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Ken Bloom | USLHC | USA

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The plot heard ’round the world (and a contrarian viewpoint)

At long last, here it is! From the Hadron Collider Physics conference in Paris, and as documented by the CMS and ATLAS collaborations, the plot you have all been waiting for:

Higgs limits from CMS and ATLAS

As we last saw, CMS and ATLAS had each set limits on the rate of production of standard-model Higgs bosons at the Lepton-Photon conference in August. Now, for the first time ever, the two collaborations have combined their results. Each experiment has recorded about the same amount of data, so to first approximation, this combination allows us to double the number of collisions that are analyzed, and thus to set more stringent limits on Higgs mass (or possibly to discover a Higgs).

Since one of my colleagues took me to task just this morning for these plots being impenetrable, let’s review what is being measured and what the plot shows. First, remember that pretty much everything in particle physics is a counting experiment. You record so much data, and then count the number of times you observe a given phenomenon in the data. On the basis of this, you can essentially say, “given that I’ve seen this happen X times, surely if I were to do this experiment over and over, it would be very unlikely for me to see this happen more than N > X times.” N is then the “upper limit” on the number of events that we would expect to observe. (I’m sure my statistical friends will forgive me for this hand-waving description). We can convert that upper limit on event counts into an upper limit on the cross section for the process; the cross section is essentially the probability for a process to occur, which is obtained after normalizing out how much data has been recorded. The vertical axis of this plot gives the upper limit on the cross section for Higgs production, normalized to the expected cross section that we calculate from the quantum mechanics of the standard model.

The points show the upper limits that are obtained as a function of putative Higgs mass. It is a different upper limit for each Higgs mass because as the mass changes, you have different Higgs production and decay rates and different sensitivity to those decays; depending on the Higgs mass, it can be easier or harder to observe. As can be observed, the points fall below y = 1 over a wide range of Higgs masses. This indicates that we are observing fewer putative Higgs events than we would expect from the standard model prediction, and thus we claim to “exclude” that prediction, and thus the possibility of a standard-model Higgs at those particular mass values.

One should also pay attention to the dotted line and the colored bands. The dotted line represents what limit we would be able to set if there were no Higgs boson at all, and all there were to observe were background processes that look similar to the Higgs but aren’t. The bands represent the one and two standard deviation uncertainties on that expected limit. In general, the limits set are about as good as those we expected to set. There are some excursions from expectations, but they are generally no worse than two standard deviations, which is not impossible. This gives us some confidence that the observed limits aren’t anything crazy.

By combining the results of the two experiments, a very wide range of possible Higgs masses is excluded. Neither experiment alone could produce a result this strong, and hence the great interest in the combined result, which took many months and much coordination between the two experiments. Each group of experimenters had to understand the others’ measurement in detail to be able to do the combination correctly. It’s a lot of work, but the improvement in the bottom-line result is worth it.

And what do we learn from this? It appears that if there is a standard-model Higgs boson, it must have a very large mass (which is disfavored by other measurements), or a mass between 114 and 141 GeV. Optimists will note that in that region, more candidate events are observed than would be expected from a no-Higgs scenario, although not with any statistical significance worth talking about. If one believes everything about a standard-model Higgs, then ATLAS and CMS are currently putting quite a squeeze on its properties.

Of course, that’s a big “if.” The contrarian in me likes to keep two things in mind. First, all of this statistical stuff is just a convention we’ve adopted to communicate with each other. (We’ll see if my statistical friends forgive me for saying that!) The definition of excluded is, in my opinion, rather arbitrary, and you could imagine doing things differently and coming up with a different range of excluded Higgs mass values. If we are are to claim a discovery of a Higgs boson someday, I would assert that the evidence will have to be even clearer than what can be obtained from such statistical analyses.

Second, why should we believe any of the predictions? They are cooked up from many ingredients, each of which have their own uncertainties with them. It is hard to believe that the predictions are to be wildly off, but how the physics really works might not be what the standard model says it is, and thus we have to keep an open mind.

Thus, even if we reach the point where we can exclude all reasonable values of the Higgs boson mass — a point that we might reach soon, given that the experiments have recorded at least twice as much data has have been included for this combined result — and we actually do exclude those values, the search will not be over! Even if the standard model is not correct and there is no Higgs as such, the signatures of Higgs production and decay are still interesting, and could still be an indication of some kind of new physics. Higgs or no Higgs, we have a very interesting few months ahead of us.

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