Wing Sheung Chan

Signal and background modelling 95 pass Events of which the leading- p T τ had - vis candidate passed the Tight RNN ID requirement. fail Events of which the leading- p T τ had - vis candidate failed the Tight but passed the Loose RNN ID requirements. fake Simulated events of which the leading- p T τ had - vis candidate originates from a misidentified gluon- or quark-initiated jet. real Simulated events of which the leading- p T τ had - vis candidate originates from a real τ -lepton or a misidentified light lepton. data Observed events in the collected data. MC Simulated events from any SM processes (except multijet events). MC p Simulated events from a specific process p . MC not p Simulated events from any SM processes except from a specific process p (and except multijet events). With the fake-factor method, the yield of fakes in a given region r † is estimated by N pass r, fake = N fail r, data − N fail r, MC , real × F r . (5.3) The (region-specific) fake factor F r for any region r is defined as a weighted average of the process-specific fake factors F p : F r = X p R p r F p = R W r F W + R Z r F Z + R top r F top + R QCD r F QCD , (5.4) where p = W , Z , top , QCD are labels representing the SM processes W ( → `ν ) +jets, Z ( → `` ) +jets, t ¯ t and QCD multijet respectively. The process-specific fake factors are derived from data in the corresponding fakes- enriched regions FR p that have been defined in Section 4.1.4: FR W = FRW, FR Z = FRZ, FR top = FRT and FR QCD = FRQ. They are defined as the ratio of the number of events with fakes passing the Tight RNN ID requirement to the number of those failing it but passing the Loose RNN ID requirement: F p = N pass FR p , data − N pass FR p , MC not p − N pass FR p , MC p, real N fail FR p , data − N fail FR p , MC not p − N fail FR p , MC p, real . (5.5) The second terms in both the denominator and numerator are there to subtract the contributions from SM other processes (except multijet), while the third terms are there to subtract contributions from events that are not with jet → τ had - vis fakes. Since there is no reliable MC simulations for multijet events, they cannot be subtracted when p is not QCD. Still and all, because the FRs are enriched in events from the process that they are † This could refer to a subregion, or a single bin in any variables, in any of the regions defined in Section 4.1.