Separate Single- and Di-Tau Likelihoods

Following up on this post where we see that there might be some advantage to having separate likelihoods for the case where a cluster contains 1 and 2 tau, I have created separate likelihoods. I used the following variables for the likelihoods:

  • Number of live towers.
  • Number of tracks.
  • Number of pi0’s.
  • Cluster pT.
  • Cluster mass.
  • Cluster 1st parallel moment.
  • Cluster EM fraction.

Below is the distribution of the single-tau likelihood for background and single-tau tagged signal events.
Likelihood comparison for single-tau likelihood
Below is the di-tau likelihood distribution for background and di-tau tagged signal events.

Likelihood comparison for di-tau likelihood

We can see that di-tau clusters are more separated from jets than single-tau clusters. Below I plot 2-dimensional histograms of the single-tau vs. di-tau likelihood for single tau events on the left and di-tau events on the right.

Likelihood Correlation

We obtain correlation coefficients of 25% for the single tau events and 22% for the di-tau events. It is interesting to note that there is a cluster of single-tau events that have a high di-tau likelihood.

Finally, I compare the efficiencies and fake probabilities of these likelihoods to the previous combined likelihood that was trained on the signal sample without looking at the tau multiplicity in each cluster. First is the performance on single-tau events.

Efficiency vs. fake rate comparison for single tau events.

We see that the single-tau likelihood has a fake probability of ~20% at 80% efficiency while the old combined likelihood had a fake probability of ~30% for the same efficiency. We also see that the di-tau likelihood is worse than either of the others with single-tau events.

When I do the same for the di-tau events, I see something slightly surprising.

Efficiency vs. fake rate comparison for di tau events.

We see that the di-tau likelihood has very slightly worse performance on di-tau events than the old combined likelihood. Looking above to the di-tau likelihood distributions for signal and background, we can see that there is a small peak for the di-tau signal around 0. I find that this is due to the correlation between pT and mass which is not being taken into account in this simple multiplicative likelihood.  It is much more probable that clusters with low pT and mass are from the jet background rather than a di-tau signal.  Because the correlation is not considered, for soft di-tau clusters the mass and pT likelihood ratios are both very background-like and when they are multiplied they become even more so.

–Dan