LHC Multilepton Search Unimpressive So Far

They looked at events with at least four leptons (electrons and muons) and some missing transverse momentum. In the inclusive selection, they observed 4 events while the expectation was 1.7 ± 0.9 events; that's roughly a 2.5-sigma excess although one should include the non-Gaussianity of the distribution to get a more accurate figure.When the Z veto was imposed, they got no events while the expectation was 0.7 ± 0.8 events which is OK within 1-sigma error. So only the veto-free figure is intriguing.

From here.

Material deviations from the Standard Model, of course, tend to support Beyond the Standard Model theories. And, greater than expected numbers of multilepton events, in particular, tend to support Supersymmetry (i.e. SUSY).

Statistical Issues

But, of course, as Motl acknowledges by remarking that the distribution is non-Gaussian, estimating a statistical significance for a discrete variable with a low value, like the predicted number of multilepton events at an experiment at the Large Hadron Collider, as a continous variable, is inaccurate. The probability of a number of events less than zero is zero, which makes a two sided set of error bars problematic. There are specific, probabilities for zero, one, two, three, four, five, etc. events under the Standard Model, and you have to compare a single data point to those probabilities.

Doing the statistical significance calculations correctly is going to reduce the statistical significance of finding 4 multilepton events, when the modal result would be 2 multilepton events, 1 or 3 multilepton events would be quite routine, and neither 0 nor 4 events is wildly improbable.

With a Z veto, which is designed to filter out false positives, you have a barely modal expectation of one event, which zero events and two events being quite likely (and zero being quite a bit more likely than two events).

Of course, when you are looking at two separate measurements that have some independence from each other, the probability that one or the other will be a given amount more than the expected value is greater, also reducing their statistical significance. You expect one 2 sigma event for every twenty trials and the more trials you do, the less notable a 2 sigma or 2.5 sigma event viewed in isolation becomes when the total context of experimental outcomes is considered.

Put another way, done right, the naiive 2.5 sigma event is probably very close to and possibly below a 2 sigma event, if the statistics is done right.

Implications For SUSY Parameter Space

Of course, since there are all sorts of SUSY theories, there is no one SUSY prediction for the number of multilepton events, although the LHC results, like those before it, imply that any deviation from the Standard Model expectation in SUSY, if it exists, must be quite subtle.

To be just a bit more refined, I have never heard anyone claim that SUSY theories for a given expected value of a result, have a materially different standard deviation from that expected value. The expected values are different, but not the variability. Therefore, if you are testing two hypotheses, one that the Standard Model is correct, and the other that a particularly SUSY model is correct, SUSY models that predict, for example, six or more multilepton events (rather than the observed two), or five or more Z vetoed multilepton events (rather than the observed zero), are strongly disfavored by the LHC results. This is potentially a pretty meaningful and precise constraint on the parameter space of SUSY models.

This is not the only constraint on SUSY parameter space. The apparent Higgs boson mass of about 125 GeV imposes real constraints, as do exclusion searches setting minimum masses of the lighest supersymmetrical particle which are fast approaching the TeV mass level. We are entering the era where fine tuning is increasingly necessary to fit SUSY theories to the data, and by implication, to fit string theory vacua to the data. LHC's experimental data won't have enough statistical power to entirely rule out SUSY even if every single one of its results is negative for its entire run, but it will impose every tighter constraints of SUSY parameter space that ties the hands of string theorists trying to fit theories to the observed data.

The simpliest versions of SUSY are already ruled out, but human ingenuity's capacity to come up with more clever versions that fit new constraints abounds.