Wing Sheung Chan

Signal and background modelling 97 expected to show charge correlations between the fake τ had - vis candidate and the light lepton. And while FRQ is defined with a SS charged ` – τ had - vis pair requirement, the charge correlation is not a concern there since multijet events are expected to be largely gg events with no charge correlations. To add more confidence to the validity of the assumption, it has been estimated using MC samples that the quark/gluon compositions of jet → τ had - vis fakes in W +jets events (which is the dominant contribution to the total fakes) are indeed similar in the SR and FRW. Table 5.1 shows the estimated quark/gluon compositions in the SR, FRW, VRSS (SR but with SS ` – τ had - vis pairs) and SS FRW (FRW but with SS ` – τ had - vis pairs). Table 5.1.: The quark/gluon compositions of jet → τ had - vis fakes in W +jets events in the SR, FRW, VRSS and SS FRW estimated using MC samples. A light quark is an up, down or strange quark. Region Composition [%] Light quark Charm quark Bottom quark Gluon SR ( eτ ) 71 . 5 17 . 4 1 . 2 9 . 9 FRW ( eτ ) 75 . 3 14 . 4 0 . 8 9 . 5 SR ( µτ ) 71 . 4 18 . 4 1 . 2 8 . 9 FRW ( µτ ) 76 . 2 13 . 7 1 . 1 9 . 0 VRSS ( eτ ) 54 . 3 15 . 7 3 . 6 26 . 3 SS FRW ( eτ ) 59 . 3 11 . 5 2 . 6 26 . 7 VRSS ( µτ ) 53 . 9 15 . 6 3 . 9 26 . 7 SS FRW ( µτ ) 60 . 0 11 . 0 3 . 2 25 . 9 5.5.2. Measurement and sources of uncertainties The fake factors are measured separately in the eτ and µτ channels. They are measured in bins of p T ( τ had - vis ) and p T ( τ track ) in 1P regions and in bins of p T ( τ had - vis ) in 3P regions. Binning in p T ( τ track ) in 1P regions is necessary for the modelling of the variable m ( `, τ track ) , which is used as an input to the neural network classifiers. The measured process-specific fake factors, F p , and the estimated relative contribution of each process to the total fakes in the SR, R p SR , are summarised in Appendix D. There are three major sources of uncertainties in the estimation of fakes via the FF method. They are: 1. The statistical errors in N fail r, data − N fail r, MC , real (the observed yields that are multiplied by the fake factors). These errors are combined bin-by-bin with the statistical errors in the MC samples for the other backgrounds in the binned maximum-likelihood fits.