The 1999/2003 Higgs predictions compared with CDF 2009 results

Two years ago I used the combined Higgs search limits produced by the D0 experiment to evaluate how well the Tevatron was doing if compared with the predictions that had been put together by the 1999 SUSY-HIGGS working group, and later by the 2003 Higgs Sensitivity Working Group (HSWG), two endeavours to which I had participated with enthusiasm. The picture that emerged was that, although results were falling short of justifying fully the early predictions, there was still hope that those would one day be vindicated.

Indeed, I remember that when in 2003 the HSWG produced its report, we felt our results were greeted with a dose of scepticism. And we ourselves were a bit embarassed, because we knew we had been a bit optimistic in our predictions: however, that was the name of the game – looking at things on their bright side, for the sake of convincing funding agents that the Tevatron had a reason to run for a long time. I felt a strong justification for being optimistic in the incredible results on the top quark mass that the Tevatron had already started achieving: early prospects of measuring the top mass to a 1% uncertainty have in fact been surpassed by the combination of dedication of the scientists doing the analyses, and their imagination in inventing new precise methods.

We now have a chance to look back at the 1999/2003 predictions for the Higgs reach of the Tevatron with a rather solid set of hard data: the CDF combination, which I briefly discussed two days ago, is based on analyzed sets of data ranging from 2 to 3 inverse femtobarns, and the comparisons do not require a lot of extrapolations to be carried out.

If we look at the 1999/2003 predictions shown above (two basically coincident results, if one considers that the 2003 results were not accounting for systematic effects, which would worsen a bit the curves of sensitivity and bring them to match the older ones), we can read off the integrated luminosity that the Tevatron experiments needed to analyze in order to exclude, by combining their results, SM Higgs production at 95% confidence level. These numbers are as follows: for a Higgs mass of 100 GeV, 1/fb was considered sufficient; for a Higgs mass of 120 GeV, 2/fb were needed; 10/fb at 140 GeV; 4.5/fb at 160 GeV; 8/fb at 180 GeV; and 80/fb at 200 GeV. You can check them on the purple band in the graph above.

Now, let us take the actual expected limits by CDF with the analyses and the data they have based their new result upon (using expected limits rather than observed ones is correct, since the former are unaffected by statistical fluctuations). At 100 GeV, CDF has a reach in the 95%CL limit at 2.63xSM; at 120 GeV, the reach is 3.72xSM; at 140 GeV, 3.61xSM; at 160 GeV it is 1.75xSM; at 180 GeV 3.02xSM; and at 200 GeV, the reach is at 6.33xSM.

(Below, the 2009 combined CDF limits are shown by the thick red curve; the data I list above is based on the hatched curve instead, which shows the expected limit.)

How do we now compare these sets of numbers ?

Easy. As easy as 1.2.3.4 (well, not too easy, but that’s how it goes).

1. We first scale up by a factor of two the 1999/2003 luminosity numbers needed for a 95% CL exclusion, which we listed above. We thus get, for Higgs masses ranging from 100 to 200 GeV in 20-GeV steps, needed integrated luminosities of 2,4,20,9,16,160/fb.
2. Then, we take the actual luminosity used by CDF for the analyses that have been combined to yield the expected limits listed above. This is slightly tricky, since the combination includes analyses which have used 2.0/fb of data (the search), 2.1/fb (the search), 2.7/fb (the , the , and the searches), and 3.0/fb (the search). In principle, we should weight those numbers with the relative sensitivity of the various analyses, but we can approximate it by taking an “average effective luminosity” of 2.4/fb for the 100 GeV Higgs search, 2.7/fb for the 120 and 140 GeV points, and 3.0/fb for the high-mass searches. This is appropriate, since the search starts kicking in above 140 GeV.
3. We now have all the numbers we need: we divide the expected luminosity needed for one experiment by the 1999/2003 study, found at point 1 above, by the effective luminosities found at point 2, and take the square root of that number: this means finding the “reduction factor” in the sensitivity that the actual CDF data suffers with respect to the data needed to exclude the Higgs boson. We find a reduction factor of 0.91, 1.22, 2.72, 1.73, 2.31, and 7.30 for Higgs masses of 100,120,140,160,180, and 200 GeV respectively.
4. Now we are done. We can compare the “times the SM” limits of CDF with the numbers found at point 3 above. The ratio of the two says how much worse is CDF doing with respect to predictions, for each mass point. We find that CDF is doing 2.88 times worse than predictions at 100 GeV; 3.06 times worse than predictions at 120 GeV; 1.33 times worse at 140 GeV; 1.01 times worse at 160 GeV; 1.31 times worse at 180 GeV; and 0.87 times worse (i.e., 1.15 times better!) at 200 GeV.

The results of point 4 are plotted on the graph shown above, where the x-axis shows the Higgs mass, and the y axis this “shame factor”. I have given a 20% uncertainty to the figures I computed, because of the rather rough way I extracted the numbers from the 1999/2003 prediction graph. If you look at the graph, you notice that the CDF experiment has kept its (our!) promise (points bouncing around a ratio of 1.0) with its high-mass searches, while low-mass searches still are a bit below expectations in terms of reach (3x worse reach than expected). It is not a surprise: at low Higgs mass, the searches have to rely on the final state, which is very difficult to optimize (vertex b-tagging, dijet mass resolution, lepton acceptance are the three things on which CDF has been spending hundreds of man-years in the last decade). Give CDF (and DZERO) enough time, and those points will get down to 1.0 too!