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Particle discovery - reading the plot

  1. Mar 2, 2012 #1
    Hi all. How to read the following plot?

  2. jcsd
  3. Mar 2, 2012 #2
    Well, the vertical axis is the hypothesised Higgs boson production cross-section, scaled relative to the Standard Model prediction (so the slice through 1 is what the Standard Model predicts it should be), while the horizontal axis is the hypothesised Higgs boson mass. Each (x,y) point therefore represents a model which makes predictions about what should be seen in the various searches the LHC groups are doing.

    The various lines drawn are all "95% confidence limits" on which of these models are excluded and which are not, derived by a statistical technique, usually a thing called "CLs" these days. It is quite technical to try and go into the true statistical meaning, but roughly you can imagine that a model is excluded at 95% confidence if the model predicts that you would see more signal than you did see in 95% of your experiments (if you imagine repeating the whole LHC millions of times). I.e. there is only a 5% chance you would get this unlucky see something that looked this much like background if that model was actually true. It is a bit more technical than that because there also has to be a high chance of the background being able to produce what you see, but forget that for now. (it is kind of nasty to try and make correct statements about what these statistics things mean, and very easy to get them wrong, which I probably did at least a little bit).

    Anyway, the solid blue line is the limit that they expected to be able to set, if their experiments saw exactly the data predicted by the mean background. Since the background actually fluctuates randomly, they draw the green band, which is where the black (real limit) curve should sit in 68% of experiments, and the yellow band, in which it should sit in 95% of experiments. When the curve goes outside the 95% band you start to be suspicious that actually there is some signal in your data, not just some fluctuation of the background. Since you are looking over a big mass range it is not too surprising to see the curve go outside this band now and again (there is this whole business called the "look-elsewhere effect"), so you can't be too sure you've seen something until the black curve goes WAY outside the yellow band.

    Finally, the black line is the limit actually set, with the real data. When the black curve drops below 1 in the vertical, it means the Standard Model higgs cross section is excluded at 95% confidence for those Higgs mass values, i.e. they say the Higgs is probably not at that mass, with pretty good confidence. It looks like Gibbs has added a red curve to show what the black curve was back in December. Or perhaps the red black curves are from the opposite months, one can't tell from the plot.
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