A Quantum Diaries Survivor

A new, hot-of-the-press, combination of the Higgs boson search results by the CDF and D0 collaborations at Fermilab is out. The combination is based on a score of analyses based on one to two inverse femtobarns of integrated luminosity collected by the two experiments at the Tevatron collider since the start of Run II. Both CDF and D0 already have collected almost twice that amount of data, but they are still analyzing the remainder. So let us look at the current status of Higgs boson searches with the very informative summary plot shown below.

It has become customary, in this search, to show as a function of the unknown Higgs boson mass the 95% confidence level limit on Higgs production as a limit on the ratio between excluded cross section and standard model prediction. A ratio smaller than unity means that the Higgs boson should not be there if we believe the standard model to hold; a ratio larger than unity still allows the existence of the particle at that mass value. As years go by, the exclusion curve has gone down in small steps as a result of the inclusion of more data and, crucially, continuous improvements in the analysis techniques.

In the plot, the black line shows the actual limit found at the Tevatron. You can see by yourself that the limit is at 1.1 times the standard model for Higgs mass of 160 GeV - the most sensitive point in the whole mass region. What that means is that CDF and D0 are not quite able to exclude the existence of the Higgs boson in any mass point, but they have gotten very, very close to achieve that. But the line also tells more. Indeed, the fact that the limit obtained is lower, at 160 GeV, than that expected from pseudoexperiments (the band called “expected limit”), shows that there is less data at 160 GeV than what was expected by backgrounds alone. A normal downward fluctuation, and in fact the black line is only one standard deviation below the average expectation. But that also gives one the scale of what the limit really means.

In fact, a 95% confidence level limit says very, very little. It is like describing a probability distribution by saying, “oh, well, on this side there is only 5% of it”. I explained elsewhere what is hidden behind a claim of a 95% cl exclusion, and will not repeat the whole issue here. Suffices to say that if the limit at the Tevatron is 1.1 x SM at 160 GeV, this could mean that the real SM cross section has indeed been “excluded” at xx% (with xx<95) confidence level, since the most probable value of the Higgs cross section implied by Tevatron data must be below the SM prediction to have produced a limit at the quoted value.

In other words, if the probability distribution for the Higgs cross section were all lying above 1.0xSM, and only 5% of it leaked above 1.1xSM, one would conclude it is a very, very narrow distribution - and indeed, it would be a measurement!, since such a narrow distribution would definitely not be compatible with zero cross section: the Higgs boson having a non-null cross section would mean it exists. But the above is of course not the case, and the probability distribution is very well compatible with zero - so it extends down and it is wide. How wide ? Well, if one examines the expected limit, one gets the scale of how wide the observed limit might be by examining the +- 1-sigma countours of the expectation. So, xx% is not small… Eighty percent ? I guess maybe 85. That would mean that the likelihood that the Higgs boson mass is at 160 GeV has already shrunk considerably if we consider all the available Tevatron data… Bad news for LHC experiments, whose sensitivity is highest if the Higgs has a mass of 160 GeV (but the LHC will find the Higgs anywhere, given enough statistics).

Finally, let me add to this note a word of self-praise. Two months ago I discussed the D0 limit on Higgs cross sections in the WW production mode, and I ventured to make the following prediction:

After seeing this plot, which reaches a x2.4 SM value at 160 GeV, I am starting to be very curious to see the combination with CDF results (which stood at x1.9 SM at 160 GeV already last August). I think we will have to wait for winter conferences to get that plot, but I smell a x1.1 limit at 160 GeV: not yet any mass exclusion for winter 2008 (for the latest combination, yielding x1.4 SM, see here).

My prediction was based on incomplete results from D0, and I did not have insider information on the CDF limit in the WW final state in my hands yet… A good call.