchell Porter says:

      I think I can say in outline what the answer to my question is. If absolutely nothing new shows up, then the “next standard model” will be the “previous standard model” with a slightly extended Higgs sector.

  2. Suppose that one takes Phil’s killer plot seriously and takes still seriously also the claim of ATLAS that there is something virtual in 140-150 GeV range decaying to W-W bosons made at Friday I think and suddenly agreed by CDF and D0 after the earlier press release that Higgs should be in the range 120-137 GeV (also experimental truths are very dynamical in quarter economy;-)).

    With these prerequisites one is led to ask whether the CDF 145 GeV bump (many months old prehistory!) was indeed real as also the 325 GeV CDF bump which received additional support at the first day of the conference. Technicolor enthusiast would talk about pions and rho and omega of technicolor hadron physics and the TGD guy who has forgotten his morning medications about M_89 hadron physics;-).

    The same TGD guy continues to talk about twistors and bosons emerging as bound states of massless fermions and anti-fermions so that massivation for spin one states is unavoidable and that massivation quite generally can be seen as a combination of massless multiplets with various spins to form massive multiplets. “Photon eats the remaining Higgs component”: this is also what the poor fellow is repeating.

  3. Han Yan says:

    Hi, Philip. Thanks a lot for your update!
    I am keeping a Chinese blog on physics, and I am planning to write about the EPS-HEP and its conclusions. Would you mind if I take your unofficial global fit figure and translate some of your words into Chinese? (Surely I will refer to the source)

  4. […] Higgs sector does not look like what the standard model predicts. There are hints of something in the light mass window but it does […]

  5. […] Higgs sector does not look like what the standard model predicts. There are hints of something in the light mass window but it does […]

  6. Leo Vuyk says:

    And what if we assume that the higgs itself is massless but only after interaction with fermions able to transform into a graviton or other gluon- photonic form?

  7. Luboš Motl says:

    Nice work – visually, those things look convincing.

    Of course, the inconsistency is not excessively strong so far…

  8. physicsphile says:

    Excluding the SM with 95% confidence intervals means essentially nothing. It is very widely recognized that to say anything conclusive in particle physics you need 5 sigma which is a lot harder to get than 2 sigma.

    • Luboš Motl says:

      Dear physicsphile, you are mistaken. 95% confidence intervals are absolutely standard a language in particle physics to *exclude* values of parameters. Look at any Tevatron or LHC paper excluding Higgs masses above something etc. You may have confused it with the *discovery* which follows different standards.

      With this being said, I do agree with you that such an exclusion is not watertight, especially if one wants to say something this far-reaching.

  9. Marc Sher says:

    Phil—I appreciate the work that has gone into making these plots (and I’m giving some Higgs lectures at a summer institute in Japan, and will use your combined plot, if it’s ok with you). I also agree with everything you have said, except the conclusion that the Standard Model is dead.

    Everyone knows that the Standard Model is at best an effective field theory. It is also known that it must break down before 10^19 GeV. All you have argued is that the breakdown must now occur at or below 10^6 GeV (where the instability arises). That is an important difference, but it is still beyond any accelerator capabilities (or even cosmic ray collision energies), and I don’t see why it has gone from life to death due to this change.

    It is, of course, a semantic difference (maybe the Standard Model is just pining for the fjords….). Still, I think your work on this is incredibly valuable.

    • Philip Gibbs says:

      You are very welcome to use the plot. It perhaps needs the caveat that it has not been soundly checked.

      This global fit excludes the standard model Higgs altogether at 90% confidence. The stability argument (which I agree is weak) is only required for higher confidence levels. Details of the combined plots from Tevatron and LHC may move the minimum of the curve up or down a little. More data could have a more dramatic effect.

  10. kassia says:

    Can you explain what do you mean by:

    “[…] In this region [115 GeV and 122 GeV] the Standard Model vacuum is unstable” ?

    Many thanks!

  11. Stability says:

    While it is true that for a Higgs mass between 115 and 122 GeV the standard model vacuum is not absolutely stable, it is still metastable with lifetime > 13.7 billion years. So its not clear that this by itself is enough to kill the standard model. Though it is quite interesting and is suggestive of new physics, but perhaps not a watertight case.

    Anyhow, we already know that dark matter, baryogenesis, strong CP problem, inflation etc are enough to kill the standard model in a certain sense; but they may all be associated with very high energy physics, so maybe not relevant to the point you were making.

    • Maybe that means our vaccum will decay on 12/21/2012!!!! OH NOES! 😀

      • Kea says:

        My Grandma, had she lived long enough, would have been 110 on that day. I think she would have enjoyed the self congratulatory patriarchy destroying spectacle.

      • Mitchell Porter says:

        Anyone who has seen the last episode of the TV series LEXX knows the exact value of the Higgs mass for which this happens. That value hasn’t been excluded yet, but we should know very soon.

  12. ohwilleke says:

    People have been doing quantum field theory without a Higgs mass for a generation. Calculations have been made, predictions have been verified. Apart from indicating that the method used may lack a fully rigorous foundation, is the Higgs mass a bit like a LaPlace Transform or a complex value for current that only matters in intermediate step and doesn’t matter in the final conclusion?

    In other words, what are the phenomenological consequences of the Higgs boson mass having one value v. another value apart from the fact that a few of them should be spit out in high energy collider experiments and that doesn’t happen.

    • Lawrence B. Crowell says:

      The simple fact is that something has to happen at around 1-10TeV in energy. The standard model of SU(2)xU(1) electroweak interactions has some experimental backing, at least with the massive W and Z bosons. At much higher energy than 10 TeV it is not possible to compute Feynman processes. In effect QFT becomes sick, and something must “happen.” The Higgs field is a form of potential which induces a change in the phase of the vacuum. It is similar to a statistical mechanics phase transition. So “something” does happen, but the basic Higgs theory appears to be in trouble.

    • DLB says:

      The difference is that the Higgs should not be a purely mathematical entity. It should be physical.

    • Ray Munroe says:

      The purpose of the Higgs boson is to supply the couplings that provide for mass, and to explain the longitudinal degrees-of-freedom (parallel to motion dgf’s required for massive particles with intrinsic spin of 1, 2, …) for the W and Z bosons (with respective masses of 80.4 and 91.2 GeV) while simultaneously breaking Electroweak symmetry and explaining the massless photon. There are enough constraining conditions here that a simple Higgs boson cannot have ‘just any mass’.

      However SUSY requires two complex scalar doublets (8 degrees-of-freedom) to properly provide for fermionic mass (there is a substantial mass difference between the top and bottom quarks). Of these 8 dgf’s, 3 yield the longitudinal modes for the W and Z bosons while the other 5 dgf’s SHOULD yield physical scalar bosons – the MSSM Higgs sector with Light, Heavy, Pseudoscalar, and plus/minus Charged Higgs. We have more non-constrained degrees-of-freedom, and more open parameter space.

      Lubos got my attention last week when he suggested that the 340-360 GeV deficit may be negative interference from a Higgs, and I do wonder what phenomenology would arise if the Heavy and Pseudoscalar Higgs are accidentally in the same mass range, but Lubos also points out that physical Higgs bosons would drown below the ‘one’ line (glub, glub, glub…).

      A Higgs boson is not the only way to accomplish these tasks, we might rather be able to use a ‘techni-pion’ (consider how important the pion is to Nuclear Physics) or a generic Nambu-Goldstone boson (such as Cooper Pairs in BCS Superconductivity Theory), but composite models such as Technicolor have other phenomenological problems.

      As Lawrence pointed out, new TeV scale Physics must exist, or else Feyman diagrams and the Renormalization Group blow up. I think that most HEP phenomenologists expect this new TeV-scale physics to be Supersymmetry, but Technicolor models were proposed in the past (I think that Technicolor is more constrined than SUSY and more easily ruled out).

      The m_0 and m_(1/2) SUSY parameters are large enough that I might expect the Light Stop Squark to be the easiest Sparticle to discover (independent of a more complex Higgs sector that need not necessarily imply SUSY – see Matti’s and Tony’s alternate theories) – look for b-tagged jets!

      Have Fun!

      • ohwilleke says:

        It is certainly obvious that a missing SM or light SUSY Higgs has all sorts of implications for the theoretical framework that makes sense to explain particle mass.

        My question was much more narrow. What are the phenomenogical implications, for example, of a 116 GeV Higgs v. of 325 GeV Higgs, aside from the fact that we can discern a particle resonnance at that mass?

        Crowell seems to be saying that it doesn’t matter much in the low energy calculations but dramatically screws up the business of doing QFT calculations somewhere around 1TeV to 10TeV (forgive me if this is an inaccurate paraphrase) in a phase transition-like. Are there any other implications? What is driving the blow up at 1TeV in the math?

      • Ray Munroe says:

        Hi Ohwilleke,

        The Standard Model Higgs is highly enough constrained that it could not have a mass of 325 GeV, but we could certainly dream up more complex Higgs sectors that would be consistent with such a mass – for instance the less-constrained Minimal Supersymmetric Standard Model Higgs sector that I described above could have a Heavy Higgs in that mass range.

        Radiative corrections (Feynman diagrams and the Renormalization Group Equations) SHOULD drive the Weak Scale mass (W, Z, Higgs? of ~100 GeV) up to the Planck Scale mass of 10^19 GeV. This is called the Hierarchy Problem, and the most generally accepted theoretical fix is Supersymmetry. This extra factor of 10^17-squared might as well be infinity when we are using perturbation theory to try to make accurate experimental predictions. Basically, Radiative corrections will consistently get more and more ‘incorrect’ around the TeV Scale, and will inevitably diverge without new physics at the TeV Scale.

        I would agree with your paraphrase of Lawrence Crowell’s comment “it doesn’t matter much in the low energy calculations but dramatically screws up the business of doing QFT calculations somewhere around 1TeV to 10TeV”.

        Have Fun!

      • Lawrence B. Crowell says:

        Something does have to change at around this energy scale. The data so far is lack luster, but we are at about 1/1000 the total data expected, so there are lots more to come. Luminosities will improve and in another year or two the picture should be much clearer. The 2-σ results in the 120-150 GeV Higgs mass range is not a Hindenburg event for the standard model, but it is a Lead Zeppelin. However, Led Zeppelin was always one of my favorite rock bands. It should also be pointed out that the INTEGRAL result on the polarization of light at different wavelengths from a Gamma Ray Burstar indicates there is no quantum graininess to spacetime far below the Planck scale. So a vast archive of physics theory and phenomenology appears to be headed for the trash can. However, at the TeV scale of energy it is obvious that something does have to change in physics, so nature is likely to tell us something. We may find that our ideas about the Higgs are naïve in some way, or maybe that the entire foundations of physics suffers from some sort of fundamental dystufunction..

        The Higgs particle is a form of Landau-Ginsburg potential theory used in phase transitions. Phase transitions are a collective phenomenon. With the Higgs field the thing which transitions is really the vacuum. This leads to two possible things to think about. Even if this transition of the vacuum takes place, we expect there to be a corresponding transition with QFT physics of single or a few particles. We might then have a problem that some people are familiar with. In a clean flask you can heat distilled water to above the boiling point with no phase change. If you then drop a grain of salt into the flask the water rather violently bumps. By doing single particle on particle scattering we may not have enough degrees of freedom to initiate the phase transition. The phase transition needs a measure of “noise” we are not providing. It might then be that the Higgs field will turn up in “messier” heavy ion experiments. The second possibility, which frankly I think might turn out to be the case, is that QFT has a problem with the vacuum. The Higgs field occurs in a large vacuum energy density, which in the light of matters such as the cosmological constant seems fictitious. It is the case QFT becomes a mess at 1-10 TeV, where the Higgs field becomes a sort of regulator which prevents divergences. However, the problem might in fact be that QFT is sick period, and the fix might involve something completely different from anything on the archives of theory.

        If we are to stay at least somewhat in line with established physical theory, Technicolor is one option for a Higgs-less world. Technicolor is a sort of “transformation” of T-T-bar condensates into another form. Sugawara did this with u-d quarks as a way of constructing meson physics in the .1-1 GeV range back in the 1970s. This is really a similar idea. In the technicolor theory the “meson” is the Higgs boson. The mechanism for Higgs production most often looked for is T T-bar — > H, or equivalently H — > T T-bar, where the latter gives the decay channels one searches for as a Higgs signature. This sounds like a small change, one where the field that induces the symmetry breaking has dynamics, and the symmetry breaking process is not spontaneous.

        However, Technicolor might lead to something. Suppose there is some momentum scale horizon, which is due to the end of conformal RG flow. This might also have something to do with the AdS ~ CFT, where gluon chains are dual to the quantum gravitation sector (graviton) on the AdS interior. We live on the boundary of the AdS, where there are no gravitons. We may find that attempting to exceed 10TeV in energy only gives more of the particles we know in the conformal broken phase. However, with the conformal breaking comes mass, and from mass we have classical gravity. So there may still be signatures of this sort of physics. The technicolor condensate might be a form of gluon chain dual to the graviton. If Technicolor leads to this type of physics, we may then have to search for different observables.

      • Bill K says:

        “In the technicolor theory the “meson” is the Higgs boson.”

        Lawrence, I have a question about this. People often make the offhand comment, “Well, maybe the Higgs boson is composite.” But if you try to build one out of fermion-antifermion pairs, as they do in technicolor, you don’t get scalars, the mesons you get are technipions (pseudoscalar) and technirhos (vector). So it seems to me that a composite Higgs boson is going to be quite a different thing from an elementary one, and there would not be much chance of confusing the two.

  13. ervin goldfain says:

    Lawrence correctly points out that:

    “At much higher energy than 10 TeV it is not possible to compute Feynman processes. In effect QFT becomes sick, and something must “happen.” The Higgs field is a form of potential which induces a change in the phase of the vacuum. It is similar to a statistical mechanics phase transition. So “something” does happen, but the basic Higgs theory appears to be in trouble.”

    Dynamics of quantum fields is no longer in equilibrium somewhere above the EW scale and reaching in the Terascale sector. Higgs-free mass generation and chiral symmetry breaking can be naturally accounted for by starting from these non-equilibrium settings, see below:


  14. Kea says:

    As I, and no doubt others that I don’t know, predicted years ago. It was always bloody obvious.

  15. At this point I would say that if that thing at 140 GeV is real, it is a Higgs, but not Peter. Just a relative, John Higgs maybe.

  16. Alex says:

    Hello Philip,

    Can you comment on what the main physics input is that drives your impressive exclusion plot so much beyond the old electroweak fit?

    • Philip Gibbs says:

      It is simply that the available direct search data from the Tevatron and LHC have advanced a great deal during the course of the EPS conference.

      • Alex says:


        Since there are excesses in this region, is this plot telling me that the SM is excluded because there are in fact too many events for there to be only a SM higgs somewhere?

      • Philip Gibbs says:

        You cannot draw any definitive conclusions from this plot. Firstly because it is only excluding the standard model at about 90% confidence and secondly because the combination method is only approximate.

        However, if we take it at face value then it tells us that over the four experiments there are less events than we would expect if there were simply a standard model Higgs in this region.

  17. Stability says:

    let me try to say it again: it is incorrect to conclude that a Higgs with mass between 115 and 122 GeV kills the standard. You say that in this range the standard model vacuum is unstable, but actually it is known that in this range the standard model can have a Planckian cutoff and it is METASTABLE with lifetime greater than the age of the universe, which is perfectly fine. (e.g., see Figure 4 in
    So this does not kill the standard model. Any thoughts on this?

    • Philip Gibbs says:

      Glashow also made the point at the EPS press conference that the instability of the vacuum is relevant here. Of course you have a point in principle but I am not convinced that even such metastability if fine.

      Does anyone have a theory that cures the instability with only much higher energy physics? My understanding is that SUSY cures it with partners near the same mass scale, so it would be interesting to know if this is necessary.

      Without the instability argument the standard model is still being made significantly less probable by this fit, but the residual probability depends on prior assumptions about the likelihood.

      • Stability says:

        Not sure what you mean. If it is metastable, than its not clear that anything needs to be “cured”. Nature doesn’t necessarily care about our desire to have nice looking effective potentials. The only thing that matters is that its an effective field theory that adequately describes our world, which has been stable for 13.7 billiion years so far, and has a Planckian cutoff.

        You say that you are “not convinced that even such metastability is fine”. Could you elaborate on why? I can imagine that there may be some deep reason why its not ok, but that is speculation. On the other hand, you are claiming that the standard model is now definitely dead, and I’m saying that I don’t think we have a definitive proof of that just yet.

      • Philip Gibbs says:

        The universe would have to come out of the Plank scale turmoil of the big bang in this metastable state and that does not seem likely to me. I know this is speculation because we don’t have a theory for that.

        i have already said that I agree that “dead” is too strong a word. I have changed the title and text to make it more clear. I used those terms because other bloggers were saying that SUSY is dead and I was providing an alternative interpretation that it is the SM that is in trouble, not SUSY. I think anyone who can read past the first few paragraphs of such a post can make their own interpretation of just how bad a hit on the SM this really is.

      • Stability says:

        Just to put this in perspective a little more: If you demand that our standard model vacuum should be absolutely stable, you are immediately erasing the whole string landscape, which is full of many, many, many AdS vacua. All of which render our vacuum metastable.

        Now, I don’t want to take it for granted that the string landscape is real or not, but just to say that your claim that our vacuum must be absolutely stable is an extremely strong claim, one that is generally not agreed upon by the majority of particle/string theorists and many cosmologists too.

        But you may be right 🙂 Perhaps AdS vacua are problematic for cosmology in some weird way (although AdS/CFT suggests they are super nice, but such constructions do not describe the big bang)

  18. Alex says:

    “Does anyone have a theory that cures the instability with only much higher energy physics?”

    Hm, there’s of course the famous funnel plot, (for the ancient version:, page 5).
    The lower boundary of which kind of gives you the instability limit on the higgs mass as a function of the cutoff scale of the theory. So I guess you could pick a light higgs mass and then read off the scale below which your solution must roughly set in to save the vacuum.

    • Philip Gibbs says:

      The plot shows the scale at which the SM goes wrong for a given Higgs mass, but this is not necessarily the scale at which it has to be modified in order to correct it.

      The only way to establish that scale is to find models that do correct it. The only one I know is SUSY and it corrects it with modifications at the Higgs mass scale. This made me wonder if there are any other models that correct it with new physics at a higher scale.

    • Alex says:

      Yes, I agree of course. I was merely suggesting that it might be an indicator of the scale below which a modification would in principle still be feasible, whereas above that, it’s too late. It’s an interesting question what alternatives there are – I could imagine, though I have to look it up again, whether maybe a Higgs that is composite at this high scale, would be a solution. SUSY for sure is the only weakly coupled solution that comes to mind.

  19. […] you compare this with my previous Standard Model Killer plot you will see that the black line is slightly lower at the minimum point because of the marginally […]

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