The systematic uncertainties on the cross section measurement are estimated by propagating the effect of the individual uncertainties to the cross section measurement, as described in Section 7, for signal and background events and the uncertainty on the estimation of the AZ, CZ factors.
8.2.1 Geometrical Acceptance
The systematic uncertainty on the AZ factor is mainly coming from the limited knowledge of the proton PDFs and the modelling of the Z boson production at a hadron collider like LHC.
Three components are varied to assess the systematic uncertainty:
• Uncertainty within one PDF set is evaluated according to the method explained in Sec-tion 4.1. The PDF set is CTEQ6.6 at NLO. The error eigenvector for this PDF set is shifted by 1σ up and down and the correspondingAiZ factors are calculated for each entry of the matrix. The uncertainty is derived via
∆AZ= 1 2
qX
(Ai+Z −Ai−Z )2 (8.17)
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• Deviations between different PDF sets. The ones considered here are MRSTLO*, the nominal one, and CTEQ6.6 and HERAPDF1.0 for cross checks. The maximal deviation is taken as the systematic uncertainty.
• Uncertainty due to the modelling of the parton shower is evaluated using MC@NLO inter-faced with HERWIG parton shower. These samples are generated with the CTEQ6.6 PDF sets and the ATLAS tune MC10 for pile-up. HERWIG does not treat correctly τ polari-sation effects, so MC@NLO samples are used for that. The correction factor is estimated to be 0.9917±0.0002 for the muon channel and 0.9904±0.0002 for the electron.
Tables 8.2 and 8.3 show the geometric acceptance for the above described variations and the relative uncertainties for the 2010 data analysis. Similarly, in Tables 8.4 and 8.5 are shown the respective geometric acceptance and the relative uncertainties for the 2011 data analysis.
Table 8.2: Central values (PYTHIA MRSTLO*) and variations (others) of the AZ geometric and kinematic acceptance factor for 2010 analysis.
Muon channel Electron channel
PYTHIA MRSTLO* 0.1169 0.1007
PYTHIA CTEQ6.6 0.1191 0.1026
PYTHIA HERAPDF1.0 0.1185 0.1020
PYTHIA CTEQ6.6mZ/γ∗>60 GeV 0.1185 0.1022
MC@NLO CTEQ6.6mZ/γ∗ >60 GeV 0.1174 0.1016
MC@NLO CTEQ6.6mZ/γ∗ >60 GeV spin effect correction 0.1165 0.1006
Table 8.3: Relative uncertainties on theAZ factors for the 2010 analysis.
Muon channel Electron channel
CTEQ 6.6 eigenvector set 1.2% 1.2%
Different PDF sets 1.9% 1.9%
Model dependence 1.8% 1.6%
Total uncertainty 2.9% 2.8%
Table 8.4: Central values (PYTHIA MRSTLO*) and variations (others) of the AZ geometric and kinematic acceptance factor for 2011 analysis.
Muon Channel Electron Channel
PYTHIA MRSTLO* 0.0976 0.0687
PYTHIA CTEQ6.6 0.0998 0.0699
PYTHIA HERAPDF1.0 0.0992 0.0692
PYTHIA CTEQ6.6mZ/γ∗ >60 GeV 0.0994 0.0698 MC@NLO CTEQ6.6mZ/γ∗ >60 GeV 0.0973 0.0679
Uncertainties due to QED radiation and the modelling of the τ lepton decays are evaluated in the 2010 analysis and are found negligible. In particular, the QED modelling by PHOTOS
Table 8.5: Relative uncertainties on theAZ factors for the 2011 analysis.
has an accuracy better than 0.2%, which is smaller than the PDF uncertainty evaluated. For theτ lepton decays, instead of TAUOLA, a SHERPA sample is generated that includes its own libraries to decay τ leptons. The total theoretical systematic uncertainty on the AZ factor is calculated by adding in quadrature all the different sources and a final 3% uncertainty is assigned on both channels in 2010 analysis and a 3.1% for τeτh and a 3.4% forτµτh in 2011 analysis.
8.2.2 Experimental Acceptance
The systematic uncertainty on experimental acceptance factor,CZ, is the sum of the uncertain-ties described in Section 7 on signal Monte Carlo. Each of the uncertainuncertain-ties is varied and a new CZ factor is calculated, listed in Tables 8.6 (2010) and 8.7 (2011).
Table 8.6: Relative systematic uncertainties in % for CZ for the 2010 estimate for both semi-leptonic channels [55].
Systematic uncertainty δCZ/CZ τµτh δCZ/CZ τeτh
lepton efficiency 3.6% 9.2%
lepton resolution (µenergy scale) 0.2% 0.2%
Problematic regions in the calorimeter – 0.4%
echarge misidentification – 0.21%
τ id efficiency 8.6% 8.6%
Energy scale lepton andτ 8.6% 9.4%
Pileup re-weighting 0.4% 0.4%
Jet cleaning 1.8% 1.8%
Total systematic uncertainty 12.8% 15.8%
Statistical uncertainty 1.2% 1.4%
Total uncertainty 12.8% 15.9%
For each of the considered systematic uncertainties, the total cross section is calculated and the result is shown in Tables 8.8 (2010) and 8.9 (2011). The total systematic uncertainty on the cross section measurement is obtained by adding in quadrature all the estimated uncertainties.
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Table 8.7: Relative systematic uncertainties in % for CZ for the 2011 estimate for both semi-leptonic channels [56].
Systematic uncertainty δCZ/CZ (%) τµτh δCZ/CZ (%)τeτh lepton trigger, reco, ID and isolation efficiency 1.7 4.8
muon resolution <0.05
Table 8.8: Relative systematic uncertainties in % for the total cross-section measurement in 2010 data analysis.
Systematic uncertainty δσ/σ τµτh δσ/σ τeτh
τ id efficiency 8.6 8.6
echarge misidentification – 0.14
kW factor 0.12 0.18
Energy scale lepton andτ 10 11
Jet Cleaning 1.9 1.9
Table 8.9: Systematic and statistical uncertainties on the total cross section measurement in the 2011 data analysis.
Systematic uncertainty δσ/σ (%) τµτh δσ/σ (%)τeτh
lepton trigger, reco, ID and isolation efficiency 1.7 5.0
muon resolution <0.05
-electron resolution - 0.1
jet resolution -
-LAr hole - 0.1
τ ID efficiency 5.2 5.2
electron-tau fake rate - 0.2
e,τ, jet and ETmiss energy scale 8.2 9.3
tau trigger efficiency - 4.7
kW normalisation factor <0.05 0.04
kZ normalisation factor <0.05 <0.05
QCD estimation 0.8 1.3
Background MC normalisation 0.1 0.2
AZ uncertainties 3.1 3.4
MC statistics 1.2 1.4
Total systematic unc. 10.4 13.2
Statistical uncertainty 1.6 2.4
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Chapter 9
Ditau Mass Reconstruction
Due to the presence of the neutrinos in theτ lepton decays, the reconstruction of the fullτ τ in-variant mass poses an experimental challenge. A number of methods have been proposed for that purpose, typically in the context ofZ/H separation. In the following section, the performance of several mass reconstruction techniques is evaluated using the relatively pure semileptonic Z → τ τ sample obtained for the cross section measurement. The methods considered are: the effective mass in Section 9.1, the collinear approximation in Section 9.2, the missing mass cal-culator (MMC) in Section 9.3, the mass bound (mbound) in Section 9.4, the “true” transverse mass (mtrueT ) in Section 9.5 and the combination of the latter two methods in Section 9.6. The motivation for this combination is given in the last section.
There are two methods that are not considered here: visible mass and transverse mass.
Visible mass is the invariant mass of the visible decay products of the twoτ leptons, electrons, muons or quarks, and it was used for the measurement of the cross section of the Z → τ τ decay. This reconstruction method is not used here, since it does not include the neutrinos of the τ decay and hence, does not reconstruct the whole event. Transverse mass is defined in Section 6.3.5 in eq. (6.1). It is used to obtain the invariant mass of the decaying particles when the parent decays into one visible lepton and a neutrino. In this case, one assumes that the mass of the decay products is zero and the parent particle is produced with zero recoil. The transverse mass is a perfect method to reconstruct a W boson, where the approximation that the missing transverse momentum is identical to the transverse momentum of the neutrino is valid. Due to the presence of two neutrinos this approximation is not applicable to aZ boson.
Hence the method is ignored for the purposes of this chapter.
For all considered methods, the invariant mass of the τ τ system is reconstructed after all standard selection cuts and an additionalETmiss requirement are applied. The distribution of the ETmiss after the standard selection is shown in Fig 9.1. The Monte Carlo does not describe the ETmiss well below 20 GeV, which is why for the mass reconstruction a requirement for
ETmiss >20 GeV (9.1)
has been implemented.