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Explanatory Figures for the Higgs Boson Exclusion Plots

Caption for Figure A
The Standard Model does not predict the mass of the Higgs boson, but does predict the production cross section once the mass is known. The "cross section" is the likelihood of a collision event of a particular type.

ATLAS uses plots like this one to seek hints for the Higgs boson and also to exclude regions of mass where the Higgs is very unlikely to be found. This example is not real data, but is a simplified plot to show how we interpret the results of our searches for the Higgs boson. The vertical axis shows, as a function of the Higgs mass, the Higgs boson production cross-section that we exclude, divided by the expected cross section for Higgs production in the Standard Model at that mass. This is indicated by the solid black line.

This shows a 95% confidence level, which in effect means the certainty that a Higgs particle with the given mass does not exist. The dotted black line shows the median (average) expected limit in the absence of a Higgs. The green and yellow bands indicate the corresponding 68% and 95% certainty of those values.

If the solid black line dips below the value of 1.0 as indicated by the red line, then we see from our data that the Higgs boson is not produced with the expected cross section for that mass. This means that those values of a possible Higgs mass are excluded with a 95% certainty. In this example, two regions would be ruled out at 95% certainty: approximately 135-225 GeV and 290-490 GeV.

If the solid black line is above 1.0 and also somewhat above the dotted black line (an excess), then there might be a hint that the Higgs exists with a mass at that value. If the solid black line is at the upper edge of the yellow band, then there may be 95% certainty that this is above the expectations. It could be a hint for a Higgs boson of that mass, or it could be a sign of background processes or of systematic errors that are not well understood. In this example, there is an excess and the solid black line is above 1.0 between about 225 and 290 GeV, but the excess has not reached a statistically significant level.

The red-gray shaded regions show what is excluded. The "bump" near a mass of 250 GeV could be a slight hint of a Higgs boson in this fictional example.

Caption for Figure B
This plot shows hypothetical data and expectations that could be used in setting the limits shown in Figure A.

The green curve shows (fictional) predicted results if there were a Higgs boson in addition to all the usual backgrounds. It could also represent the predictions of some other new physics. The dashed black curve shows what is expected from all background processes without a Higgs or some new physics. The black points show the hypothetical data.

In this case, the data points are too low to explain the Higgs boson hypothesis (or whatever new physics the green curve represents), so we can rule out that hypothesis.

Nonetheless the data points are higher than the expectations for the background processes. This could yield an excess such as shown on the left in Figure A. There are three possible explanations for this excess:

  1. It is a statistical fluctuation above the expected background processes.
  2. It is a systematic problem due to an imperfect understanding of the background processes.
  3. The excess is due to some different new physics (than that hypothesized) that would predict a smaller excess.

If instead, the black points lay close to the green curve, that could be evidence for the discovery of the Higgs boson (if it were statistically significant).

If the black points lay on or below the dashed black curve (the expected background), then there is no evidence for a Higgs boson and depending on the statistical significance, the Higgs boson might be ruled out at the corresponding mass.

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