Discriminant sideband
6.7. Final Event Selection
For all events passing the common preselection requirements the KinFitter-based algorithms test the compatibility of the kinematics of the input objects with the topology of the Wt events. The events are then selected exploiting the KinFitter response. After the fit proce-dure, the top quark and its W boson daughter are completely reconstructed for any successful hypothesis, while the longitudinal component of the momentum of the spectator W boson remains unknown. With such ingredients, the following cuts are applied to further reject the background events:
• Convergence: This cut demands that the reconstruction of a single top quark and a W boson by the KinFitter algorithm converged.
• t¯t Veto: If the reconstruction of a semi-leptonically decaying top pair by the KinFitter with a same-mass constraint was successful, i.e. the KinFitter yields a P(χ2) higher than 0.001, the event is rejected as t¯t background.
• Signal Hypothesis Match: In order to reduce the background rate in the final event count, the separation power of the P(χ2) distribution for the fit combination shown in Fig. 6.8e is exploited. The fitted events are rejected if they yield a probability score lower than 0.1 to match the Wt single top hypothesis.
• W+t Balance: For the events passing the selection operated by the kinematic fit (fully displayed in Fig. 6.1) a cut on the pt of the system composed by the top quark and the associated W boson reconstructed by the fit is applied, in order to reduce the signal-to-background-ratio. The top and the associated W boson are the only physical objects produced in the Wt events, and their system is therefore expected to appear more balanced in the transverse plane of the signal events than in t¯t, where at least one more jet initiated by a b quark in the hard final state is present. This is shown in the comparison of the histogram shapes in Fig. 6.9c. The (~ptop+~pWass)t =pW tt < 35 GeV selection cut is chosen, in order to reject the phase space region dominated by the
t¯t background. The rejection power of this kinematic observable able is not corre-lated with the one displayed by the P(χ2) in Fig.6.8e, thus providing an independent criterion for the selection of the signal events.
3 Jets Selection
Process e µ
Wt Channel 143.92 196.04
t-Channel 35.91 49.60
s-Channel 1.86 3.17
t¯t 601.37 860.47
W+LF Jets 55.53 94.73
W+HF Jets 233.13 450.27
Z+Jets/Diboson 29.55 34.87
QCD 18.59 33.12
S/B 0.147 0.128
Total expected 1119.87 1722.30 Total observed 1191.00 1705.00
Table 6.3.: Event yield after the final event selection. For all the events where the convergence of the Wt hypothesis fit occurs, the P(χ2)>10 % andpW tT <35 GeV consecutive cuts are applied in the three-jet bin for the electron and muon channel separately. After the cuts the agreement between the number of expected and observed events is maintained. The numbers in the table are used as input rates for the signal extraction described in Sec. 7.2.4.
In Fig.6.9the stacked distribution of the transverse momentumpW tt of the system composed by the single top quark and the associated W boson reconstructed by the kinematic fit is shown. As it is seen in the normalised shapes provided in Fig. 6.9c, the distribution of the pW tt quantity provides a sizable discrimination power between Wt and t¯t events.
The cut at 35 GeV is chosen at the point where the Wt and t¯t shape cross, selecting the region richer in Wt events. The number of events surviving the selection is presented in Tab.6.3. A combined total of 340±18 signal events and of 1502±39 background events are expected, corresponding to a signal over background ratio of X% and a statistical significance of S/√
B =N. The total expected event yield is 2842.2 ±53.3 , which is in agreement with the observed 2895 events.
χ2
Figure 6.8.: Distribution of the χ2 and χ2-probability of the Wt fit for the 3 jet bin in the muonic (c), (a) and electronic, (b), (d) channels after the decision explained in Sec. 6.3 and 6.4.
The exclusion lines indicate the cut used for signal enrichment,P(χ2)>0.1 . Histograms(c)and(d) are populated with the events for which the convergence of the kinematic fit is reached. The single top Wt,t,s-channel, t¯t, Z+jets and diboson samples are normalised to their theory predictions; the
Wt system pt show the stacked distribution in the exemplary 3 jet bin. Histograms (a) and (b) are populated with the events for which the convergence of the kinematic fit is reached. In (c) the pure shape of the distribution is shown for each input sample. The histograms in (c) are normalised to the number of entries, in order to identify the shape differences and exploit the separation power of the observed quantity. The Wt and t¯t shapes are put into evidence drawn in bold azure and red lines respectively. A cut at 35 GeV is chosen at the point where the Wt and t¯t shapes cross, selecting the region richer in Wt events.
η
(a)Pseudorapidity of the Neutrino.
(GeV) Mtop
171 171.5 172 172.5 173 173.5 174
Number of Entries
(b)Invariant Mass of the Top Quark.
(GeV)
(c)Invariant Mass of the W Boson (Top Decay).
(GeV)
(d)Invariant Mass of the W Boson (Associate).
Figure 6.10.: The plots represent, for the “leptonic top” case in the µ+3 jets channel, the distri-bution of the pseudorapidity of the neutrino (a) and of the invariant mass of the top quark (b), the leptonically decaying W boson (c) and the hadronically decaying associate W boson (d). All histograms are populated with the events for which the convergence of the kinematic fit is reached, and ap-value greater than 10% is found for the signal hypothesis.
η
(a)Pseudorapidity of the Neutrino.
(GeV) Mtop
171 171.5 172 172.5 173 173.5 174
Number of Entries
(b)Invariant Mass of the Top Quark.
(GeV)
(c)Invariant Mass of the W Boson (Top Decay).
(GeV)
(d)Invariant Mass of the W Boson (Associate).
Figure 6.11.: The plots represent, for the “leptonic top” case in the e+3 jets channel, the distri-bution of the pseudorapidity of the neutrino (a) and of the invariant mass of the top quark (b), the leptonically decaying W boson (c) and the hadronically decaying associate W boson(d). All histograms are populated with the events for which the convergence of the kinematic fit is reached, and a p-value greater than 10% is found for the signal hypothesis.
(GeV) Mtop
170 171 172 173 174 175
Number of Entries
(a)Invariant Mass of the Top Quark.
(GeV)
(b)Invariant Mass of the W Boson (hadronic).
(GeV) Mtop
170 170.5 171 171.5 172 172.5 173 173.5 174 174.5
Number of Entries
(c)Invariant Mass of the Top Quark.
(GeV)
(d)Invariant Mass of the W Boson (hadronic).
Figure 6.12.: The plots represent the invariant masses reconstructed by the fit for the “hadronic top” hypothesis in the electron (above) and muon (below) channel. The distribution of the invariant masses of the top quark (a),(c)) and the hadronically decaying W boson originated from the top quark (b), (d)are shown for the analysis of the three-jet bin. All histograms are populated with the events for which the convergence of the kinematic fit is reached, and a p-value greater than 10% is found for the signal hypothesis.
The purpose of the analysis is the measurement of the inclusive Wt production cross section.
As mentioned in Chapter 3, this observable is directly related to the number of observed signal events, therefore it can be extracted directly from the results yielded by the selection obtained exploiting the discrimination power of the kinematic fit, after applying the quality requirements of the ATLAS common prescription for the preselection of top quark physics events.
The measurement of the cross section is affected by two types of uncertainties. On one hand, a first source of uncertainties is caused by the limited statistics of the data and MC samples utilised for the simulation of the events composing the signal and the background.
Secondly, the measurement is affected by the systematic uncertainties associated to the reconstruction methods and to the modelling of the data. The different sources of systematic uncertainties are therefore discussed in Sec. 7.1.
In Sec.7.2the statistical treatment of the event yield is described, leading to the determi-nation of an upper limit on the inclusive cross section σWt for the production of single top quarks in association with W boson, presented in Sec. 7.2.4. In conclusion, a comparison of the result of this analysis with the latest measurements performed at the LHC is presented in Sec.7.2.5; in Sec.7.3, the possible further developments of the current analysis are presented.