As outlined in Section2.2, the decay of a tau lepton happens via intermediate resonances. The reson-ances are theρ(1p1n) and thea1(1pXn, 3p0n). With the reconstruction of individual decay products, it is possible to reconstruct the resonances. Thus, calculating the invariant mass of the decay products should recover the resonance masses in the corresponding decay channels.
True visible Tau Reconstructed byCellBased+PanTau
Resonance Mean/ MeV RMS/ MeV Mean/ MeV RMS/ MeV
ρ 823±188·10−3 188±132·10−3 831±294·10−3 288±208·10−3 a1(1pXn) 1.19·103±261·10−3 175±184·10−3 1.28·103±757·10−3 417±535·10−3 a1(3p0n) 1.17·103±294·10−3 174±208·10−3 1.14·103±328·10−3 186±232·10−3 Table6.3:Mean and RMS values alongside their errors for the different invariant resonance masses. The table shows the values obtained from the generated tau (second and third column) and the ones obtained in the simulated reconstruction. Values are obtained in the cases in which the reconstructed decay mode is also the true simulated decay mode. The mean agrees reasonably well in all cases, the RMS is subject to the calorimeter energy resolution, as can be seen in the different RMS values fora1(1p2n).
[GeV]
true pT
0 5 10 15 20 25 30 35 40 45 50
true T,vis) / Etrue T,vis - Ereco T resolution: (ETE
-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
CellBased+PanTau Cell Based Resolution
π0
Metric II:
τ τ
→ Z
True & Reco 1p1n taus Points show mean and its error
(a)Mean and its error of the transverse energy resolu-tion as a funcresolu-tion ofπ0 pT.
[GeV]
true pT
0 5 10 15 20 25 30 35 40 45 50
true T,vis) / Etrue T,vis - Ereco T resolution: (ETRMS of E
0.1 0.2 0.3 0.4 0.5
CellBased+PanTau Cell Based Resolution
π0
Metric II:
τ τ
→ Z
True & Reco 1p1n taus Points show rms and its error
(b)RMS and its error of the transverse energy resolution as a function ofπ0 pT.
Number of vertices
0 5 10 15 20 25 30
true T,vis) / Etrue T,vis - Ereco T resolution: (ETE
-0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
0.16 CellBased+PanTau
Cell Based Resolution
π0
Metric II:
τ τ
→ Z
True & Reco 1p1n taus Points show mean and its error
(c)Mean and its error of the transverse energy resolution as a function of number of vertices.
Number of vertices
0 5 10 15 20 25 30
true T,vis) / Etrue T,vis - Ereco T resolution: (ETRMS of E
0.22 0.24 0.26 0.28 0.3
0.32 CellBased+PanTau
Cell Based Resolution
π0
Metric II:
τ τ
→ Z
True & Reco 1p1n taus Points show rms and its error
(d)RMS and its error of the transverse energy resolution as a function of number of vertices.
Figure 6.11: The mean (left), RMS (right) and their respective errors of the transverse energy resolution as a function ofπ0 pT (top) and the number of vertices in the event (bottom).
true T,vis
) / E
true T,vis reco - E ) resolution: (ET
π0 T( E
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
a.u.
0 0.02 0.04 0.06 0.08 0.1
0.12 8 vertices
24 vertices Resolution
π0
Metric II:
τ τ
→ Z
True & Reco 1p1n taus Figure6.12: ET resolution ofπ0 in
correctly classified 1p1n decays for two bins of the number of vertices.
Both distributions are normalised to unity. The resolution in events with 24 vertices shows a bigger high en-ergy tail than the resolution for events with 8 vertices. The low energy tail stays the same. As a result, both the mean and the RMS increase with pile-up.
mass for all reconstructed 1p1n decays7. The mean and RMS of the invariant mass distributions for all resonances (ρ,a1(1p2n),a1(3p0n)) are listed in Table6.3. In case of theρresonance, the reconstructed mean of 831 MeV agrees very well with the simulated one (823 MeV), and the RMS is≈ 50% larger, because of the energy resolution of the EM calorimeter (c.f. theπ0resolution in Figure6.9).
The mean as a function of the resonance pT is shown in Figure6.14, which shows that it is constant at 800−900 MeV for trueτhad-vis pT between 15 GeV and 100 GeV. ThePanTaucurve follows the curve of the generated true visible tau in both the mean and the RMS, the only difference is that the RMS ofPanTauis higher than the generated one.
Figure6.15shows the dependence of the mean and RMS of the invariant 1p1n visible mass on the number of vertices in the event. The mean increases by roughly 100 MeV over 30 vertices, and the RMS by≈ 80 MeV. Because the composition of the tau is fixed to one charged PFO and oneπ0-PFO in 1p1n decays, the increase of energy has to come from pile-up particles that partially or completely overlap with theπ0-PFO, increasing its energy and thus the mass of the complete tau. As can be seen from Figure6.12, the contribution of pile-up to the overestimation of the energy is one source of the increasing RMS.
a1Resonance
Thea1 resonance decays into both 1p2n and 3p0n. Decays into three charged pions are easier to re-construct, because the charged pions produce a track in the inner detector, which can be resolved very well. Decays into one charged and two neutral pions however need to rely on the subtraction of the charged pion in the EM calorimeter and the correct measurement of the two neutral pions, making the reconstruction less accurate.
Figure 6.16shows the invariant mass in 3p0n decays. In part 6.16a, only correctly reconstructed 3p0n taus are considered, while part6.16b shows the invariant mass distribution of all reconstructed 3p0n taus. For correctly reconstructed 3p0n taus, the mean of simulated and reconstructed mass agrees within 30 MeV, the RMS also agrees well within 12 MeV (c.f. Table6.3).
The dependence of the reconstructed invariant mass on the trueτhad-vis pT is depicted in6.17. While the mean is constant slightly below 1.2 GeV, the RMS increases by 40 MeV when raising the trueτhad-vis pT from 15 GeV to 100 GeV. It is consistent with the behaviour of the generated mass.
Because the reconstruction of 3p0n decays depends solely on tracks, the pile-up stability is excellent (c.f. Figure6.18). There is no visible shift in the mean of the reconstructed mass (Fig. 6.18a) and no clear trend in the RMS, shown in Figure6.18b.
The situation is less optimal ina1 → π±π0π0 decays. The reconstructed invariant mass spectrum is shown in Figure6.19. Clearly visible is the bad resolution compared to the 3p0n case, which is due to two of theπ±being replaced withπ0, measured in the calorimeter with a worse resolution. This results in the reconstructed RMS being more than twice as large as the generated one as Table6.3 shows.
However, the shift in the mean of the distribution is rather small (overestimation<10%).
The dependency on the true τhad-vis pT is depicted in Figure 6.20. The reconstructed mass as a function ofpT is stable within≈150 MeV, the RMS increases from 300 MeV to 600 MeV. This is due
7The appearence of entries at theπ±-mass is understood and corrected in newer versions of the code that produces these figures (pages 53 and 200 in [57]).
: Invariant Mass [GeV]
ρ
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
a.u.
0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045
True vis. Tau Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1p1n Taus ρ
(a)Invariant mass in true and reconstructed 1p1n de-cays.
[GeV]
mvis
0 0.5 1 1.5 2 2.5
a.u.
0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
0.009 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
All Reco 1p1n taus
(b)Invariant mass in reconstructed 1p1n decays.
Figure6.13:Invariant mass in 1p1n decays. The mean of the distributions agrees very well, the peak position is also correct. The RMS is larger because of theET resolution of theπ0. Whether the reconstructed mode is also the true mode has no big effect on the shape of the mass distribution (right).
[GeV]
true pT
20 30 40 50 60 70 80 90 100
: Invariant Mass [GeV]ρ
0.75 0.8 0.85 0.9 0.95
True vis. Tau Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1p1n Taus ρ
Points show mean and its error
(a)Mean and its error of true and reconstructed 1p1n decays as a function of trueτhad-vis pT.
[GeV]
true pT
20 30 40 50 60 70 80 90 100
: Invariant Mass [GeV]ρRMS of
0.15 0.2 0.25 0.3 0.35 0.4
0.45 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1p1n Taus ρ
Points show rms and its error
(b)RMS and its error of true and reconstructed 1p1n decays as a function of trueτhad-vis pT.
Figure6.14:Mean, RMS and their errors in true and reconstructed 1p1n decays as a function of trueτhad-vispT.
Number of vertices
0 5 10 15 20 25 30
: Invariant Mass [GeV]ρ
0.76 0.78 0.8 0.82 0.84 0.86 0.88 0.9
0.92 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1p1n Taus ρ
Points show mean and its error
(a)Mean and its error of the invariant mass of true and reconstructed 1p1n decays.
Number of vertices
0 5 10 15 20 25 30
: Invariant Mass [GeV]ρRMS of
0.2 0.25 0.3 0.35
0.4 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1p1n Taus ρ
Points show rms and its error
(b)RMS and its error of the invariant mass of true and reconstructed 1p1n decays.
Figure6.15:Mean, RMS of the invariantτhad-vismass and their errors as a function of the number of vertices.
: Invariant Mass [GeV]
a1
0 0.5 1 1.5 2 2.5
0.005 0.01 0.015 0.02
(a)Invariant mass in correct 3p0n decays.
[GeV]
mvis
0 0.5 1 1.5 2 2.5
0.002 0.004 0.006
(b)Invariant mass in reconstructed 3p0n decays.
Figure 6.16: Invariant mass of 3p0n decays. The reconstructed masses are very close to the generated ones, thanks to the excellent tracker resolution.
[GeV]
true pT
20 30 40 50 60 70 80 90 100
: Invariant Mass [GeV]1a
1.1 1.15 1.2 1.25
1.3 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 3p0n Taus a1
Points show mean and its error
(a)Mean and its error as a function of trueτhad-vis pT.
[GeV]
true pT
20 30 40 50 60 70 80 90 100
: Invariant Mass [GeV]1RMS of a
0.16 0.18 0.2 0.22 0.24 0.26
0.28 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 3p0n Taus a1
Points show rms and its error
(b)RMS and its error as a function of trueτhad-vis pT. Figure6.17:Mean and RMS of the invariant mass in 3p0n decays as a function of trueτhad-vis pT.
Number of vertices
0 5 10 15 20 25 30
: Invariant Mass [GeV]1a
1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2
1.21 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 3p0n Taus a1
Points show mean and its error
(a)Mean and its error in bins of reconstructed vertices.
Number of vertices
0 5 10 15 20 25 30
: Invariant Mass [GeV]1RMS of a
0.16 0.17 0.18 0.19
0.2 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 3p0n Taus a1
Points show rms and its error
(b)RMS and its error in bins of reconstructed vertices.
Figure6.18:Mean and RMS of the invariant mass of 3p0n decays in bins of reconstructed vertices in the event.
: Invariant Mass [GeV]
a1
0 0.5 1 1.5 2 2.5
a.u.
0.005 0.01 0.015 0.02 0.025
True vis. Tau Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1pXn Taus a1
(a)Invariant mass in correct 1p2n decays.
[GeV]
mvis
0 0.5 1 1.5 2 2.5
a.u.
0.001 0.002 0.003 0.004 0.005
Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
All Reco 1pXn taus
(b)Invariant mass in reconstructed 1p2n decays.
Figure 6.19:Invariant mass of 1pXn decays. Because of the presence of twoπ0, the mass resolution is worse than in 1p1n decays and 3p0n decays. The peak position is not affected as much as the width of the distributions.
[GeV]
true pT
20 30 40 50 60 70 80 90 100
: Invariant Mass [GeV]1a
1.1 1.2 1.3 1.4 1.5 1.6
True vis. Tau Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1pXn Taus a1
Points show mean and its error
(a)Mean and its error of the invariant mass in true and reconstructed 1pXn decays as a function ofpT(a1).
[GeV]
true pT
20 30 40 50 60 70 80 90 100
: Invariant Mass [GeV]1RMS of a
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 True vis. Tau
Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1pXn Taus a1
Points show rms and its error
(b)RMS and its error of the invariant mass in true and reconstructed 1pXn decays as a function ofpT(a1).
Figure 6.20: Mean, RMS and the corresponding errors in the reconstruction of thea1 resonance in true and reconstructed 1p2n decays as a function of the resonance pT.
Number of vertices
0 5 10 15 20 25 30
: Invariant Mass [GeV]1a
1.2 1.3 1.4 1.5 1.6 1.7
True vis. Tau Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1pXn Taus a1
Points show mean and its error
(a)Mean and its error of the invariant mass in true and reconstructed 1pXn decays as a function ofNVertex.
Number of vertices
0 5 10 15 20 25 30
: Invariant Mass [GeV]1RMS of a
0.2 0.3 0.4 0.5 0.6 0.7
True vis. Tau Cell Based CellBased+PanTau Metric III: Resonances
τ τ
→ Z
: True & Reco 1pXn Taus a1
Points show rms and its error
(b)RMS and its error of the invariant mass in true and reconstructed 1pXn decays as a function ofNVertex. Figure 6.21: Mean, RMS and the corresponding errors in the reconstruction of thea1 resonance in true and reconstructed 1p2n decays as a function of vertices in the event.
: Invariant Mass [GeV]
a1
0 0.5 1 1.5 2 2.5
0 0.01 0.02 0.03 0.04 0.05
0.06 True & Reco 1pXn taus
Figure 6.22: Invariant mass from PanTau in correctly classified 1pXn decays, for low (green) and higher (red) resonance momenta.
It is visible, that the mass is overestimated for higher resonance momenta and that the distri-bution is broadened.
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 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
(a)Linear y-axis scale.
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.
10-4
10-3
10-2
10-1
1
10 Cell Based
CellBased+PanTau Metric IV: Tau Resolution
τ τ
→ Z
(b)Logarithmic y-axis scale.
Figure6.23:Inclusive transverse energy resolution, with linear (left) and logarithmic (right) y-axis in order to see the core and the tails. TheCellBasedandPanTauresolutions are very similar, especially in the core region.
In the tails,PanTauperforms a bit better thanCellBased.
to an overestimation and broadening of the mass, shown in Figure6.22. The effect is visible for both CellBasedandPanTau, so that it is not because of a wrong selection ofπ0. One reason for this can be that with increasing pT, the decay products are more boosted, so that it is harder to accurately resolve individualπ0-PFOs, which deteriorates the mass resolution.
As a function of the number of vertices in the event, thea1 mass reconstruction performs as shown in Figure6.21. The mean of the mass increases from 1.2 GeV to 1.4 GeV over 30 vertices, the RMS increases from 400 MeV to 500 MeV.