Wing Sheung Chan

Statistical interpretation and results 109 The prefit TES and its uncertainties are estimated using measurements in so-called “tag-and-probe” analyses, where simulated Z → τ τ events are compared to observation from data [81] . However, these estimations are not entirely applicable to this analysis for several reasons: the measurements in the tag-and-probe analyses are performed based on Z → τ τ MC samples generated using Powheg+Pythia with a vastly different set-up than what is used for the Z → τ τ MC samples in this analysis; the measurements in the tag-and-probe analyses are performed inclusively for 1-prong and 3-prong τ had - vis candidates, while distinctions are made between 1-prong and 3-prong τ had - vis candidates in this analysis; the estimated TES uncertainties in Reference [81] are only based on the measured peak in the m vis ( ` , τ ) distribution, but in this analysis, the entire m coll ( ` , τ ) spectrum in CRZ τ τ is used to constrain the TES. Furthermore, by considering all the events in the SR and in CRZ τ τ , this analysis makes use of more data than what is used in the tag-and-probe analyses. In other words, the maximum-likelihood fit in this analysis is basically remeasuring the TES and its uncertainties to a higher precision. Because of this, the postfit values of the TES NPs can be expected to be different from the prefit values and more constrained. Simulated Z -boson production As mentioned in Section 5.3 in the previous chapter, the dominant source of theory uncertainties in the simulated signal, Z → τ τ and Z → `` events is the uncertainties in the predicted σ ( Z ) and p T ( Z ) . However, by applying corrections derived from measurements, the impact of these uncertainties are reduced. The statistical uncertainties in the derived p T ( Z ) correction scale factors are assigned to the Z → `` , Z → τ τ and signal samples. The systematic uncertainty in the measured Z production cross section (2.0%) [62] is assigned to the overall normalisation of the Z → `` sample. Since the normalisation of the signal and Z → τ τ samples are determined by a maximum-likelihood fit to data, no associated uncertainties are assigned. ` → τ had - vis fakes For the Z → `` events with ` → 1-prong τ had - vis misidentification, the uncertainties in the correction scale factors derived from CRZ `` (see Section 5.4) are assigned to the Z → `` samples in the maximum-likelihood fit. For the events with ` → 3-prong τ had - vis misidentification, there is no corrections derived or applied. Instead, extra uncertainties are assigned to the corresponding samples. The uncertainty in the efficiency of correctly vetoing e → 3-prong τ had - vis events using the e -veto BDT algorithm is considered by assigning a conservative variation of ± 50% at ± 1 σ on the expected yield of Z → ee events. On the other hand, The uncertainty in the (in)efficiency of incorrectly vetoing e → 3-prong τ had - vis events is considered by varying the expected yields of Z → τ τ and signal events by ± 50% of the inefficiency of applying the