All the systematic uncertainties on the background prediction are summarised in Table 7.6 for the 2010 measurement and in Table 8.7 for the 2011 measurement. For theW+jets background,
(a) muon channel (b) electron channel
(c) muon channel (d) electron channel
Figure 7.1: Stability of the OS vs SS ratio as a function of calorimeter isolation (top) and the τ identification (bottom) for muons (left) and electrons (right) in data.
the statistical and systematic uncertainty is included, as described in Section 7.6. The same is true for the kZ factor used in 2011 analysis (Section 6.4.2). In the case of the QCD multijet background, except for the systematics on the stability of the ROS/SS ratio the uncertainties relating to Monte Carlo predictions are taken into account. That is done by shifting the Monte Carlo up and down by the relevant amount simultaneously in the signal and the control regions.
The final effect on the signal measurement is calculated by adding all the partial effects in quadrature.
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Table7.6:Summaryoftheeffectofallsystematicandstatisticaluncertaintiesonthefinalpredictedsignal(Nobs−Nbg)forboththe electronandmuonchannelsonthe2010data. muonchannel(%Deviation)electronchannel(%Deviation) SystematicN-BkgrdmultijetW+Jetsγ? /Z+t¯tN-BkgrdmultijetW+Jetsγ? /Z+t¯t leptonefficiency0.241.63.02.8(Z/γ? )0.312.77.05.0(Z) 5.9(t¯t)9.0(γ? /t¯t) leptonresolution(µenergyscale)0.0180.0920.20.20.0120.0650.20.2 Problematiccalorimeterregions0.00230.016000.0220.140.40.4 echargemisidentification0.00230.016000.0140.0640.210.21 τidefficiency0.0780.54000.110.5500 Energyscaleleptonandτ1.71018.824.3(Z)1.38.821.429.1(Z) 18.0(t¯t)13.1(t¯t) lepton-jetτfakerate1.150240.663.9021 pile-upreweighting0.0290.170.350.350.020.120.350.35 JetCleaning0.0670.4101.80.0660.5102.5 kWfactor0.123.68.2000.182.211.10 OS/SSRatio0.765.20021000 Theoret.crosssection0.21.405.0/8.30.121.305.0/8.3 Totalsystematicuncertainty2.21321342.5142535 Statisticaluncertainty9.8278.3312279.93.8 Totaluncertainty1030223412302735
(a) (b)
(c)
Figure 7.2: Top: In 2011 data, the dependence of ROS/SS as a function of the isolation variables (Ip0.4T/pT (left) and IE0.3
T/pT (right)) in theτµτh channel, in the multijets-pure region of inverted τ identification requirements. Bottom: In 2011 data, the dependence of ROS/SS as a function of the cutflow for the semi-leptonic channels.
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Chapter 8
γ ∗ /Z → τ τ Cross Section Measurement
8.1 Experimental Measurement
The cross section of theZ →τ τ →` τh+ 4ν decay is estimated using the formula σ(Z →τ τ)×BR(τ →l ν ν, τ →τhadν) = Nobs−Nbkg
AZ·CZ· L (8.1)
where
• Nobs is the number of observed events in data
• Nbkg is the number of estimated background events
• AZ denotes the kinematic and geometric acceptance for the signal process. It is calculated by the ratio of the number of events at generator level that fall within the fiducial regions defined below,Ndressedgen kin, over the number of events at generator level whose invariant mass at Born level lies within the mass window 66< mZ<116 GeV,Nborngenminv.
AZ = Ndressedgen kin
Nborngenminv. (8.2)
A “dressed” τ decay product is a lepton or a τ candidate that has been associated to photons radiated by either theτ leptons or by the decay products themselves. The photon should be radiated within a cone of ∆R < 0.1 for electrons and muons and ∆R < 0.4 for hadronic decay products. This process allows to perform a partial QED final state radiation correction back to the Born level, although it excludes the radiation at wide angle. The AZ factor by construction includes a correction for events that migrate from outside the invariant mass window in the fiducial cuts.
The central values for theAZ factor were determined using a default PYTHIA Monte Carlo sample generated with the modified LO parton distribution function (PDF) MRSTLO*
[91] and the corresponding ATLAS MC10 tune1 [92]. Although AlpGEN is used in the analysis for signal and background processes, it is avoided in the estimation of the AZ
1Although the combination of a leading order PDF with a NLO plus the matrix element is wrong, we are doing it here for technical reasons.
factor because it underestimates the Z production at low rapidity. The source of the problem is that the leading order PDF (CTEQ6L1) used in AlpGEN cannot describe accurately the distributions from higher order corrections. In contrast a next-to-leading order PDF, like CTEQ6.6, provides a more realistic description of the data. This problem is not expected to affect the reconstruction-level description of event kinematics, but could affect the extrapolation to the total cross section. Therefore, PYTHIA with MRSTLO*
PDF is used for the determination of the geometrical acceptance.
The lower bound on the invariant mass of the default sample is 10 GeV and therefore the sample includes a tail of low-massγ∗/Z events from outside theZ peak that can possibly migrate to the fiducial region. The obtained central values are reported in Tables 8.1 (top) for the 2010 data and (bottom) for the 2011 data. TheAZ value is small compared to the acceptance values at theZ →e+e− and Z →µ+µ− processes [12] because the neutrinos, which carry a large fraction of theτ lepton momentum, are not included in the definition of the fiducial regions.
Table 8.1: Central values for the AZ acceptance factor from PYTHIA ATLAS MC10 Monte Carlo generated with MRSTLO* PDF at generator level and CZ correction factor determined using the same sample at generator level and after full detector simulation for the 2010 (top) and 2011 (bottom) data analysis.
Muon channel Electron channel AZ 0.11691±0.00023 (stat.) 0.10073±0.00021 (stat.) CZ 0.2045±0.0024 (stat.) 0.1197±0.0017 (stat.)
Muon channel Electron channel AZ 0.0976±0.0002 (stat.) 0.0687±0.0002 (stat.) CZ 0.1417±0.0016 (stat.) 0.1009±0.0013 (stat.)
• CZ is the correction factor that accounts for the experimental imperfections, such as trig-ger, reconstruction and identification inefficiencies within the geometrical acceptance. It is defined as
CZ= Nreco pass
Ndressedgen kin (8.3)
whereNreco pass is the number of signal events that pass the analysis cuts after full simula-tion corrected with data-driven factors as described in Secsimula-tions 6.3.2, 6.3.3, 6.3.5. Ndressedgen kin is the same as for theAZ numerator. By constructionCZ includes a correction for migra-tions from outside of the acceptance. CZ is calculated with AlpGEN using CTEQ6L1.
• Ldenotes the integrated luminosity for the channel of interest.
Using eq. (8.1) and theAZ andCZ values from Table 8.1 one can calculate the total inclusive cross section for the two channels.
• 2010 data analysis:
σ(Z →τ τ)×BR(τ →µ ν ν, τ →τhadν) = 192.9±19.0(stat)±28.1(syst)±6.6(lumi) pb (8.4) 118
for theτµτh channel,
If the AZ is set to unity then the cross section can be calculated for the fiducial regions defined below. The measurement becomes independent of the extrapolation procedure to the full phase space and thus less dependent on the theoretical uncertainties of the model. The fiducial regions are defined by the following cuts (the first number refers to the 2010 selection and in parenthesis the 2011):
The fiducial cross section is measured via
σf id(Z →τ τ)×BR(τ →l ν ν, τ → τhadν) = Nobs−Nbkg
CZ· L (8.8)
If one plugs in the measured values into eq. (8.8), the final fiducial cross section is
• 2010 data analysis:
• 2011 data analysis:
Finally, the inclusive cross section after correcting for the (τ → l ν ν, τ → τhad) branching ratio, 0.2250±0.0009 for theτµτh channel and 0.2313±0.0009 for theτeτh channel [4], is
• 2010 data analysis:
σ(Z →τ τ, minv : [66−116] GeV) = 857.6±84.3(stat)±124.7(syst)±29.2(lumi)±2.8(theo) pb (8.13) for theτµτh channel,
σ(Z →τ τ, minv : [66−116] GeV) = 1142±138.6(stat)±197.7(syst)±38.9(lumi)±2.6(theo) pb (8.14) for theτeτh channel.
• 2011 data analysis:
σ(Z →τ τ, minv : [66−116] GeV) = 912.4±15.0(stat)±94.7(syst)±33.7(lumi) pb (8.15) for theτµτh channel,
σ(Z →τ τ, minv: [66−116] GeV) = 998.1±23.7(stat)±131.9(syst)±36.9(lumi) pb (8.16) for theτeτh channel.