Wing Sheung Chan

90 Signal and background modelling samples, which only account for a relatively small fraction of background events in the SR, their normalisations are fixed at the prefit value in the maximum-likelihood fit, with the uncertainty in the cross section measurement, ± 0 . 057 nb , considered as a systematic uncertainty. The p T ( Z ) distributions for each of the the Z -decay MC samples is corrected by reweighting the simulated events to match the measured p T ( Z ) spectrum [122] . The measurement was performed with pp collision data at √ s = 13 TeV , where events with dielectron or dimuon final states are analysed in a fiducial phase space that is close to the detector acceptance for leptons in p T ( ` ) , η ( ` ) and m ( `, ` ) . The unfolded normalised p T ( `, ` ) spectrum after correcting for the detector effects was reported at Born level (before final-state radiations). Since the Z → τ τ , Z → `` and signal samples are generated with different MC generators, PDF sets and tunes, correction scale factors are derived separately for each of them. For each simulated event in the fiducial region where the p T ( Z ) spectrum was measured, the true value of p T ( Z ) is retrieved or recalculated from the truth event records. The obtained p T ( Z ) distributions are then compared to the measured p T ( Z ) spectrum to derive scale factors as functions of p T ( Z ) . The uncertainties in the scale factors, which are dominated by MC statistical errors, are considered as a systematic uncertainty in maximum-likelihood fits. Figure 5.2 shows the simulated p T ( Z ) distributions in comparison with the measured distribution, and derived correction scale factors and their uncertainties. The obtained values of the correction scale factors are consistent with the data-model comparisons reported in Reference [122] . 5.4. Corrections to simulated events with ` → τ had - vis misidentification As mentioned, Z → `` events, where an electron or muon is misidentified as a τ had - vis candidate, are modelled by simulations. However, the simulations are not perfect in modelling the rate of ` → τ had - vis misidentification. To improve the accuracy of the prediction, Corrections are derived using data in CRZ `` and applied to simulated Z → `` events in the other regions. Correction scale factors, binned in p T ( τ ) and | η ( τ ) | , are calculated as the ratio of the observed number of events minus the predicted number of non- Z → `` SM events to the predicted number of Z → `` events. Given the low misidentification rate of 3-prong τ had - vis candidates, the corrections are only derived for events with 1-prong τ had - vis candidates. Separate scale factors are derived for Z → ee and Z → µµ events. The binning, values and errors of the derived scale factors are shown in Figure 5.3. The statistical uncertainties in the scale factors are considered as a systematic uncertainty in maximum-likelihood fits. The systematic uncertainties in the derivation of the scale factors due to the subtraction of other SM background events are negligible compared to the data and MC statistical uncertainties.