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TheZ resonance is described by a Breit-Wigner distribution if no detector effects are taken into account. On the other hand, the experimental resolution of the energy (1/pT) measurement on the electrons (muons) is approximately described by a Gaussian distribution. To account for this, the Z resonance is fitted by a convolution of the Breit-Wigner and the Gauss functions in the evaluation of the performance of the mass methods. For the case that the Z decays to τ leptons, the τ reconstruction effects are dominating and hence, the Z resonance is better described by a Gaussian distribution than by a Breit-Wigner. Nonetheless, a Gaussian and a Breit-Wigner function are fitted to the data and the signal Monte Carlo for all the mass methods after all relevant cuts have been applied. The data are fitted after subtracting the background

132

(a)meff electron channel (b) meff muon channel

(c) mcollelectron channel (d) mcollmuon channel

(e) MMC electron channel (f) MMC muon channel

Figure 9.6: Mass distributions of theτ τ system forτeτh (left) andτµτh (right). The distribu-tions are plotted after all standard cuts includingETmiss>20 GeV.

(a) mboundelectron channel (b) mboundmuon channel

(c)mtrueT electron channel (d) mtrueT muon channel

(e)mbound ormtrueT electron channel (f) mboundormtrueT muon channel

Figure 9.7: Mass distributions of theτ τ system forτeτh (left) andτµτh (right). The distribu-tions are plotted after all standard cuts includingETmiss>20 GeV.

134

(a) electron channel (b) muon channel

Figure 9.8: Collinear approximation forτeτh(left) andτµτh(right). The distribution is plotted after all standard cuts includingETmiss >20 GeV and |∆φ(τ,lepton)|<2.9.

contribution from the Monte Carlo predictions. The resulting curves are shown in Fig. 9.9 and 9.10 and mean values and widths are summarised in Tables 9.1 and 9.2.

To check the stability of the methods, the masses are reconstructed after varying the domi-nant systematic uncertainty of the process, the energy scale, and the deviation from the nominal value is given in Table 9.3. For the MMC two extra systematic uncertainties are checked, the ETmiss and the jet energy resolution. The corresponding effects are presented in Table 9.4. The systematic uncertainties are discussed previously for each method separately.

A final check of the performance of the methods is done by estimating the ratio of the signal over the background contributions, which is summarised in Table 9.5. The muon channel has a higher background rejection efficiency due to the stronger suppression of theZ+jets background.

Amongst the studied methods, the ones that constrain the phase space using theτ decay topol-ogy, like the MMC and the mbound methods, provide a better separation between signal and background. However, the collinear approximation offers comparable separation power without using statistical methods that might introduce additional systematic uncertainties.

(a) signal data – electron channel (b) signal MC – electron channel (c) signal data – electron channel

(d) signal MC – electron channel (e) signal data – electron channel (f) signal MC – electron channel

(g) signal data – electron channel (h) signal MC – electron channel (i) signal data – electron channel

(j) signal MC – electron channel (k) signal data – electron channel (l) signal MC – electron channel

Figure 9.9: Fit all mass distribution for the τeτh channel after the necessary cuts have been applied, for signal Monte Carlo (right) and data after subtracting the background expectation from Monte Carlo (left).

136

(a) signal data – muon channel (b) signal MC – muon channel (c) signal data – muon channel

(d) signal MC – muon channel (e) signal data – muon channel (f) signal MC – muon channel

(g) signal data – muon channel (h) signal MC – muon channel (i) signal data – muon channel

(j) signal MC – muon channel (k) signal data – muon channel (l) signal MC – muon channel

Figure 9.10: Fit of mass distribution for the τµτh channel after the necessary cuts have been applied.

Table 9.1: The Gaussian (g) and Breit Wigner (BW) mean and width values of the

Table 9.2: The Gaussian and Breit Wigner (BW) mean and width values of the reconstructed masses for data.

Table 9.3: The shift of the mean and width of the Gauss fit function for the different masses

Table 9.4: The shift of the mean and width for the Gauss fit functions for MMC when the ETmiss resolution (METr) and the jet energy resolution (JER) are varied.

mMMCeτh] µ [GeV] σ [GeV]

Table 9.5: Signal over background efficiency of the mass methods.

τeτh s/bg

Chapter 10

Conclusions

In this thesis, the measurement of the semi-leptonicZ →τ τ decay was presented with the data collected in 2010 and 2011 by ATLAS. The latter set of data was also used to study τ τ mass reconstruction methods.

Studying and understanding the Z →τ τ signal and, as a matter of fact, allZ andW boson decays is a pre-requisite for any searches for the Higgs boson or new physics. That is because the properties and the decays of the Z and the W bosons are known to a great accuracy and can serve as calibration tools for the data and the methods used. Especially, for Higgs boson searches, theZ →τ τ process is an irreducible background lying in the same mass range that a light Higgs boson is expected. Hence, before claiming discovery or exclusion of the latter, it is necessary to prove that the former is well-modelled.

The first step is the measurement of the cross section of the process. For that the semi-leptonic decays were used, where oneτ lepton decays to pions and the other to either electrons or muons. The main background contribution comes from the QCD multijets, the suppression of which is achieved with an isolation requirement on the electrons and muons. Moreover, the remaining events are modelled with a two-dimensional template fit, called ABCD method.

Further kinematical and identification requirements have been implemented to suppress the electroweak background events.

The final measured inclusive cross section when taking into account the branching fraction of the τ leptons to pions and electrons or muons is:

• with the data collected in 2010:

σ(Z →τ τ, minv : [66−116] GeV) = 857.6±84.3(stat)±124.7(syst)±29.2(lumi)±2.8(theo) pb (10.1) 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 (10.2) for theτeτh channel.

• with the data collected in 2011:

σ(Z →τ τ, minv : [66−116] GeV) = 912.4±15.0(stat)±94.7(syst)±33.7(lumi) pb (10.3) for theτµτh channel,

σ(Z →τ τ, minv: [66−116] GeV) = 998.1±23.7(stat)±131.9(syst)±36.9(lumi) pb (10.4) for theτeτh channel.

The measurements agree within uncertainties with the theoretical NNLO expectation value, 960

±50 pb−1.

After having established the selection criteria and methods for theZ →τ τ decay, the process is used to evaluate the most prominent reconstruction methods for theτ τ system. These meth-ods are: effective mass, collinear approximation, missing mass calculator, bound mass, “true”

transverse mass and the combination of the last two. The effective and the “true” transverse mass, although they are reconstructing the full event, they are not utilising τ properties and hence, do not constrain the event. Nonetheless, they are able to reconstruct the Z resonance with 100% efficiency. Therefore, they can be useful if one is limited by statistics but has a good knowledge of the background processes. The opposite is true for the collinear approximation and the bound mass, in which case, 40-50% of the events are rejected from the phase-space con-straints of the methods, but a good signal over background separation is possible. The combined method seems to overcome the disadvantages of the two separate methods, but, nonetheless, it inherits some of the disadvantages, more notably, the events reconstructed with the “true” trans-verse mass suffer from low background rejection. Finally, the missing mass calculator constrains the τ τ system in almost 95% of the phase-space and thanks to the likelihood method it uses, it succeeds in providing good signal to background separation. One drawback is the sensitivity of the method on the mis-measurements of the angular coordinates between the visible decay products and the missing transverse momentum. Additionally, due to the need for initial tuning of the discriminant, the method is not flexible to any changes in the event selection.

To summarise, a first measurement of the Z → τ τ cross section was done with the data collected in 2010, which was then improved by the measurement in the data collected in 2011.

The latter were used to further reconstruct the invariant mass of the τ τ system and evaluate different methods. Further improvements are always possible, specially the better understanding of the detector and the tools is acquired. A larger statistical sample is not necessary for the cross section measurement, rather a better estimation of the energy scale uncertainties is necessary. In contrast, the reconstruction of the full invariant mass still suffers from statistics, so an extension of the studies to the full 2011 dataset would be beneficial. Then, it would also be possible to study and evaluate the uncertainties on the background events and hence, more concrete conclusions could be drawn on the discovery power of the methods. Nonetheless, the methods and selection criteria developed have already been used for the evaluation of systematic uncertainties on the identification and reconstruction of the hadronicτ candidates in tag-and-probe studies in data.

Also, in Higgs boson searches in theτ τ decay mode, several of the studied methods are already used and the others are currently under consideration.

142

Appendix A

Monte Carlo Samples

All simulated samples used in this study are listed in Table A.1 for 2010 and Tables A.2, A.3, A.4 and A.5 for 2011. In the tables are given the number of generated events, the particular dataset number and reference tags (AMI tag) for the specific ATLAS reconstruction campaign.

Additionally, the NNLO cross sections and the K-factors, where applied, are listed.

TableA.1:ListofMonteCarlosamplesusedforthisanalysis.AllsamplesweregeneratedwithPYTHIA,exceptfort¯twhichwasgeneratedwithMC@NLOandthedibosonsamplesgeneratedwithHERWIG.

DatasetDatasetNumberAMITagEventsCross-Section/pbZ→ee(m``>60GeV)106046e574s933s946r1831r20405M990Z→µµ(m``>60GeV)106047e574s933s946r1831r20405M990Z→ττ(m``>60GeV)106052e574s934s946r1833r20402M990W→eν106043e574s933s946r1831r20407M1046W→µν106044e574s933s946r1831r20407M1046W→τν107054e574s934s946r1833r17002M1046t¯t105200e598s933s946r1831r17001M91.50J1e(electronfilterpT>8GeV,|η|<3)109271e600s934s946r1833r1700998k8.81×10 5

J2e(electronfilterpT>8GeV,|η|<3)109272e574s934s946r1833r1700497k2.54×10 5

J3e(electronfilterpT>8GeV,|η|<3)109273e574s934s946r1833r1700499k3.72×10 4

J0mu(muonfilterpT>8GeV,|η|<3)109276e574s933s946r1831r1700967k8.48×10 5

J1mu(muonfilterpT>8GeV,|η|<3)109277e574s933s946r1831r1700997k8.14×10 5

J2mu(muonfilterpT>8GeV,|η|<3)109278e574s933s946r1831r1700495k2.21×10 5

J3mu(muonfilterpT>8GeV,|η|<3)109279e574s933s946r1831r1700499k2.85×10 4

γ /Z→ττ(10GeV<m``<60GeV)107055e574s933s946r1831r2040190k396.7γ /Z→ee(15GeV<m``<60GeV)108320e574s933s946r1831r1700996k146.2γ /Z→µµ(15GeV<m``<60GeV)108319e574s933s946r1831r1700999k146.2WW105985e598s933s946r1831r2040250k11ZZ105986e598s933s946r1831r2040250k1.0WZ105987e598s933s946r1831r2040250k3.4

144

TableA.2:ListofMonteCarlosamplesfortheZ+jetsproduction.ThesamplesaregeneratedwithAlpGENandaresplitpernumber ofinitialpartons(NpX,X=0,...,5).AminimumpartonpTcutat20GeVisappliedatproduction. ProcessDatasetNumberAMITagLOCrossSection*NNLO-factor[pb]Events Zττ(m``>40GeV)+Np0107670e844s933s946r2302r2300668.40*1.256608784 Zττ(m``>40GeV)+Np1107671e844s933s946r2302r2300134.81*1.251327672 Zττ(m``>40GeV)+Np2107672e844s933s946r2302r230040.36*1.25403864 Zττ(m``>40GeV)+Np3107673e844s933s946r2302r230011.25*1.25109947 Zττ(m``>40GeV)+Np4107674e844s933s946r2302r23002.79*1.2529977 Zττ(m``>40GeV)+Np5107675e844s933s946r2302r23000.77*1.259990 Zee(m``>40GeV)+Np0107650e737s933s946r2302r2300668.32*1.256612265 Zee(m``>40GeV)+Np1107651e737s933s946r2302r2300134.36*1.251333745 Zee(m``>40GeV)+Np2107652e737s933s946r2302r230040.54*1.25404873 Zee(m``>40GeV)+Np3107653e737s933s946r2302r230011.16*1.25109942 Zee(m``>40GeV)+Np4107654e737s933s946r2302r23002.88*1.2529992 Zee(m``>40GeV)+Np5107655e737s933s946r2302r23000.83*1.258992 Zµµ(m``>40GeV)+Np0107660e737s933s946r2302r2300668.68*1.256619010 Zµµ(m``>40GeV)+Np1107661e737s933s946r2302r2300134.14*1.251334723 Zµµ(m``>40GeV)+Np2107662e737s933s946r2302r230040.33*1.25403886 Zµµ(m``>40GeV)+Np3107663e737s933s946r2302r230011.19*1.25109954 Zµµ(m``>40GeV)+Np4107664e737s933s946r2302r23002.75*1.2529978 Zµµ(m``>40GeV)+Np5107665e737s933s946r2302r23000.77*1.259993

TableA.3:ListofMonteCarlosamplesforW+jetsproduction.ThesamplesaregeneratedwithAlpGENandaresplitpernumberofinitialpartons(NpX,X=0,...,5).AminimumpartonpTcutat20GeVisappliedatproduction.

ProcessDatasetNumberAMITagLOCrossSection*NNLO-factor[pb]EventsWτν+Np0107700e844s933s946r2302r23006918.60*1.203259564Wτν+Np1107701e844s933s946r2302r23001303.20*1.202496467Wτν+Np2107702e844s933s946r2302r2300378.18*1.203764804Wτν+Np3107703e844s933s946r2302r2300101.51*1.201008514Wτν+Np4107704e844s933s946r2302r230025.64*1.20248864Wτν+Np5107705e844s933s946r2302r23007.04*1.2064950W+Np0107680e600s933s946r2302r23006921.60*1.203455037W+Np1107681e798s933s946r2302r23001304.30*1.202499513W+Np2107682e760s933s946r2302r2300378.29*1.203768265W+Np3107683e760s933s946r2302r2300101.43*1.201009641W+Np4107684e760s933s946r2302r230025.87*1.20249869W+Np5107685e760s933s946r2302r23007.00*1.2069953Wµν+Np0107690e600s933s946r2302r23006919.60*1.203466523Wµν+Np1107691e798s933s946r2302r23001304.20*1.202499513Wµν+Np2107692e760s933s946r2302r2300377.83*1.203768893Wµν+Np3107693e760s933s946r2302r2300101.88*1.201009589Wµν+Np4107694e760s933s946r2302r230025.75*1.20254879Wµν+Np5107695e760s933s946r2302r23006.92*1.2069958

146

TableA.4:ListofMonteCarlosamplesforthelowmassZ+jetsprocess.ThesamplesaregeneratedwithAlpGENandaresplitper numberofinitialpartons(NpX,X=0,...,5).AminimumpartonpTcutat20GeVisappliedatproduction. ProcessDatasetNumberAMITagLOCrossSection*NNLO-factor[pb]Events γ/Zττ(10GeV<m``<40GeV)+Np0116270e844s933s946r2302r23003055.1*1.25959877 γ/Zττ(10GeV<m``<40GeV)+Np1116271e844s933s946r2302r230084.93*1.25296945 γ/Zττ(10GeV<m``<40GeV)+Np2116272e844s933s946r2302r230041.47*1.25498804 γ /Zττ(10GeV<m``<40GeV)+Np3116273e844s933s946r2302r23008.36*1.25149953 γ /Zττ(10GeV<m``<40GeV)+Np4116274e844s933s946r2302r23001.85*1.2539980 γ /Zττ(10GeV<m``<40GeV)+Np5116275e844s933s946r2302r23000.46*1.259995 γ/Zee(10GeV<m``<40GeV)+Np0116250e660s933s946r2302r23003055.2*1.25999859 γ/Zee(10GeV<m``<40GeV)+Np1116251e660s933s946r2302r230084.92*1.25299940 γ/Zee(10GeV<m``<40GeV)+Np2116252e660s933s946r2302r230041.41*1.25499880 γ/Zee(10GeV<m``<40GeV)+Np3116253e660s933s946r2302r23008.38*1.25149940 γ/Zee(10GeV<m``<40GeV)+Np4116254e660s933s946r2302r23001.85*1.2539973 γ/Zee(10GeV<m``<40GeV)+Np5116255e660s933s946r2302r23000.46*1.259995 γ/Zµµ(10GeV<m``<40GeV)+Np0116260e660s933s946r2302r23003054.9*1.25999869 γ/Zµµ(10GeV<m``<40GeV)+Np1116261e660s933s946r2302r230084.87*1.25299890 γ/Zµµ(10GeV<m``<40GeV)+Np2116262e660s933s946r2302r230041.45*1.25499864 γ/Zµµ(10GeV<m``<40GeV)+Np3116263e660s933s946r2302r23008.38*1.25149939 γ/Zµµ(10GeV<m``<40GeV)+Np4116264e660s933s946r2302r23001.85*1.2539988 γ/Zµµ(10GeV<m``<40GeV)+Np5116265e660s933s946r2302r23000.46*1.259996

TableA.5:ListofMonteCarlosamplesfort¯tprocessgeneratedwithMC@NLOandfordibosonproductiongeneratedwithHERWIG.

ProcessDatasetNumberAMITagCrossSection[pb]Eventst¯t(nofullyhadronicdecays)105200e844s933s946r2302r230090.1514845714WW105985e598s933s946r2302r230017.022495756ZZ105986e598s933s946r2302r23005.54249906WZ105987e598s933s946r2302r23001.26249923

148

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