Wing Sheung Chan

Chapter 5. Signal and background modelling “The fake is of far greater value. In its deliberate attempt to be real, it’s more real than the real thing.” — Ishin Nishio, “Desh¯u Kaiki”, Nisemonogatari To be able to compare the observed data with predictions, one must be able to model the probability distributions of all relevant observables according to the SM or the hypotheses that are to be tested. However, given the many coupled degrees of freedom, it is virtually impossible to calculate the distributions analytically. In this chapter, we will discuss the methods used to model the LFV Z → `τ signal and the SM background events. These methods are partly based on MC simulations and partly based on measurements in regions that have little or no signal contamination expected (data-driven). The signal and the contributions to the SM background can be classified into three main categories: 1. Events with a single Z -boson decay. These are the signal, Z → τ τ and Z → `` events. 2. Events with a quark- or gluon-initiated jet misidentified as the τ had - vis candidate (fakes). They are dominantly W ( → `ν ) +jets and multijet events, with little contri- bution from Z ( → `` ) +jets and t ¯ t events. 3. Other events that are not single Z -boson decays or fakes. These include t ¯ t , diboson, H → τ τ , H → WW and W ( → τν ) +jets events. Events in the first category are modelled using MC simulations with data-driven corrections for the production cross section and p T spectrum of the Z bosons, and for the ` → τ had - vis fake rate for Z → `` events. The generation of the MC samples will be described in Section 5.1 while the data-driven corrections will be described in Sections 5.3 and 5.4. Events in the second category are predicted using a data-driven method known as the fake-factor method, which will be detailed in Section 5.5. Events in the third category, which have only minor contributions to the total SM background, are purely modelled by MC simulations. 85