Wing Sheung Chan

92 Signal and background modelling 0.08 ± 0.88 0.07 ± 0.80 0.08 ± 0.91 0.05 ± 0.92 0.05 ± 1.07 0.08 ± 1.19 0 0.5 1 1.5 2 2.5 )| had-vis τ ( η | 30 40 50 60 70 80 ) [GeV] had-vis τ ( T p 0 0.2 0.4 0.6 0.8 1 correction scale factors had-vis τ → e (a) 0.16 ± 1.42 0.10 ± 1.17 0.08 ± 1.31 0.12 ± 0.90 0.08 ± 0.93 0.12 ± 1.32 0.5 1 1.5 2 2.5 )| had-vis τ ( η | 30 40 50 60 70 80 ) [GeV] had-vis τ ( T p 1 1.1 1.2 1.3 1.4 correction scale factors had-vis τ → µ (b) Figure 5.3.: The (a) e → τ had - vis and (b) µ → τ had - vis correction scale factors and their uncertainties. While the plot only shows p T ( τ had - vis ) up to 80 GeV , the actual bin boundaries are at infinity. The observed and expected distributions of several kinematic variables in CRZ `` after the correction are shown in Figures 5.4 and 5.5 for the eτ and µτ channels respectively. The data and the corrected predictions agree well with each other within uncertainties. 5.5. Modelling of events with jet → τ had - vis misidentifcation Modelling events with jet → τ had - vis fakes purely by MC simulations is extremely challeng- ing. This is because it requires detailed and accurate modelling of the hadronisation of quarks or gluons and the interactions between the particle showers and the materials in the calorimeters. Adding to the challenge, there is simply no robust MC simulation for purely QCD multijet events because of the difficulties in calculating QCD matrix elements at low-energy scales. Therefore, a data-driven method broadly known as the fake-factor (FF) method is used to model such background processes. The method also partially addresses jet → ` fakes indirectly for the cases where these fakes come from multijet events. This section describes in details the implementation of the FF method in our analysis. 5.5.1. Concept and definitions In this section, the following definitions of subscripts or superscripts are used: