Ok, everyone; by now you’ve all learned that the ATLAS experiment at the Large Hadron Collider [LHC] announced recently their measurement of the mass of the Higgs particle, in its decay to two photons, is at 126.6±0.3±0.7 GeV/c²; and meanwhile they measure the mass for apparently the same particle, in its decay to two lepton/anti-lepton pairs, to be 123.5±0.9+0.4-0.2 GeV/c², about 3 GeV/c² lower. “So bizarre”, wrote Michael Moyer at Scientific American, bandying about the idea that there are two Higgs-like bosons in this data (though, having pointed out the ambulance to you, and neglecting also to mention CMS’s data from November that directly disfavors this interpretation of the ATLAS data, he tells you later that some physics bloggers say you shouldn’t chase it…)
Well. How bizarre is this 2.7 standard deviation discrepancy really?
At the end of this post are 20 plots showing randomly generated data, in amounts comparable to those used in the current measurement of Higgs decaying to two lepton/anti-lepton pairs (often called “four leptons” for short). [Warning: This certainly hasn't been done with the level of care needed to match the ATLAS measurement in any precise way; I'll say a bit more below about the caveats.]
- In some of the plots, there’s just a random flat background of about 40 events, similar (though not identical) to what arises in the four-lepton Higgs measurement.
- In some of the plots, there’s a Higgs-like peak of about 20 events — a very sharp peak with a perfect detector, but one which is smoothed out a bit by the inevitable imperfections in a real particle detector.
- In each plot with a peak, the mass of the Higgs has been chosen to lie somewhere between 122 GeV/c² and 127 GeV/c² [not equally populated].
- Can you tell which plots have a Higgs-like signal, and which ones don’t?
- In each plot where there is a signal, can you estimate the Higgs mass? Again, in each plot, it lies somewhere between 122 and 127 GeV/c². You’re not going to get it exactly right — that’s impossible — but do your best, and let’s see what happens.
A couple of additional comments to help you:
- The resolution on the measurement (i.e., the effect of imperfections in the measurement) is such that with infinite amounts of data, the peak that you’d observe would be a bump whose width, at half the bump’s maximum height, would be about 4 GeV/c².
- The bins in each plot are 1 GeV/c² wide; the bin just to the right of the number 2 in “125” runs from 125 to 126, the next from 126 to 127, and so forth.
Lastly, a caveat: in the real ATLAS or CMS measurement, the mass of the Higgs is not measured simply by fitting a Gaussian peak over a flat background. So don’t take this exercise too seriously! It’s just a useful learning experience, and nothing more. What the experiments actually do is far more sophisticated, accounting for the properties of each event separately!!
Here we go: Good Hunting! (If your browser has trouble with the figure, try clicking on it.)