Where does Higgs fit best?

When I looked at this picture of Easter Island and matched it to a recent picture of Peter Higgs the best fit was the first statue, but where does the Higgs Boson fit best on the search plots from the LHC?

It may be a little late now to try to analyse the latest public data from the LHC given that the collaborations themselves are now looking at 3 times the amount of integrated luminosity, but Tommaso Dorigo is claiming that the summer data best fits a Higgs boson at 119 GeV and Peter Woit is pressing the case for no Higgs at all.  I have my doubts about either claim, so how can we see what really fits best?

To answer this we first have to think about what the familiar brazil band plots mean such as this one showing the recent Higgs combination for the summer data from the LHC.

If you look at the 140GeV point you will see that the observed CLs line is crossing the red line. The naive interpretation is that the probability for no Higgs boson at this mass is 0.95 so it is ruled out at the 95% confidence level. However, this is wrong. Such a probability can only be calculated when we plug in our prior probabilistic beliefs for the existence or not of a Higgs boson at that mass. The correct interpretation of the plot is that if there were a Standard Model Higgs boson at 140 GeV then the probability of getting a stronger signal than the one seen would be 0.95. This is a very different statement.

Looking at the plot again we see that there is also a nearly three sigma excess at the 140 GeV point. We tend to discount it because of the exclusion, but again this is the wrong thing to do. The excess tells us that if there were NOT a Higgs boson (SM or otherwise) at this point then the probability of getting a weaker signal than the one seen would be about 99% (roughly). So actually the signal indicating a Higgs boson at 140GeV is five times stronger than the one tending to exclude it. The symmetry between the signal and no signal possibility is best seen on this signal plot that uses the same information differently.

If we were being Bayesian, our prior probability for no Higgs at this point would probably be higher than the probability that one exists because there should be more places where it isn’t than where it is. If we favoured a light Higgs mass for theoretical reasons and discounted non-standard models we might assign a probability of 0.8 to no Higgs boson at around 140 GeV and 0.2 to a SM Higgs at 140GeV. In this case we would look at the 140GeV point on the plot and come down slightly in favour of the Higgs boson at  that mass.

However, the plot contains much more information because it covers the whole mass range where a Standard Model Higgs might be. We can compare the probabilities for a Higgs boson at any mass in the range and see which one is favoured. For this we need to use our prior beliefs for where the Higgs might be over the whole range. For simplicity lets just assume that we believe in a single standard model Higgs boson and we favour equally each of the mass points where they plot a square on the graph. To apply this we need to know the width of the signal that a Higgs boson at a given mass would produce on the signal plot. The underlying decay width for a Higgs boson is predicted by the standard model as shown in this plot.

Below twice the mass of the W the width is very narrow and it is the resolution of the detectors that counts. This varies depending on the channel and the mass but I am going to assume that it is ±5 GeV at worst and fit to a bell curve on that assumption. If you think differently you may get a different result from me. The method is to overlay the bell curve on the signal plot with a peak at 1.0 where we think the mass of the Higgs may be and tending to zero either side. At each mass point we read the signal strength and use the observed data to tell us the conditional probability for that signal strength (assuming a flat normal PDF) . These probabilities are all multiplied together to give the conditional probability for the fit. We can then try all the curves for different Higgs masses we believe in and see which one has the best fit. Here is the result.

As you can see the best fit is actually at 141 GeV. Perhaps we should see how it works for the separate plots from ATLAS and CMS

ATLAS sees the Higgs at 144 GeV and CMS sees it at 141 GeV. That is pretty consistent given the resolution of the detectors. What about using different channel combinations. I will limit this to the three with the most data.

The best fits are 132 for WW (which has poor resolution), 143 GeV for ZZ and 139 GeV for diphoton. So it is a pretty consistent result.

I don’t think it is safe to conclude that the Higgs boson has mass around 140 GeV. All we can say is that the limited data published so far supports that as best fit. The summer data has not probed the 120 GeV region well enough so there could be something there with a stronger signal when we look at the 5/fb data for this winter. Rumours are that there is not much of a signal anywhere with 120 GeV being the best chance, but I am waiting until I have seen the data myself and repeated this objective analysis.

43 Responses to Where does Higgs fit best?

  1. Albert Z says:

    Aside from Ruby Begonia, do duh names phlogiston and N-rays ring a bell?

    Albert Z

  2. Tony Smith says:

    What does your analysis show for the viXra combo plots for some of the smaller peaks, particularly:

    at 300 GeV
    at 240 GeV
    at 220 GeV
    at 200 GeV

    Based on my 3-state Higgs-Tquark model (see viXra 1110.0015 and other material in links on the last page) I would predict that:

    300 GeV and 220 GeV will go away eventually
    200 GeV and 240 GeV will be supported by more data


    that the cross sections of the three surviving peaks will have the following percentages of a full single SM Higgs cross section

    140 GeV about 50 percent of full single SM Higgs
    200 GeV about 15 percent of full single SM Higgs
    240 GeV about 35 percent of full single SM Higgs

    for a total of 50+15+35 = 100 percent.


    PS – It is interesting that for the currently announced data (about 2/fb) it seems that

    ATLAS sees the 240 GeV peak but not the 200 GeV
    CMS sees the 200 GeV peak but not the 240 GeV.

    In a comment on his blog, Tommaso Dorigo, in the context of the current 2/fb level of data which there are only a few events in the Higgs to ZZ to 4l channel that is so important in the range from a little below 200 GeV up to about 300 GeV:
    “… the most likely circumstance for two experiments that globally see a signal compatible with the SM cross section is that one sees more of it and the other sees less …”.

    Maybe with a lot more data the ATLAS and CMS results may converge with both 200 GeV and 240 GeV peaks emerging.

    • Philip Gibbs says:

      I could run the analysis with models having multiple Higgs-like bosons but I don’t think the current data is sufficiently good to test that and I don’t want to dwell on the old data. Perhaps with 5/fb I will do it.

  3. ondra says:

    Thanks Phillip for nice analysis. I was wondering whats your opinion why there is a huge difference between ATLAS(deficit) and CMS(signal-like) at 120 GeV signal plots. One can also see in ATLAS and CMS low mass analysis H>tautau and H> bbbar, that while ATLAS signal is like -1 sigma, CMS is around +1 sigma, Could it be some systematic effect?
    There also seems to be something like that going on in over 500 GeV region.

    • Philip Gibbs says:

      The blue bands are wide in those regions, so such fluctuations are the norm. The tautau and bb from LHC do not have sufficient stats to be worth looking at on their own yet.

    • anna v says:

      CMS has better photon detection, I believe.This might make an extra difference if there is a higgs there.

    • ondra says:

      Well, it would be nice to see plots after 2,3, 4 fb-1 and so on, to see how it develops. Of course, the exclusions in tautau and bbbar is insufficient but number of events isnt that low.

    • Guybrush says:

      The “signal” at 120 GeV in the CMS plot is due to the gammagamma channel I think. A lot more data points in the invariant mass diphoton plot are above the MC points (but not at ATLAS!). Maybe they have a energy calibration problem at CMS. Or maybe they are underestimating their errors. I dunno… The CMS “signals” at 120GeV and 140 GeV could be statictical fluctuations which are additional to this systematic issue, which fakes this broad signal from 120 to 140 GeV.

      • anna v says:

        When CMS was being designed a lot of thought went into photon identification particularly in view of the higgs to gamma gamma channel. Hence the crystal calorimetry which gives better angular resolution of photons.

        The problem with photon identification lies in the small mass of the pi0, which, when it decays into two photons and has the large energies of the LHC can easily seem like one prompt photon. Pi0 gamma separation is crucial in the extraction of a signal from the background, as each interaction has very many pi0s.

        If the effect were that ATLAS favored a gamma gamma peak and CMS did not show it, I would be more suspicious. The fact that it is seen in CMS is consistent with the possibility of a real signal existing which is diluted in the ATLAS analysis by the worse pi0 photon separation.

      • Guybrush says:

        Hi anna v,
        the lead-tungsten EMCal of CMS has a better energy resolution, while ATLAS has a better shower shape analysis compatible EM calorimeter with its three separate layers and finer angular resolution. My thought was that the pion^0-background could be better under control at ATLAS due to the first layer of the EM calorimeter which consists of many fine segments in eta so that pion^0 decays can be distiguished from the single isolated photons.

        Therefore I think CMS would have an advantage when it is all about to measure the Higgs-Mass precisely, after its discovery. But for the discovery itself I could imagine that ATLAS could have an advantage, due to the better background reduction.

      • anna v says:

        I would be interested in a link comparing the two detectors on gamma pi0 separation, if you have one?

      • anna v says:

        In the following link we see that CMS has higher luminosity than ATLAS in the gamma gamma channel :

        The extra statistics may also explain better resolution.

      • Guybrush says:

        Hi Anna,

        no sorry I havent seen any pion^0-reduction related comparison plots of both calorimeters yet.

        But thanks for the link, yes the CMS lumi is actually higher for the gammagamma channel. But look at this plot here:

        You see that all in all the datapoints are above MC, and especially around 120 GeV and 140 GeV. Even down to 80 GeV.
        It seems to me that they dont have a precise SM background model yet. Also the statictics of the MC background seems to be poor. I wonder how large the error bars would be…

        I dont know whether the CMS guys compared the datapoints to the MC results, or used their background model fits for their contribution to the brazil band plot. Do you know that?

      • anna v says:

        Hi Guybrush

        Sorry, I have no inside info. In the plot you link I expect that the unknown is the relative contribution of the various channels to the monte carlo, that is why the data is over all mc plots.

    • ondra says:

      If this difference is seen consistenly we could be looking at serious issues and another D0/CDF type of problem 🙂

  4. Ian Sample says:

    Hi Phil
    Do you expect the full 2011 stats for Atlas and CMS SM Higgs searches to be released separately, or will the next official word be the combination of those?
    Be good to hear your thoughts…

    • Philip Gibbs says:

      That’s what we are all wondering. I know the separate ATLAS and CMS results are supposed to be available for the CERN Council meeting in mid-December and there wont have been time to do a (proper) combination by then, but the CERN council is a partly closed meeting so it is not sure that they will be made public until later when a combination could be ready.

  5. Luboš Motl says:

    Let me admit that I have no clue how to understand your “derivation” of the preferred 141 GeV mass through the width. Visually, it’s clear that 119 GeV is favored over 140 GeV, for example. Did you get a preference of 140 GeV relatively to e.g. 119 GeV because the width is larger for 140 GeV than for 119 GeV?

    In that case, I think that this argument of yours is based on a misconception because the width is well below 1 GeV (for mass below 200 GeV) and zero for all purposes and the width one would see in the graphs would be due to experimental errors, not the actual decay rate.

    When the decay rate is small, the decay rate is irrelevant for the detection of the Higgs. What influences how many events you get is the cross section for the Higgs production, not its decay rate (and not the product of both). The Higgs decay for these low Higgs masses is low enough so that you may completely neglect the “theoretical” contribution to the width it produces in the graphs. On the other hand, it is large – rapid – enough so that the Higgs decays almost instantly. where it’s created. For the detection purposes, it doesn’t matter at all whether the width is 0.01 GeV or 0.05 GeV.

    • Philip Gibbs says:

      I mentioned that the width is dominated by the detector resolution in the post. The actual width varies so I just fitted to a variety of widths up to 5 GeV, so that should not bring in a bias. The 119 GeV bump is disfavoured because the error bands are larger there, but the 140 GeV signal is good enough to be preferred over the possibility that it remains in the area not yet well explored.

      • Luboš Motl says:

        OK, but the 140+ GeV Higgs is also disfavored by negative evidence, right? Do you completely neglect it?

      • Philip Gibbs says:

        Yes I know there is a two sigma evidence against it but that is not much and a much larger exclusion was expected. I am not saying that it is at 140 GeV or even that the signal is strong, just that if I do the most objective test I can think of that uses all the information in the plot I find that 140 GeV is the preferred location for a single SM Higgs. Dorigo did a different analysis and got a different answer of 119GeV. I would prefer theoretically. I am not saying he is wrong, just that a different equally reasonable analysis can get a different answer.

      • JollyJoker says:

        I think that means “yes” 😉

      • Philip Gibbs says:

        No it is not neglected. The nearly three sigma excess in favour of the signal at 140 GeV is stronger than the two sigma excess disfavouring it. This was explained in the post. 🙂

  6. ohwilleke says:

    From a Baysean perspective, the electroweak precision data (for which we have means and CIs to work with) and issues of stable/metastable vacuums would seem to strongly favor the light end of the range over the heavy end of the range. If we saw a 600 GeV Higgs, the odds that it is a SM Higgs seems remote.

    The argument for 119 GeV is basically that this is in the dark alley away from the lightpost where we haven’t looked yet, so any result in that mass vicinity is consistent with a SM Higgs, and the 119 GeV is the strongest peak in the area.

    The argument against the 140 GeV as a SM Higgs, as I understand it, is basically that this area is much more “well lit” and yet we don’t see what we expect to see. Best fit or no, it still doesn’t look like what we are trying to see. There may be something interesting at 140 GeV since we are getting some sort of signal there, but whatever it is seems likely to be something other than a SM Higgs.

    The interesting question at 140 GeV seems to be, “what other than a SM Higgs at that mass could it be?”

    • Philip Gibbs says:

      I dont agree with that conclusion and that is why I did this test. The 140 GeV level is just two sigma below expectations if there is a Higgs there, but it is three sigma (almost) above the null hypothesis. It is more likely that there is a two sigma fluctuation down than a three sigma fluctuation up. My analysis measures this in an unbiased way and reaches the same conclusion as I saw by eye.

      I am not saying that the signal is strong, it is just the best fit from the limited data so far if you assume that there is just a single SM Higgs somewhere. The match for no Higgs is also worse than the match for the 140 GeV boson by the way.

      The electroweak precision data is interesting as a rough indication that the boson is light, but I don’t trust it to distinguish 120 GeV in preference to 140 GeV. For one thing it prefers even lighter masses and could be affected by any number of other BSM particles yet unknown, as well as systematic errors.

      You can factor in your preference for lighter masses if you wish and rerun the test, but unless your weight is strong it will not make enough difference.

      • Tony Smith says:

        As to “… electroweak precision data is interesting as a rough indication that the boson is light …”

        it is also interesting that, if the Tquark mass is allowed to float (as it would in a 3-state system of Higgs as Tquark condensate) then
        the Gfitter preferred Higgs mass is 141 GeV (+209 -74).


        PS – The physical reasons for my other two Higgs masses are,
        as you run up the renormalization curve from 141 GeV:

        at about 200 GeV the Higgs encounters the Triviality Boundry;

        at about 240 GeV the Higgs encounters the Critical Point involving both Triviality and Vacuum Stability.

  7. AnonymouS says:

    140 GeV was clearly special, but can you explain how/if this is read from the “blue band” plots, given that it comes from the ZZ channel which has less statistical weight than the WW channel?

    • Philip Gibbs says:

      The 140 GeV is seen in digamma and ZZ. The WW has low resolution but is still consistent with something in that area. I don’t know if that answers your question.

  8. Very interesting analysis.

    There is a fundamental difference between “seeing” and “ruling out”.

    For seeing something, it is instantaneously (that is, in minutes of the event) although the verification can take months.

    For ruling out something, it is a tedious work, that is, every stone must be removed and every hole must be checked. Of course, during the ruling out process, we can see something.

  9. Kea says:

    I’ve been to Easter Island, and I don’t think P. Higgs looks like any of the statues.

  10. physicspet says:

    Ok, there are enough stone heads to also fit Brout, Englert, Guralnik, Hagen, and Kibble. What gives?

    • Philip Gibbs says:

      That would have confused the point I was trying to make. I know that others deserve some credit for the Higgs mechanism. Perhaps one day i will do a post about the history and who contributed what, but I know it is a controversial topic and I don’t want to spark a discussion about it here. Some people add other names especially if they are American.

      In any case it is hard work doing it with just MS-paint.

      • physicspet says:

        Thanks for reply. I would word one sentence differently. “Some people exclude names, especially if they are European.” 🙂

        Thanks again.

  11. Mike says:

    From some other rumors, there is likely to be a 90% exclusion of Higgs from 114 – 140 GeV based on current data (to be distributed internally at CERN around Dec. 15th)?

  12. Albert Z says:

    Why should particle physicists model nature, given its spoil-sport attitude and insistence on rational laws?

    Why not just model the Platonic “world”, which is so much more cooperative, and leave it at that?

    Theoretical physics has evolved and no longer needs the template of nature for judging its “beauty” and “elegance”.

    It’s the brave new fizzics. It transcends reality!

    Albert Z

  13. The explanation here is marvelous, but I still wonder: Is the red line theoretically fixed with respect to the theoretical background and not vary with the data collection? And does it need to be redrawn to reflect poor resolution of energy?

    • Philip Gibbs says:

      The red and green line are fixed. They indicate the levels corresponding to the standard model with and without a Higgs boson at the given mass. All the uncertainty including statistical, theoretical and detector systematics should be included in the error bands in blue.

    • chris says:

      it should be fixed. there are theorists however that see wiggle-room by more than a factor 2 instead. this is a theory error and the main part comes from the change in event kinematics as one goes to higher order, which is currently being ignored by MC generators.

  14. George T. Fleming says:

    What happens to your 140 GeV Higgs if you also include the Tevatron limits?

    • Philip Gibbs says:

      Even the Tevatron data on its own fits best to 143 GeV. When combined with the LHC data it dampens the signal at 120 GeV and does not affect much else, so the best fit remains at 141 GeV.

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