Thursday, October 20, 2011

Trilepton Events At LHC Probably Mean Nothing

When you smash two protons at a particle accelerator this typically produces 0, 1, 2 or 3 stable or near stable charged leptons in the final state and some amount of missing traverse energy that varies in amount. In theory, there can be more than 3 charged leptons produced, but they are too rare to make statistically significant statements about even with the amount of activity going on at the large hadron collider (LHC): the data set has 14,516 three lepton events but just 78 four lepton events. Multilepton events with three or four leptons are very rare - they occur less often than one in a 100 billion collisions.

The 3 charged lepton states are the most rare for which a statistically significant analysis can be conducted, and raw LHC data on the frequency of various types of charged lepton states that is observes is as follows:

MET is a measure of whether invisible particles are present; HT is a measure of how much energy is in visible particles. No-OSSF means that if there is an electron there is no positron; if there is a muon there is no antimuon; etc. No Z means there are no lepton-antilepton pairs that came from a Z-particle's decay; if there is no-OSSF there cannot be a Z, so that isn't marked. . . . N(tau) means the number of taus and anti-taus observed in the event.

Looking a bit closer there are two bins marked with little red dots that are a little above confidence intervals, and there are two bins (unmarked) htat are outside confidence intervals on the low side (one to within rounding error, the other a bit more clearly, but well within three sigma). These four bins, that don't follow any clear pattern are precisely the kind of slight deviations from 95% confidence intervals that you expect to see in a random sample with this many bins.

But, the three big red dots in three of the four bins where there was probably no Z boson involved in the event and there were not tau generation charged leptons involved in the decay, each at at least the three sigma level of excess, is worth watching.

The absolute number of excess events is pretty small, however. One of the three notable excess bins has five events when the expected value was two. The second of the three notable excess bins has nineteen events when twelve were expected and eight to fourteen would have been within the 95% confidence interval. The third of the three notable excess bins has five events when the expected value was two. A single event excess beyond a confidence interval range also is usually assumed to be random chance. So really, eight events in a particular group of bins (the fourth of which has 82 events when 61-93 events would have been within the confidence interval), isn't much to hang your hat upon.

Indeed, if you lump all four bins in the no Z boson, no tau lepton category together, the expected value was 97.5, the observed value was 111, and the 95% confidence interval (crudely overestimating by simply adding them up without reduction for interfering random variation of the different subbin margins of error i.e. +/- 25.4) is 72-123 events in the group of four bins. Calculated properly the confidence interval would be roughly 80-115, which would still include the observed value of 111.

In short, this looks like it is probably a case of seemingly significant effects appearing as a result of excessively fine bin divisions. There is no very sensible physics theory that would explain by the three bins with no taus and no Z bosons in the event should look different from the fourth bin of the same type given the other variables that are used to break up the bins.

SUSY theorists are particularly interesting in trilepton events as an experimental mark of supersymmetry, but this is the kind of result that one expects to see go away when the data set gets large enough to make the law of averages apply more strongly to each of the bins. The official CMS line that “Observed data are essentially consistent with background expectations; no smoking gun for new physics yet.”, is right on target in this case.

Hat Tip to The Reference Frame.

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