Adding Mass & SumpT to Cluster Likelihood

I have added two more variables to the cluster likelihood. They are the mass of the cluster and the sumpT of the cluster. The likelihood ratios y=B/S for these two variables are plotted below.

SumpT sumpT Likelihood Ratio

This is parameterized by

  • if(sumpT<32 GeV) 5th order polynomial
  • if(32<112) 2nd order polynomial
  • if(sumpT>112) poly2(112).

Mass

Mass Likelihood Ratio

This is parameterized by

  • if(M<0.2) poly5(0.2)
  • if(0.2<2.1) poly5
  • if(2.1<12.2) a different poly5
  • if(M>12.2) the 2nd poly5(12.2)

Below is the comparison of the likelihoods for the 3 samples. Note that the signal likelihood peaks more strongly at 1 with the addition of the new variables. Also note that there is peak near 0 for the signal that wasn’t there before. We investigate this further below.

Likelihood Comparison

First we compare the efficiency vs. fake rate for this likelihood and the old one.

Efficiency vs. fake rate comparison

We see that there is some small reduction of the fake rate. Next I investigate where the peak at 0 in the new likelihood histogram is coming from. I suspect that this is an effect of the addition of the mass variable to the likelihood. Clusters that contain only 1 tau in them will have a peak in the mass distribution very close to the kinematic peak from jets and will appear more “jet-like” to the likelihood. You can see this feature in the mass plot.
M(TP0)

To check this assumption, I make a stacked histogram where I separate the likelihoods coming from clusters with 1 generated tau found in them from the clusters with 2 taus.

Likelihood by ntau

It is clear that the peak at low likelihood is coming from clusters with a single tau in them. This likelihood is better at discriminating di-tau clusters from jets than it is at discriminating single tau clusters from jets.

–Dan