6.9 t¯t pair reconstruction
6.9.5 Scaled χ 2 algorithm
The scaled χ2 algorithm is a variant of the χ2 algorithm. The χ2 algorithm tries to identify all the reconstructed objects in the nal state of the t¯t pair. It uses reconstructed jets calibrated at the EM+JES scale. The EM+JES calibration as discussed in Section 4.7.4.1 corrects the energy and momentum of the calorimeter jets, using the kinematics of the corresponding Monte Carlo particle jet as a reference. The objective of the scaled χ2 algorithm is to calibrate jets to their partonic scale instead of the particle jet scale, in order to improve the resolution of the t¯t invariant mass. For events without a jet with mjet > 60 GeV, the light jets selected by the χ2 method as coming from the W boson decay are scaled to the W boson mass, MW, which is
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(a) (b)
(c) (d)
Figure 6.18: mt¯t distribution for matched events (left) and for non matched events (right) for Z0 with mZ0 = 700 GeV (up) and mZ0 = 1300GeV (bottom).
(a) (b)
Figure 6.19: Reconstruction e ciency using the four hardest jets, dRmin, χ2 (same for χ2 scaled) methods as a function of (a) the average number pp collisions per bunch crossing, < µ >
(left) and (b) the number of reconstructed primary vertices (right) for the SM t¯t sample.
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(a) (b)
(c) (d)
(e) (f)
Figure 6.20: Reconstruction e ciency using the (a,b) four hardest jets, (c,d) dRmin and (e,f) χ2 method as a function of the average number pp collisions per bunch crossing, < µ > (left) and the number of reconstructed primary vertices (right) for dierent Z0 samples.
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known with a high precision (of the order of 30 MeV [13]). The jets associated to the b−jets produced in the top-quark decay are scaled to the top-quark mass, Mtop. For events with at least one jet with mjet > 60GeV where two of the reconstructed are assumed to be merged, the scaling to the W boson mass is not done. But the two jets used to reconstruct the hadronic top quark are rescaled to the top-quark mass. Three dierent scalings are applied:
6.9.5.1 Hadronic W mass scaling
For events without a jet with mjet > 60 GeV, the two jets associated to the hadronic W boson decay are rescaled to the PDG value of the W boson mass, MW = 80.4 GeV. The scaling factor is given by:
α = MW
mnocalW , (6.8)
where mnocalW corresponds to the W boson invariant mass calculated using the two chosen jets.
No scaling is applied in events with a jet with mjet > 60GeV, since the χ2 method assume that the merging can not only occurs between both quarks from W boson decay, but also between one quark from W boson decay and the b−quark from the top-quark decay.
6.9.5.2 Top-quark mass scaling
For events without a jet with mjet > 60 GeV, the chosen jet associated to the b−quark from the top quark decay (either leptonic or hadronic) is rescaled to the PDG value of the top-quark mass, Mtop= 172.5GeV. The scaling factor corresponds to the positive solution of the quadratic equation aβ2+ bβ + cwhere:
a = m2b (6.9)
b = m2top− m2W − m2b (6.10)
c = −Mtop2 + m2W, (6.11)
where mb is the invariant mass of the jet associated to the b−quark and mtop is the top-quark invariant mass calculated using the three jets chosen by the χ2 algorithm. In the case of the hadronic top quark, mW is used after the W mass scaling. For events with a jet with mjet >
60 GeV, the jet associated to the b−quark in the leptonic side is scaled by β. In the case of the hadronic top-quark decay the situation is dierent since the two jets chosen by the χ2 method to built the hadronic top quark will be directly rescaled to the PDG value of the top-quark mass using a scaling factor given by:
γ = Mtop
mnocaltop , (6.12)
where mnocaltop corresponds to the top-quark invariant mass calculated using the two chosen jets.
Figure 6.21 and 6.22 show the reconstructed t¯t mass resolution and the reconstructed t¯t mass spectra before and after the dierent rescalings for the SM t¯t samples and three dierent Z0 resonances masses, using only matchable events. For matchable events and SM t¯t and low resonance mass samples the reconstructed t¯t mass resolution is improved after applying the χ2 scaled method. The method is built to calibrate the jets produced in the top-quark decay, but when the jets selected by the χ2 method do not come from the top-quark decay the scaling introduces left tails in the reconstructed t¯t mass. This is the case of high resonance masses as is shown in Figure6.22. The eect is more pronounced when we look at the reconstructed mass and the corresponding mass resolution for all events in Figures 6.12e and 6.12h. The reconstructed
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t¯t mass is shown as a function of true mass for SM t¯t production and Z0 with mZ0 = 2000 GeV in Figures 6.13dand 6.14d, respectively. All events were considered.
(a) (b)
(c) (d)
Figure 6.21: Reconstructed mt¯t resolution for matchable events before and after χ2 scalings for (a) SM t¯t, (b) Z0 mZ0 = 500GeV, (c) Z0 mZ0 = 1000 GeV and (d) gKK mgKK = 1300GeV.
Figure 6.23 shows the agreement between data and expectation from the sum of all back-grounds in the t¯t mass spectra. Both channels have been combined. Two signal points are also shown, a Z0 with mZ0 = 800GeV and a KK gluon with mgKK = 1300GeV. Figure 6.24 shows the relative dierence in reconstructed t¯t mass between data and expectation for the dierent methods. A data de cit is observed when using the χ2 method around 1 TeV.
The χ2 method is sensitive to the pile-up and the e ciency of the four hardest jets method is smaller than the one obtained when using the dRmin method. Therefore, the dRmin method has been chosen as the reconstruction method to be used in the analysis. The impact of pile-up on the reconstructed t¯t mass for dierent samples is shown Figure 6.26. Small dierences are seen between high and low pile-up events.