Combined Higgs Search Limits, Circa 2011
    By Tommaso Dorigo | July 24th 2011 10:02 AM | 50 comments | Print | E-mail | Track Comments
    About Tommaso

    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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    In the last few days I described in some detail (here and here) the six searches for the Standard Model Higgs boson just produced by CMS, the experiment at the CERN Large Hadron Collider to which I proudly belong.

    The prompt reporting of these new results was not a totally painless activity on my side, because I am currently on vacation in southern Crete (you can have a look below at the beach where I spent most of the early afternoon today, Skinaria): my time these days is precious, and my connection with the experiment and with the rest of the world is granted by a internet USB stick by "Cosmote" which, despite working surprisingly well, still provides less bandwidth than I could use.

    I am thus the last in a small crowd of bloggers to comment on the recently produced "combined exclusion" results on the Standard Model Higgs boson. Having failed in promptness, and being seriously challenged in insight (most of all by Jester), I can only offer here my very own feelings on the results and their meaning. To guide my discussion, let me first of all paste here the ATLAS and CMS combined exclusion figures. The ATLAS plot is extracted from Kyle Cranmer's excellent talk at the EPS, so bear with me for the annoying extra coloured arrows.

    ATLAS (above) and CMS (below) produced 95% C.L. upper limits employing the same limit-setting procedures, which imply a profile likelihood ratio as test statistics and the modified frequentist CL_s technique to extract results. CMS also tries the Bayesian procedure with flat cross section prior as an alternative, but we well know that this is almost coincident with CLs. In any case, these are details which I do not want to spend time on. The only important thing to note is that luckily ATLAS does not report their limits with their recently proposed "16% PCL" technique, which was effectively a patched up CL_sb technique which would make comparisons with other experiments results unnecessarily difficult.

    Again, I need to advise you to visit the Resonaances site for a few very important points on the whole matter. I can only echo here the ones I find useful to stress, giving my own slant. However, the last one I think is not discussed elsewhere:

    1) Significant portions of the high-mass region are now excluded by the two experiments; it does not take a computer brain to add two and two, and realize that even the smallish regions where CMS leaves hope that a Higgs boson might hide above 200 GeV would be excluded by a combination of the two LHC results. So the whole region between 145 and 450 GeV is not where a SM Higgs can hide from us. However, please keep in mind that if we "exclude at 95% CL" the existence of a Higgs boson with mass M(H)=x, this means really little in terms of the reality of things. That is, the Higgs might still have mass x and a negative background fluctuation there might have fooled us into excluding it. This happens once in twenty cases, which is really a not so rare occurrence: a 95% CL exclusion will never give you any certainty. Of course, the confidence level for some mass points is much, much higher than 95%; for 160 GeV, for instance, the Higgs is certainly ruled out, since the chance that we missed it there are really much smaller than 5%.

    2) Implicit in the existence of the above figures, with black lines spending a significant portion of their free time below 1.0, is the fact that the Tevatron is now out of business on Higgs limit setting, with one important exception. The only region where they could still have anything meaningful to say with their full 10/fb datasets is in the whereabouts of 115 GeV, which is however a very important mass point. In the meantime, the data that the LHC will provide before the end of 2011 - four times as much data as the one used for the graphs you see above- will make these conclusions even stronger.

    3) Some of the most sensation-seeking physicists in my experiment and in its competitor have already started to speculate that the 140 GeV mass point could be the place where the Higgs boson actually hides: both ATLAS and CMS have more Higgs candidates there than they expect from background sources alone, and both quote local significances in excess of two standard deviations for that mass. Let me be a sceptic this time again: I do not see these results as anything compelling in this respect. Of course if the Higgs has a mass above 115 and below 145 GeV, 140 GeV is a good place to put your money on -chances are better than one in ten it is there, and given the data shown above probably a more honest payoff would be three-to-one. In any case, if the mass is 140 GeV we will probably have a discovery by the end of the year!

    4) I think the most important thing to draw home from the above results is their very existence. You might have overlooked this fact, but please consider that some of the data used to produce the graphs (and the hundreds of ancillary figures that belong to the individual searches summarized in those graphs) have been produced just one month ago! This is unheard-of in hadron collider physics experiments, and you should compare it with the Tevatron, where the most up-to-date results use data which are six months old or more -a time where the LHC still had to start the 2011 running... Such a display of power and focus on results is real news, and quite remarkable in my humble opinion. Not only were the data processed and calibrated in no time; they were also validated and analyzed basically overnight. Plus the internal groups and review committees have really worked around the clock to make the deadline of EPS.

    5) Connected with the former observation is a sad note for a researcher who would like to think he has a life -yes, me. The rush with which the data is produced, reconstructed, and analyzed makes everybody unhappy -actually, nobody even realizes it because nobody even has the time to stop and think about it. It is a continuous frenzy of meetings, requests for additional checks, new data pouring in, jobs being sent around the world on a thousand computers at a time. Is this the life of a physicist in the 21st century ? If so, maybe I should consider focusing on teaching!

    6) Thanks for your interest in Higgs boson searches - if you got this down the article, you give me a reason to continue reporting on it.


    The "observed" versus "expected" appears to be consistently at the edge of the yellow all the way up to 190, and only comes down after that. Does that have any significance for the "expected" result? (Non-scientist asking.)

    (Sorry, referring to the second graph)

    Hi David,

    I am not sure I understand your question. The fact is that there are globally slightly more events observed than expected from background sources alone in that mass range. This means very little -maybe the cause could be that some of the background processes are underestimated; but I doubt it. Overall, the black curve spends enough time within the 1-sigma band that I do not see any pathological behaviour.

    Thank you Tommaso, I think you nailed the question and the answer both!

    Daniel de França MTd2
    Unfortunately whoever bets on 140GeV will lose. Tevatron combined results and excluded down to 137GeV. The results will be out on Wednesday:
    Thanks. They are very interesting points for people out of LHC (like me).

    Of course we could all just come out of this learning that PDFs are poorly modeled, and we should have built a lepton collider.

    The Stand-Up Physicist
    Enjoy that beach with the family! If I ever get out to Crete, I know where to go now.
    There's snow here.

    wow - snow is good :) but I enjoy the sun at the moment.

    There will not be any Higgs. The Higgs model has very deep problems. The blatant one is that it is unstable and need something like susy to stabilize. But susy is failing spectacularly at the LHC. Another is that cosmological observations don't show the vacuum to be populated vith superheavy vacuum fields.

    That is the problem with most physical theories today. We populate the vaccuum with all manner of fields. You have the higgs... then there is another heavy field needed to break the susy necessary to stabilize the higgs...then you add the super higgs of the gut theories . . . The vacuum now is a hot soup of all sorts of stuff - - - it is all very simmilar to the medieval argument that the earth sits on a turtle and then it's turtles all the way down.

    I think the lhc will soon hit us in the face with the realization that the vacuum is empty. That's why it is called a vacuum. And the uncertainty principle postulating virtual particles all over is just a mathematical artifact.

    Quite right. No collision 'on earth' can bring out Higgs. I literally mean 'on earth', because these are not the condition which can take us back to the so-called big bang. Further, Higgs is theory. In practice gravity is due to particles whose spin is of course 0, but the rest is not so definitive as being thought in the SM.

    Don't you dare even think about not continuing, please. Thanks!


    There are many Higgs-free theories awaiting their chance to take center stage. Getting to the bottom of what is truly causing EW symmetry breaking is hopefully only few months away. Finding the SM Higgs is not likely to solve any of the deep challenges associated with the Higgs sector of SM.



    Bonny Bonobo alias Brat
    There are many Higgs-free theories awaiting their chance to take center stage
    Any good links for these please Ervin?

    My article about researchers identifying a potential blue green algae cause & L-Serine treatment for Lou Gehrig's ALS, MND, Parkinsons & Alzheimers is at
    Ok. Helen. Here is a good discussion:

    I'm hoping you'll convince Tommaso here to discuss alternate models more often.


    You can do a Google search under "Higgs-free" and "Higgsless", although these links do not cover all models that have been developed over the years.


    I find your points 4 & 5 interesting, but also somewhat concerning. Validation is certainly an important aspect of experimental work, in particular for experiments as complicated as the Higgs search at a hadron collider. Should we even trust these "rushed" results?

    Now, to be more concrete, comparing the current CMS exclusion plot with the one leaked about two weeks ago, it seems that CMS figured out the reason for the under-fluctuation in the ZZ->4 lepton channel in the 350 GeV region, and probably also the excess around 220 GeV (although that might have been fixed by statistic alone). On the other hand Atlas still seems to have a large downward fluctuation in the 350 region, so maybe they didn't figure out how to fix the background estimate there?
    From the old projection plots I recall that anything above 200 GeV is dominated by H -> ZZ -> 4 leptons. The mass resolution is quite good there, so a statistical fluctuation in this region should produce more narrow features in the exclusion band, while the Atlas downward fluctuation between 300 and 450 and upward above 450 might indicate some systematic problem. But who knows.

    Ok, so the real question is: Assuming that Atlas came to the same conclusion, that there might be a systematic problem in the region above 300 GeV: Would holding back the results, or only showing the region below 300 GeV, have been an option for Atlas, in the current environment where results are expected within weeks after the data has been collected?

    At least the time between the end of the pp program this fall and the winter conferences 2012 is longer. I'm looking forward to those Higgs results. However I fear these analyses might also affect the winter holidays for many experimenters.


    Dear full stop,

    first of all, don't even try to discuss the comparison between an internal, non ufficial plot, and the one published. You will not learn anything from that, really.

    Second, the internal scrutiny that these results underwent is very deep, and so is the data validation step which precedes that.

    In the high-mass region the H->ZZ may be narrow (in the 4-lepton mode) or wider (in other decay final states sought). In any case a limit tighter than the expectation signifies that fewer events were seen than expected backgrounds. This may happen in a wide mass region, explaining a wide downward fluke. It has therefore nothing to do with signal shapes. It may, however, have to do with background estimates, which may affect larger portions of the spectrum. The uncertainties on the backgrounds are accounted for in the analysis, and I do not see anything troublesome in the slight departure of expected and observed limits.

    In other words, the correlation lengths of upward flukes is determined by the signal shape, but the correlation length of downward flukes is dominated by the background systematics.


    Mr. T - you have spoken many times in the past about how CDF and D0 understand their detectors very well; that is, they are extremely well calibrated. Can we say the same thing about Atlas and CMS? And at what level of confidence?

    Don't forget that CMS and ATLAS are newer machines. The technology has not stood still in the last ten years or so. ATLAS and CMS exhibit a great understanding of their efficiencies, measurement systematics, and artifacts. Only things such as the jet energy scale may need to wait before the CERN experiments can measure the top quark mass at a level comparable to that of the Tevatron experiments. But there are other ways to do that particular thing.

    Dear Tommaso,

    thanks for your detailed reply.


    I did read all the way to the bottom. Though I don't understand all of it, I am very grateful you take the time to explain, with such clarity, and such regularity. Thank you.

    Hi Tommaso,
    I've red that these plots are obtained using a technique called "profiling". Can you explain it briefly?


    Very quickly, the test statistics is a likelihood ratio between two hypotheses. Since the likelihood depends on the assigned value of many systematic uncertainties on which the measurement depends (these are called "nuisance parameters"), the maximum of the likelihood for the two hypotheses is sought in the space of these nuisances, and in this sense what is used is the "profile" of the likelihood in the neighborhood of its maximum. Cheers, T.
    Indeed point 5 makes me wonder if it is possible to do physics in the 21st century and not make my toddlers science-orphans and myself a second-time divorcee.

    At present, analysis is driven on a 24/7 basis by (in increasing order of age):
    - staunch graduate students
    - eternal bachelors that have no intention of having a family
    - senior professors whose children have taken off to university

    At the pace that the LHC is providing luminosity, it seems that this will not change for quite some time.

    "It is a continuous frenzy of meetings, requests for additional checks, new data pouring in, jobs being sent around the world on a thousand computers at a time. Is this the life of a physicist in the 21st century ?"

    When we work with big money projects it is always like this. Higgs particle is a "fashion", not just a scalar field ;)

    From Dzero web page

    Hi Tommaso,

    I recall that particle physicists only consider a particle's existence truly established once they pass the 5 sigma significance level. Does the same go for ruling out a particle's existence? Is it necessary to rule out Higg's existence for 5 sigma? Or would 2 sigma be sufficient?


    Hi Martin!

    Sorry for not answering before - at the time of your writing, I was waiting to board a flight in Crete.

    The question is important for the sanity of this thread... Indeed, 2-sigma should be utterly insufficient as a proof of non-existence. I would say that in the case of the SM Higgs we would not throw the towel before we had a confidence level equal to 4-sigma or so. 5-sigma would be very taxing, but 3-sigma would be still insufficient to start working at such deep foundations of particle theory.

    I think the question deserves to be bounced in the statistics committees of CMS and ATLAS. We meet on Thursday and I'll mention it -would like to have my colleagues' opinion.

    The lighst Higgs mass is = 119,61 Gev

    The Higgs potential for a collision energy of particles is given by:

    \ V(x)=2x^{4}-(1-T^{2})x^{2}+\frac{1}{8} \

    Where T is the collision energy and x is the mass of the Higgs boson
    In a vacuum state, that is during the collision energy is 0 and when the potential V (x) = 0 (“empty”) we have:

    \ V(x)=2x^{4}-x^{2}+\frac{1}{8}=0 \

    Which brings us to:

    \ V(x)=16x^{4}-8x^{2}+1=0 \

    And this equation has 4 solutions: x = -1 / 2, -1 / 2, 1 / 2, 1 / 2
    Discarding the negative mass solutions have the mass of the Higgs boson is x / 2
    Now, as to what is x / 2?
    The answer is about the equivalent mass Higgs vacuum which is given by the Fermi constant
    1.16637 x 10 ^ -5 GeV ^ -2
    To become mass to the mass of the electron gives the following dimensionless number:
    Higgs vacuum equivalent mass = 481841.46525
    Mass of the Higgs boson would be a maximum = 481841.46525 /2
    Now you can easily show that this value of the higgs vacuum must meet the following equation:

    \ m_{vH}^{2}=(Sum\: mass\: leptons)^{2}+(Sum\: mass\: quarks)^{2}+m_{w}^{2}+m_{z}^{2}+m_{H}^{2} \

    Where: mVH = equivalent mass of the Higgs vacuum given by the Fermi constant and related to the electron mass = 481841.46525
    Boson mass Mw = w to the mass of the electron = 157332.3391
    Z boson mass Mz = to the mass of the electron = 178449.6957
    Lepton mass sum to the mass of the electron = 3684.91855
    Quark mass sum over electron mass = 347515.614091
    Solving the above equality, we have that the mass of the Higgs boson to the mass of the electron is equal to:

    SQR( 481841,46525^2 -347515,614091^2 -178449,6957^2-157332,3391^2 -3684,91855^2) = 234078,5299
    Since the Z boson mass = 178449.6957 times the mass of the electron and Mz = 91.1876 GeV, one has the mass of the Higgs boson is = 119.61 GeV
    It is noted that equality need 5 terms, which is related to the group SU (5) of the 5 Higgs, 2 and 3 loaded loaded, SU (2) and SU (3)
    SU (5) has dimension group = 5 ^ 2 -1 = 24 = 6 quarks leptons + 6 + 3 electroweak bosons + 1 photon + 8 gluons
    The standard model gives a value to the boson mass
    Higgs with a stranger lambda parameter:

    \ m_{H}=v\sqrt{\frac{\lambda}{2}} \

    \ \frac{2\cdot(1+\cos(\frac{2\cdot\pi}{5}))}{\cos(\frac{2\cdot\pi}{5})}=\lambda \

    The 5 Higgs bosons divide the angular space
    symmetry group SU (5) generates the standard model particles 24 with an angle:

    \ \frac{2\cdot\pi}{5} \


    \ \frac{v}{\sqrt{\frac{1+\cos(\frac{2\cdot\pi}{5})}{\cos(\frac{2\cdot\pi}{5})}}}=mh \

    \ \bigl\lfloor\alpha^{-1}\bigr\rfloor=137 \

    DIM[E(8)] = 240 roots = number particles + number antiparticles
    120 particles ====> SU(11 ) ; 11 dimensions; order icosaedral group

    \ \bigl\lfloor2\cdot\ln\frac{planck\; mass}{electron\; mass}\bigr\rfloor=103=1^{2}+2^{2}+3^{2}+5^{2}+8^{2} \

    103 + 137 = 240 ; DIM[E(8)] = 240 roots not equal to 0
    Fibonnaci numers, serie: 1,1,2,3,5,8 ; 1 x 1 x 2 x 3 x 5 x 8 = 240
    sum of square divisors of 240, the first 6 Fibonacci numbers, and generators of symmetry groups U (1), SU (2), SU (3), SU (5) and SU (8)
    Important twin primes associated with quantum entanglement
    103 and 137 belong to pairs of twin primes
    120 = sum of a pair of twin primes = 59 + 61 (entanglement )
    The group E (8) = E (6) x SU (3) = 162 +78 = 240
    240/ 78 is very close to tan(2PI/5)
    78 = 2 x ( 1^2 + 2^2 + 3^2 + 5^2 ) ; the factor 2 is for particles + antiparticles
    Fibonacci numbers of SU(5): 1,1, 2, 3, 5
    162 is the sum of consecutive states of the sum of squares of the first 6 Fibonacci numbers, divisors of the nonzero roots of E (8) = 240

    \ 1^{2}+(1^{2}+2^{2})+(1^{2}+2^{2}+3^{2})+(1^{2}+2^{2}+3^{2}+5^{2})+(1^{2}+2^{2}+3^{2}+5^{2}+8^{2})=162 \

    sum of 5 states, factorial of 5 = 120 = dimension group SU (11), 5 Higgs bosons
    If we add other state, first number Fibonacci serie, thus:
    162 + 1 = 163; with 6 states

    (1-\frac{\ln24-1}{10})^{^{2}}+\frac{163}{6}=\alpha^{-1}-\left\lfloor \alpha^{-1}\right\rfloor

    Where In24 is the number of microstates of DIM( SU(5) ) = 6 quarks + 6 leptons + 8 gluons + 1 photon + 3 bosons electroweak

    10 = sum particles interactin solely electromagnetic filed whit not color QCD ( 6 leptons + 3 bosons electroweak + 1 photon )
    Higgs mass = mh

    \ \frac{v}{\sqrt{\frac{(1+\cos(\frac{2\cdot\pi}{5}))}{\cos(\frac{2\cdot\pi}{5})}}}=mh \

    \ \frac{\frac{mh\cdot(1+\cos(\frac{2\cdot\pi}{5}))}{\cos(\frac{2\cdot\pi}{5})}}{\ln(\frac{1+\cos(\frac{2\cdot\pi}{5})}{\cos(\frac{2\cdot\pi}{5})})}=\sum m_{l}+\sum m_{q}+m_{W}+m_{Z} \

    ml = sum leptons masses ; mq = sum quarks masses; mw= mass W boson;
    mZ = mass Z boson
    There is a privileged reference frame with respect to the ratio of the masses of the particles.
    The prime reference is the electron mass, the stable particle with mass smaller load and electric charge
    The information is 2-dimensional holography by
    the squares of the first 6 Fibonacci numbers, dividers dimension of the group E (8)
    Fibonacci spirals could correspond to superstrings
    Here is a strange equality:
    11 dimensions is the sum of the first 4 numbers of the Fibonacci series, not counting the one that is repeated.
    If we calculate the length of the spiral generated by sequentially stacked areas of these Fibonacci numbers have this strange very approximate equality:

    \frac{\frac{11\cdot2\cdot\pi}{4}}{5+(\tan(2\cdot\pi/5)-1)^{-2}}\approxeq Lplanck11D

    Where Lplanck11D is the lenght Planck in 11D
    Lplanck11D = 3.3027159159, Fairly close to the length corresponding to the inverse of the fine structure constant, given by the expression:


    speaking of the huge amount of work you guys had to do for EPS... yeah, great, but... when are you going to start over and provide us with updated results? ;-)

    I mean, there's more than 1.5/fb now, and 2/fb will come soon... we're curious! :-)

    Hi Anon,

    indeed this was a huge amount of work, and it can only be done in steps. In other words it cannot be a continuous update of the results, for several reasons. For instance, the triggers used to collect the data change abruptly as data taking progresses, and the data taken before and after needs to be treated differently. It makes sense to update results only two or three times a year, typically. On the other hand, it is true that the LHC luminosity profile is steep, such that one quickly finds oneself sitting on enough new data to provide significant improvements in the results. Compromises have to be taken. I think we'll have improved results for selected analyses in Fall 2011, and all major results will be ready for the winter of 2012.

    I'd just like to remind people of Cristoph Schillers Higgsless, SUSY less, extradimenisonless etc etc strand theory that was published on the internets with predictions three years ago. I see that one of the bloggers here has linked to it as well so i guess its starting to gain ground now.

    There are many other Higgsless, SUSY less, extradimensionless models that will probably start to get more traction after the dust settles. In my opinion, nobody should jump to premature conclusions before convincing experimental evidence is collected and properly analyzed. Extraordinary claims require extraordinary evidence.



    Just read volume VI of Motion Mountain Ervin, you will be impressed i assure you.

    I read your work and I remain skeptical on many points. Again, there are MANY competing BSM models that look promising but is really premature to jump the gun before solid evidence is made available. We are not at this point yet.

    Great posts, Tommaso. Thanks.

    Was there, or is there going to be, any results on bounds on superpartners masses at the EPS conference ?
    I thought by now we would already know about new lower bounds on gluinos, etc.

    Of course Anon, but I am just back from vacations with a long list of errands to take care of. I want to try and give some summary on that, but it will have to wait.

    In the meantime, you will be happy to read the recent analysis made by Sven Heinemeyer et al. I am posting about it tonight (I hope!).

    Just for the record, i'm not Schiller :).

    Hi Tommaso,

    I know not every question deserves an answer but perhaps you might take a look at my post at "07/25/11 | 13:08 PM"? Possibly you got distracted by the lengthy calculations that followed it ("Now you can easily show that ....") ;-)

    Answered above.
    "I am posting about it tonight (I hope!)."

    Great to know you're going to post about that, in due time. The last thing I'd want to do is wading through conference slides or, even worse, the arXiv.

    In case it's a consolation for you about your future in particle physics, I haven't had summer vacations for as long as I can remember. It's not that bad, worse things can happen. Getting hit by a freight truck, for example...

    Anon, I understand. There are worse things indeed. And things change. I wish you will see Crete one day.


    Correction: ATLAS does show both Bayesian comparison and PCL limits in the backup.


    Correction: ATLAS does show both Bayesian comparison and PCL limits in the backup.

    What if the Higgs decays in unexpected channels ? (maybe new light particule non-interacting with matter)
    How many more data would we need to see something ?

    Hi T -- Thanks for taking the time to discuss these exciting results and also for your personal insight that you often provide on your blog. I am a bit confused how a 130-150 GeV mass Higgs could decay into two W's as each W has an 80 GeV or so mass. Are these virtual W's going to the leptonic final state? If this is the case what about other processes through virtual Z's going to same final state that cannot be distinguished and will therefore interfere?
    Referring to:

    Hi Ravi,

    yes, if the Higgs has a mass lower than 2*Mw it can still decay to a pair of those. One of the W will then be virtual, i.e. it will have a mass much lower than the average 80.4 GeV; but you will still get two charged leptons and two neutrinos in a fraction of the cases. This can indeed be mimicked by another Higgs decay, the one to ZZ pairs when one Z decays to two leptons and the other to neutrinos; but the WW state will have "mixed leptons" too, e.g. (e nu_e) (mu nu_mu) events which the ZZ final state has a harder time mimicking (it still can, through Z->tau tau -> (e nu_e nu_tau) (mu nu_mu nu_tau) but there are distinguishing features. Kinematics tells these apart rather easily...

    Re: Crete

    Hi Tommaso,
    I think Anon is simply jealous. I'm sure you enjoyed a well earned holiday.
    Thinking about Crete evokes pictures of sea, sun, drinking Retsina and deciphering* Linear B ( clay tablets.

    *Only joking

    Hi Martin,

    yeah, I know about that riddle well. I have seen specimens both in the archaeological museum in Heraklion and earlier in Athens and in a small museum near the Nestor palace, in a town near Pilos whose name escapes me now...

    Retsina I did not drink, but many local wines and ouzo.