LHC Combination Of Higgs Limits: MH<141 GeV
    By Tommaso Dorigo | November 19th 2011 05:29 AM | 18 comments | Print | E-mail | Track Comments
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    I am an experimental particle physicist working with the CMS experiment at CERN. In my spare time I play chess, abuse the piano, and aim my dobson...

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    Totally overshadowed by the news of the new Opera measurement of neutrino speeds, yesterday CERN officially released the combined result of ATLAS and CMS searches for the Higgs boson. The news has been given already in two prominent particle physics blogs (Resonaances and Not Even Wrong), so I think I am not obliged to do anything more than point you to those, who cover the matter quite accurately.

    Furthermore, both Jester and Peter also point out that the result was precisely anticipated by an independent analysis at the VixRa blog by Philip Gibbs. Doing combined limits on Higgs masses is not conceptually harder than doing the weighted average of two measurements, although immensely more complicated (incidentally: about just how hard it is to make the weighted mean of two measurements of a random variable I will have something to write tomorrow, as I will try to explain the meaning of my latest "guess the plot").

    Despite all that, I do want to write here my personal thoughts on the message that the combined LHC result provides. Let us take the figure which shows the upper limit in units of "times the Standard Model cross section", as a function of the unknown value of the Higgs boson mass: see below.

    Although most of you already know what the plot signify, I reiterate its meaning: the black curve shows  as a function of the hypothesized Higgs mass how large the Higgs boson cross section can be without coming in conflict with the experimental observations of ATLAS and CMS, who did not see any evidence of an excess of events in any of the dozen channels they have sought the darn particle. The cross section is calculated in units of the predicted SM value (which is also a function of Higgs mass), such that by comparing the location of the black curve with the horizontal line at 1.0 you immediately get to see where the Higgs boson cross section has been constrained to be smaller than what the SM predicts: all points of the black curve laying below 1.0 correspond to Higgs boson mass values which are experimentally excluded, at 95% confidence level.

    Now, the "brazil band" in yellow and green show what limit was predicted by ATLAS and CMS they would set, given the experimental methodology and available statistics, in case the Higgs did not exist anywhere in the mass range investigated. The agreement of the black curve with the brazil band indicates that the data did not fluctuate up or down too much -observed event counts are consistent with expectations. Small departures here and there are however still visible. Let us then concentrate on those.

    You may see, for instance, that there is a upward fluctuation of the observed limit at 120 GeV; another fluctuation spans a broader range between 135 and 150 GeV. Which of the two is consistent with the possible contribution of real Higgs events ?

    By eye it would not be possible to answer this question, although of course the 120 GeV fluctuation occurs in a region where the black curve is head and shoulders above the line at 1.0, indicating that there the Higgs is alive and well; while the broader fluke around 145 GeV is fighting with the line and losing the battle. Let us instead look at the much more interesting figure shown below, which indicates what is the "best fit" value of the Higgs cross section given the data, in units of the Standard Model cross sections and again as a function of Higgs mass.

    The figure is horribly complicated, so let me guide through it. The upper portion shows the "local p-value" of the observed event count seen by the two experiments, once different final state results are combined. All is as always as a function of the unknown Higgs mass. If you concentrate on the black curve (combination of red and blue), you see several downward spikes, corresponding to points where the two experiments saw some upward fluctuation in the number of observed events with respect to predicted backgrounds. Crucially, the dotted green curve shows what kind of "local p-value" (a probability of the fluctuation observed) would be on average seen if the Higgs boson existed. Again as a function of M(H). You thus see that all the downward spikes are much smaller than they would be if the Higgs were there, except one, the one at 120 GeV.

    In the lower part of the figure you see (black curve with blue "one-sigma" band overlaid)  the "best fit" Higgs cross section, again in SM units. Here you see that while the 135-150 GeV fluctuation is only consistent with a Higgs boson that has a cross section much smaller than SM predicts, the 120 GeV one is in the right range: in other words, a 120 GeV Higgs (or rather, 119 GeV Higgs, as I predicted some time ago) would fit the bill quite nicely.

    At the 2012 winter conferences ATLAS and CMS will present their search results employing three-times more statistics -all the data collected in 2011. By then we will know more about the possibility that the 120-GeV fluke is the real thing. And, since Philip has shown he can combine results quicker than the experiments can, we will then ask him to give the definitive answer, with quite some advance with respect to summer 2012 conferences (when CERN expects that a official combined result will be released)!


    Sounds like the waiting is almost over, finally!

    Hello Tripi,
    yes, if the beast is there, we'll (sort of) know soon!
    Would a 119 GeV Higgs have been found with an extra year of LEP?
    We were lucky it didn't, or the LHC would have been cancelled!

    Tommaso, your bet for 120 has two things going for it:
    1 - it is within the preferred band for Gfitter comparison with ElectroWeak data
    2 - its peak has enough cross section for a single SM Higgs
    those factors have some problems:
    1 - Gfitter EW comparison really favors 95
    2 - the 120 cross section is about 30 per cent HIGHER than SM Higgs

    On the other hand, as to my Higgs = 3-state (140 and 200 and 240) bet:
    1 - if the Tquark mass is NOT a single fixed value (as it also has 3 states)
    then Gfitter EW prefers 141 and a band (+209 -74)
    with the 200 and 240 well within the band
    2 - If the SM Higgs cross section is spread among the 3 states,
    then the 140 and 200 and 240 together give the SM cross section:
    the 140 peak has 50 percent of it
    the 200 (very small) peak has 15 percent of it
    the 240 peak has 35 percent of it
    for a total 50+35+15 = 100 percent of the SM cross section.

    Perhaps by December it will be clear which bet holds up better with 5/fb
    it may be March (or even summer) before the public is told.


    You know, Tony, while I do not buy the three-states top quark model, I'll admit that a multiple-resonance Higgs is more appealing -and more theoretically motivated. Indeed, the Higgs mechanism might live with a multiplicity of different realizations of the Higgs field.

    In any case, please consider that the "120 GeV Higgs xs is higher than SM prediction" is not a meaningful statement, given the large uncertainty in the measurement. It is like I measured my own weight with a scale bearing a +-30 kg error and I said I've fattened because it says I weigh 100 kg (when I'm in fact 70 usually).

    Hope gives life reason. Congratulation on narrowing it down to 119 Gev. You'd need a plane load of scientists to fly down to Oslo, indeed! We'd be licking our wounds, meanwhile.

    Isn't a value of 120 GeV already ruled out by FermiLab?

    Nope Anon, the lower limit by CDF and DZERO combined is somewhere around 108 GeV or so, and so the real lower limit is LEP II's 114.4.
    Two comments:
    - The feature at 120 is present only in the CMS data (clearer from slide 23 of ).
    - The feature at 120 is at ~ 1.6 sigma significance (p.20 of ).
    - The Combination by Gibbs was done only for the upper limits, not the best-fit values (which are more interesting).

    Dear Andre,

    your two comments look like three to me. In any case, the value of combining results (and you agree the best fit values are "more interesting") is exactly the one of seeing the data as a whole.

    But I would rather draw your attention to the fact that 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 - so the first point you make is rather irrelevant to me.

    Second, I do not understand what you mean when you quote the significance at 120 GeV. I did not talk about that in my post, I just said that if the Higgs boson is anywhere, it is most likely there. Do you concur ? From the tone of your text you sound slightly annoyed by something, but I cannot really figure out what that is. Perhaps that I give credit to Phil for doing publically what many of us had done privately ?

    Hi Tommaso,

    I am not annoyed. And yes, age leads one to forget how to count. My comments go in the sense that simple combinations work as long as things are uncorrelated, as you recently very pedagogically explained here in the blog.

    As "for one sees more and the other sees less", my point is that for equal expected sensitivity, one seeing and the other not seeing reduces the significance of the observation of the one seeing if you are to believe the one not seeing. I hope I have not overlooked some reason why this reasoning could be incorrect.



    Oh, very good then. I agree that if both CMS and ATLAS are expected to get -say- 2 sigma for a given Higgs mass and one of the two does not, this is a turnoff. But I must say I continue to be optimistic.


    simple question: for a pretty large window (from ~125 up to ~165 GeV) the upper limit experimentally set is at least 2 sigmas larger (and worse) than the expected value. Does this mean that there's something fishy going on? Related to this: how could I possibly trust a 3 sigma excess (showing perhaps in the near future) if another broad excess isn't under control?

    The feature you observe is due to the WW mode, where more events are seen but the mass resolution is very lousy, so the excess contributes to a wide region. One cannot make inferences about the goodness of fit of the global combined result by looking at how much and how frequently the black curve departs from the expected value (a median, btw).
    So there's nothing really fishy. There is probably some excess at 119 due to a few Higgs events, and normal fluctuations here and there.
    If a 3-sigma effect is LEE-corrected, you should trust it.

    I think you are all too impatient. If the Higgs boson has a mass of 120 GeV or so, the pattern we have been observing in the last 12 years of searches is exactly the right one.

    The desert exists, but it is from 200 GeV to the planck mass ;-)

    My prediction depends on inflation, but it's around 123 Gev, so just as John Ellis emphasized, ~ 120 Gev is the promised land ! I guess the real reason we are All impatient is we want to see old man Higgs get his Nobel before his time is up !
    I would argue that the desert extends far beyond the Planck scale. INTEGRAL recently measured the polarization dispersion in gamma rays from GRBs at cosmo distances, & predicted a New quantum gravity scale, corresponding to ~ 10^ - 49 meters or ~ 10^ 33 Gev, some 14 decades beyond Planck.

    if the Higgs is indeed at 120GeV, the desert can't stretch beyond ~10^9GeV. And if it's not found at all in the 114-140GeV window, there is no desert but TeV scale new physics.

    As to "The desert exists ... from 200 GeV to the planck mass",
    I agree with chris that if the Higgs is at 120 GeV then the desert will not get to the Planck scale
    if there is a Higgs around 140 GeV then the desert can get up to the Planck scale
    so in the latter case I agree with you if you would raise its beginning from 200 to about 240 GeV.

    In any event, it seems that some relevant questions are:

    What would the LHC expect to see in the desert above EW symmetry breaking energy ?

    With no mass-giving broken EW symmetry,
    what happens to the Kobayashi-Maskawa matrix and CP Violation ?

    How to distinguish among the generations
    if the only experimental tool we have (mass observation) is not there ?
    i.e., will a Tquark look just like an Up quark in the desert,
    and will an electron look just like a muon and also a tauon ?

    How can neutrino oscillation be observed in the desert ?