Understanding Tau Identification in ATLAS: A Brief Overview

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I have some questions concerning this paper (mainly about the tau identification):
http://arxiv.org/pdf/1201.5466v1.pdf

especially the figures 3-6...

I don't understand what is the inverse background efficiency, neither the likelihood score. As a result, I am unable to understand what info the figures give. Any help?
 
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Inverse background efficiency is also called the rejection rate. A value of 100 means you identify 1 out of 100 background events as signal.
The higher the signal efficiency you want to be, the more events you have to keep, which means you will identify more background events as signal, which gives a lower inverse background efficiency.
The different curves are different tau decay modes, pT regions, background samples and so on.

A boosted decision tree will give you a numerical value for each event, where larger values mean "more signal-like". Figure 3 shows the distribution of the BDT outputs for signal and background events. You can then choose different cut values, each cut value will give you one point in the diagrams 4-6.
 
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Thanks,
I still have some further questions in case you can help me.
In the paper I mentioned in the OP (in Sec 2), as well as here
http://arxiv.org/pdf/1409.0343v1.pdf In Sec 2, is mentioned how to reconstruct the hadronic tau.
It says:

A barycenter is formed consisting of the sum of the four-vectors of the constituent topological clusters, assuming zero mass for each of the constituents. Then, the τ_had detector axis is calculated by using clusters within ∆R =...< 0.2 around the barycenter. The four-vectors of those clusters are recalculated using the tau vertex coordinate system and the vectors are summed up.

Does that mean that the barycenter is like a disk within the ∆R<0.2 ?
And by that you are able to identify the vertex coordinate system by running back the jet's trajectory and see where the trajectories intersect?
So then you know they should come from taus and you are able to sum the jet's four vectors and calculate the tau's energy?