Wing Sheung Chan

96 Signal and background modelling designed for, the impact of not having simulated multijet events or that of the potential mismodelling in the subtracted simulated events on the derived fake factors is expected to be negligible. The weights R p r in Equation (5.4) are the relative contributions of events from the process p to the total yield of events with fakes in region r . They are estimated using the formulae: R p r = N fail r, MC p , fake N fail r, data − N fail r, MC , real (5.6) for p = W , Z , top, and R QCD r = 1 − X p 6 = QCD R p r = 1 − R W r − R Z r − R top r (5.7) for p = QCD. Since Equations (5.5) and (5.6) rely (partially) on the fakes estimated by MC simula- tions, offset can be introduced by virtue of the fact that these estimates are not scaled to data. Given that the FRs are enriched in the processes they are dedicated for, they can be used to extract normalisations for the MC estimates of the corresponding processes by subtracting other processes and truth-matched events from data. The correction factors k p pass = N pass FR p , data − N pass FR p , MC not p − N pass FR p , MC p , real N pass FR p , MC p , fake and (5.8) k p fail = N fail FR p , data − N fail FR p , MC not p − N fail FR p , MC p , real N fail FR p , MC p , fake (5.9) are derived for each process p that has a corresponding FR (except p = QCD). The simulated fakes can then be corrected by multiplying predicted yields with the correction factors. Expressed more explicitly, with the corrections, Equations (5.5) and (5.6) would become: F p = N pass FR p , data − N pass FR p , MC not p, real + k p pass · N pass FR p , MC not p, fake − N pass FR p , MC p, real N fail FR p , data − N fail FR p , MC not p, real + k p fail · N fail FR p , MC not p, fake − N fail FR p , MC p, real , (5.10) R p r = k p fail · N fail r, MC p , fake N fail r, data − N fail r, MC , real . (5.11) The described method relies on the assumption that for the same background process, the quark/gluon compositions are the same or similar in the FRs and in the region where the fakes need to be estimated. Such an assumption can be justified: The FRs, with the exception of FRQ, have the same charge correlation requirement as the SR and CRZ τ τ , i.e. they all require the ` – τ had - vis pair to carry OS charges. This ensures that the quark/gluon composition is similar in the FRs and the SR for processes like W +jets, which is indeed