Wing Sheung Chan

70 Event selection and classification actually beneficial as they are useful for constraining the predicted background yields in the maximum-likelihood fits. Events with identified b -jets are vetoed in order to suppress events from t ¯ t , single-top or Wt productions (collectively known as the “top background”). Additionally, in the µτ channel, events with 1-prong τ had - vis candidates reconstructed in the crack region of the muon spectrometer ( | η | < 0 . 1 ) are rejected. This is because of the large µ → τ had - vis misidentification rate due to the inefficacy of the µ – τ had - vis overlap removal in the region. With the above mentioned selection criteria, the remaining major background processes are Z → τ τ , where one of the τ leptons decays leptonically and the other hadronically; Z → `` , where one of the light leptons is misidentified as the τ had - vis candidate ( ` → τ had - vis fakes); and events with a quark- or gluon-initiated jet misidentified as the τ had - vis candidate (jet → τ had - vis fakes, or simply “fakes” without further clarification), which are dominantly W +jets and multijet events. These background events can be effectively separated from the signal events by the transverse mass variables and outputs of neural network classifiers. The transverse mass, m T , of a system of any two objects, X and Y , is defined by m 2 T ( X, Y ) ≡ ( E T ( X ) + E T ( Y )) 2 − ( p T ( X ) + p T ( Y )) 2 ≡ m 2 ( X ) + m 2 ( Y ) + 2 ( E T ( X ) E T ( Y ) − p T ( X ) · p T ( Y )) . (4.2) Its value is invariant under Lorentz boosts in the z -direction, making it a useful quantity when one of the considered objects is the missing transverse momentum, which has an unknown z -component. In the case where X and Y are both approximately massless (i.e. highly relativistic), the transverse mass is approximately m T ( X, Y ) = p 2 p T ( X ) p T ( X ) (1 − cos ∆ φ ( X, Y )) , (4.3) where ∆ φ ( X, Y ) is the angle between the transverse momenta of X and Y . When X and Y are collinear in the transverse plane, m T ( X, Y ) vanishes. On the other hand, when they are back-to-back, m T ( X, Y ) is proportional to the magnitudes of their transverse momenta. This property is exploited in the event selection for the SR. Figure 4.1 shows the typical topology of a signal Z → `τ event in the transverse plane, compared to that of a Z → τ τ or W +jets event. For a signal event, the neutrino from the single τ decay is expected to be the sole contributor to the E miss T and travel in a direction close to that of the τ had - vis but back-to-back to that of the light lepton. This can be reflected by a relatively small m T ( τ had - vis , E miss T ) but large m T ( `, E miss T ) . In contrast, the neutrinos from both the τ decays in a Z → τ τ event contribute to the total E miss T , resulting in a E miss T that could either line up with the τ had - vis or the light lepton. Therefore, a large fraction of Z → τ τ events have a small m T ( `, E miss T ) but large m T ( τ had - vis , E miss T ) . In a W +jets event, the scenario is again different. The τ had - vis candidate, which is a misidentified jet, is generally not aligned with the E miss T , nor the light lepton. This results in both m T ( τ had - vis , E miss T ) and m T ( `, E miss T ) being large in general.