ison to the barrel. There, the energy is overestimated by 1%. This could be corrected for by applying a method similar to the one that is used in the tau reconstruction during the first data-taking period [58].
The method described there applies an correction factor, which is binned inη, the number of tracks and taupT, to scale the measured momentum to the true momentum. The basic idea of that method is also applicable in substructure based tau reconstruction. Figure6.29bshows the RMS of theET resolution as a function ofη, and except for the transition region, it is flat.
The difference between the generated and the reconstructed azimuthal angleφ, as well as the differ-ence in the corresponding pseudorapidities of tau candidates is shown in Figure6.30. Both distributions are sums of the distributions for the different decay modes. As a result, they have two components, the core and the tails. The former is because of the fact that the 1p0n and 3p0n modes are measured solely with the tracker, which provides an excellent position resolution. The latter is mainly due to measure-ments in the EM calorimeter, which have a greater impact on the resolution with increasing number of π0in the decay.
Taking the tails into account, the position precision in φ and η is better than 0.04 in both cases, corresponding to∆φ <2.3◦and∆θ <2.0◦atη=0.
η true -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
true T,vis) / Etrue T,vis - Ereco T resolution: (ETE
-0.05 0 0.05 0.1
0.15 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
Points show mean and its error
(a)Mean and its error of the inclusiveET-resolution as a function of pseudorapidityη.
η true -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
true T,vis) / Etrue T,vis - Ereco T resolution: (ETRMS of E
0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26
Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
Points show rms and its error
(b)RMS and its error of the inclusiveET-resolution as a function of pseudorapidityη.
Figure6.29:Inclusive transverse energy resolution as a function of pseudorapidityη
[rad]
true
φvis reco - φvis
φ :
∆
-0.04 -0.02 0 0.02 0.04
a.u.
0.02 0.04 0.06 0.08 0.1
0.12 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
(a)Difference in generated and reconstructedφon a linear scale.
[rad]
true
φvis reco - φvis
φ :
∆
-0.04 -0.02 0 0.02 0.04
a.u.
10-4
10-3
10-2
10-1
1
10 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
(b)Difference in generated and reconstructedφon a logarithmic scale.
true
ηvis reco - ηvis
η :
∆
-0.04 -0.02 0 0.02 0.04
a.u.
0.02 0.04 0.06 0.08 0.1
Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
(c)Difference in generated and reconstructedηon a linear scale.
true
ηvis reco - ηvis
η :
∆
-0.04 -0.02 0 0.02 0.04
a.u.
10-4
10-3
10-2
10-1
1
10 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
(d)Difference in generated and reconstructedηon a logarithmic scale.
Figure 6.30:Difference between generated and reconstructedφ(top) andη(bottom) on a linear (left) and log-arithmic (right) scale. The distributions are inclusive over all reconstructed modes. The sharp peaks at 0 are due to the excellent tracker resolution of only a few percent, which is exploited in to its full extend in 1p0n and 3p0n modes (≈ 33% of all hadronic modes). The tails stem from the other modes, which need to rely on the EM-calorimeter forπ0reconstruction. Like outlined in the discussion of theET resolution, the distributions are highly non-Gaussian.
true T,vis
) / E
true T,vis reco - E resolution: (ET
ET
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
a.u.
0.005 0.01 0.015 0.02 0.025 0.03
0.035 Cell Based
CellBased+PanTau Default Metric IV: Tau Resolution
τ τ
→ Z
(a)Inclusive transverse energy resolution.
R(reco, vis. true)
∆
0 0.01 0.02 0.03 0.04 0.05 0.06
a.u.
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
0.18 Cell Based
CellBased+PanTau Default Metric IV: Tau Resolution
τ τ
→ Z
(b)Inclusive spatial resolution.
Figure 6.31: Transverse energy resolution and spatial resolution of all reconstructed tau leptons passing the selection cuts. The transverse energy resolution has a much more pronounced core, while the far tails are worse than in the default reconstruction. The accuracy in the reconstruction of the position increases drastically.
Figure 6.32:Abundances of the five decay modes of fake taus as obtained in Z → µµ +Jets events from simulations (yellow) and data (black). The red shaded area is the systematic uncertainty, which is obtained by varying the energy of neutral PFOs by 20%
and then subsequently adjusting the decay mode to account for neutral PFOs passing or failing the ET cut (c.f. Table5.1). Data and simulations agree within the expected uncertainties. Figure taken from [52].
Application: Polarisation Studies in Z → ττ
This final chapter presents a possible application of the new substructure based tau reconstruction method. It discusses a short simulation-based study of how well the tau polarisation in Z → ττ de-cays can be measured with the new tau reconstruction. The outline is as follows.
Section7.1motivates, why a polarisation measurement is of interest. In Sections7.2and7.3, the setup of the analysis and the event- and object-selection are described. Section7.4 presents the polarisation sensitive variable,Υ, that is used to measure the polarisation. The behaviour ofΥunder the event selec-tion is discussed in detail in Secselec-tion7.5. Finally, Section7.6describes how the actual measurement of the polarisation is performed. A short summary is given in Section7.7.
namely those that try to measure Higgs boson properties. These kind of analyses require a clean sample of Higgs bosons to study, so that all other processes, for instance Z boson production, are considered background processes. When investigating the channel of a Higgs decaying into two tau leptons1, one of the few things that separates the Z boson background from the Higgs signal is the invariant mass of the di-tau system. For Higgs decays, the invariant di-tau mass is a bit higher than for Z bosons, because of the Higgs mass ofmH ≈ 125 GeV (mZ ≈ 91 GeV). However, the Z boson is a spin-1 particle while the Higgs boson is a spin-0 particle.
Thus, being able to measure the polarisation in tau decays allows for additional separation between Z- and Higgs bosons.
In Section2.3, a method to gain access to the tau polarisation is described. The method makes use of the energy asymmetries in the tau decay products. Chapters4 and5 introduced the concepts of a new tau reconstruction and discussed thePanTau-algorithm in detail. Using the new approach to tau reconstruction and thePanTaualgorithm, it is possible to follow the method described in2.3and study whether a measurement of the polarisation is indeed possible.
It should be noted that the studies presented in the following are by no means a full-fledged analysis.
The study should be seen as a proof of principle, that the substructure based tau reconstruction allows for a polarisation measurement. It was performed to gain insight on these two subjects:
• How well does the substructure based tau reconstruction retain polarisation sensitive variables?
How are they affected by a typical event & object selection forZ→ττevents?
• Is it possible to measure the mean tau polarisation by using the benefits of the new tau reconstruc-tion method?