A Quantum Diaries Survivor

Just one week ago, a new combination of CDF and D0 results on Higgs boson searches has been approved for public consumption - in a timely fashion, to allow its presentation at the International Conference on High Energy Physics (ICHEP) that was held in Moscow from July 26th to August 2nd.

The plot attached below is quite a busy one, and the amount of work that went into producing the colored lines you see in it is astounding. Each different line represent years of analysis activity by a different group, or more than a group, of CDF or D0 physicists.

Bearing that in mind, let’s discuss what it is about. Basically, if the Higgs boson exists, then the Standard Model dictates how often a proton-antiproton collision at the Tevatron will produce one. From that, and given the total number of collisions collected by the experiments, one can predict how many Higgs bosons one should see in a given dataset, selected with so-and-so requirements to reduce backgrounds. That number will depend on the (as-of-yet) unknown mass of the Higgs. If we can prove that the observed rate of Higgs-like events is smaller than the prediction for a given mass, then we can exclude the existence of the Higgs, at that particular mass value.

Of course, we’d rather discover the Higgs than prove it does not exist, but both things are interesting - you search for a signal, and if you do not find it you quantify the likelihood of the existence of what you sought.

Let’s take a specific example. In a particular analysis, one observes 10 events compatible with Higgs production at a given Higgs mass, but one knows that 8±1 of them must be due to backgrounds. So one has an excess of 2±1  events attributable to Higgs production. Statistics actually tells one that under those circumstances, in the 10 observed events (with 8 estimated backgrounds) it is quite unlikely (meaning “it does not happen more than 5% of the times”) that there are more than 5 Higgs boson events or so, if the mass is the one hypothesized.

So 5 events is the limit we obtain on Higgs production, in our analysis. If Higgs bosons were produced, the production rate cannot be higher than 5 events in the sample of data analyzed.

That number can be translated in a upper limit in the production rate. The whole business can be done as a function of the unknown mass of the Higgs boson, if the selection cuts depend on that variable. So in the end, one obtains a function of Higgs mass that represents an upper limit in the production of that particle. Of course, the mass is important, since a lighter Higgs boson is more readily produced, and a curve of limits is thus more informative than a single limit.

Now, let’s look at the plot below. In it, different searches for the Higgs are summarized in different curves. CDF results are continuous lines, D0 results are dashed lines. The difference in the searches is due to the fact that the Higgs boson can be produced in several ways, and can decay in different final states. Each of these will produce different “signatures”, and each signature dictates a search strategy. But overall, the global combination of all curves, represented by the curved thick red line, is the final Tevatron result.

Bear in mind that the y axis of the plot is the ratio between the limit and the Standard Model expectation for the rate of Higgs boson production. That means that the red curve is not excluding any particular Higgs boson mass, as would instead happen if in some region it went below the black line at unity.

What is the bottomline ? That the Tevatron experiments have not yet managed to exclude Higgs production in any mass range, but - and here is the news - they are getting very close. In particular, for 160 GeV Higgs bosons, the limit is 3.5 times off the SM line. And at lower masses many analyses have not yet studied the total available statistics so far (1 inverse femtobarn). Things are getting rosier for the Tevatron…