5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space
5.3.1 Basic Kinematic Quantities
Charged lepton The distributions of transverse momentum, the pseudo-rapidity, and az-imuthal angle of the muon for events in the “2 jets, 0 btags” are shown in fig. 5.9. The transverse-momentum distribution peaks at pT ≈ 35 GeV/c and steeply falls towards higher momenta. The pseudo-rapidity distribution for muons is flat, except for binning effects in the endcaps, and the muon-reconstruction efficiency is slightly higher in the central region of the detector. The CMS detector fully covers the azimuthal-angle (φ) range. The resulting φ distri-butions of muon and electron are uniformly distributed around the beamline. The observed and simulated φ distributions well agree in all categories. As an example, the φ distribution for muons in the “2 jets, 0 btags” category is shown in the bottom-left plot in figure 5.9. The simulation well describes the kinematic distributions over the whole spectrum. Some minor residual corrections can be attributed to the description of the QCD-multijet contribution, and are covered by the normalization uncertainties of both QCD-multijet and W-boson-plus-jets production. Moreover, figure 5.10 confirms that the pT and η distributions are well described for muons and electrons in the tt enriched phase space (“≥ 4 jets, 1 btag” category).
Events / 5 GeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 5 GeV
400 KS-test prob.: 0.38
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.2
300 KS-test prob.: 0.91
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.2
350 KS-test prob.: 0.93
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Figure 5.10: Distributions of the electron pT (top left), electron η (bottom left), muon pT (top right), and muon η (bottom right) in the “≥ 4 jets, 1 btag” category.
The observed distribution of the muon charge (fig. 5.9, bottom right) in W-boson-plus-jets events is poorly described. This is surprising, since dedicated measurements observe a good agreement between data and prediction. First, the inclusive ratio of W+-to-W−production well agrees between data and simulation (POWHEG BOX NLO+PS description with three different
146
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space
PDF sets), as well as with NNLO calculations [165]. Second, the differential distribution of the
|η|-dependent-charge asymmetry, which is defined by [232]
AW±production(η) =
dσ
dη(W+→ l+νl)−dσdη(W− → l−ν¯l)
dσ
dη(W+→ l+νl) +dσdη(W− → l−ν¯l), (5.3) shows a reasonable agreement between data and simulation [232, 233].
The lepton charge is expected to be asymmetric for W-boson-plus-jets production (cf.
eq. 5.3). Positively charged leptons are preferred for similar reasons as for t-channel produc-tion (cf. sec. 4.2). The producproduc-tion of W+and W−bosons is mostly determined by the valence quarks of the colliding protons, and is sensitive to the PDFs. W+ bosons are mostly produced by valence-up quarks, and W− bosons are mostly produced by valence-down quarks. The charge asymmetry is expected to be η-dependent, since valence-up quarks carry on average a higher fraction of the proton momentum than valence-down quarks [233]. Instead, tt produc-tion is lepton-charge symmetric due to q ¯q or gg initial states.
Figure 5.12 (left) shows the differential distribution of the W-boson-charge asymmetry (eq. 5.3) as measured in data and predicted by simulation. The distributions are shown for events with a muon in the “2 jets, 0 btags” category. The observed charge asymmetry is lower than the simulated distribution over the full|η| acceptance. Since dedicated measure-ments [232, 233] show a reasonable agreement between data and simulation, the observed dif-ferences in the description of the charge asymmetry are expected to be either due to the choice of the PDF set (CTEQ6L1 [52]) or due to the modeling of the W-boson events with additional partons with MADGRAPHandPYTHIA.
Figure 5.12 (right) shows the observed difference in the charge asymmetry between data and simulation. It is mostly independent of|η|. The difference is slightly larger for higher |η| values.
The residual differencedata - prediction
prediction in the charge asymmetry between data and simulation can be parametrized as
f (AW±production)(|η|) = (−0.437 ± 0.034) + (0.056 ± 0.025) · |η|. (5.4) The inclusive measurement of the t-channel-production cross section is uncorrelated w.r.t. the lepton charge, and independent of the observed discrepancy in AW± for W-boson-plus-jets events. The measurement of the ratio of top-quark-to-top-antiquark production in t-channel events takes this mismodeling into account.
The distribution of the lepton charge in the tt-enriched phase space for events in the
“≥ 4 jets, 1 btag” category confirms that W-boson-plus-jets events with a negatively-charged lepton are underestimated for both events with electrons and muons (fig. 5.11). The disagree-ment is less pronounced in this category due to the overall lower yield of W-boson-plus-jets events and due to the fact that tt is charge symmetric. Moreover, the overall yield of W-boson-plus-jets events is underestimated by a few percent for W-boson-W-boson-plus-jets events with muons (fig. 5.11, left plot).
Jets The transverse-momentum and pseudo-rapidity distributions for the leading jet and second-leading jet of W-boson-plus-jets events are shown in figure 5.13. A reasonable agree-ment between data and simulation is observed, even if the transverse-moagree-mentum distribution for jets is softer in data than predicted by the simulation. The jet-η distributions show a good agreement between data and simulation, except for jets within 3 < |η| < 4. Here, signifi-cantly more events are observed in data than predicted by the simulation. The excess in data
Events / 1 e
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 1 e
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Figure 5.11: Distributions of the lepton charge in the “≥ 4 jets, 1 btag” category for events with electron (left) or muon final states (right).
η|
MCData - MCMuon-Charge Asymmetry
-1
Figure 5.12: Charge asymmetry of the W boson as measured in events with a muon in the
“2 jets, 0 btags” category (left), and residuals between data and simulation (right).
148
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space
is most prominent at|η| ≈ 3.5, and is about 10% when considering shape-effects only. Two sources of systematic uncertainties have an effect on the shape of the jet-pT and jet-η distri-butions, namely the jet-energy calibration and the Q2 scale. The shape of the observed jet-pT
distributions is compatible with the Q2-scale variations at 1σ level. Furthermore, the Q2-scale variations predict±( 5-10)% more (less) jets close to the beamline than in the central-detector region. The jet-energy-calibration uncertainties cover the observed discrepancies within 2σ in both jet-pT and jet-η distributions. Furthermore, the uncertainty of the normalization of the W-boson-plus-jets events covers even larger variations.
Events / 10 GeV Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
(GeV) leading jet pT
50 100 150 200 250 300
MCData - MC -0.4-0.200.20.4
Events / 0.4 Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
η leading jet
-4 -2 0 2 4
MCData - MC -0.4-0.200.20.4
Events / 10 GeV Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
(GeV) jet2 pT
50 100 150 200 250 300
MCData - MC -0.4-0.200.20.4
Events / 0.33 Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
η jet2
-4 -2 0 2 4
MCData - MC -0.4-0.200.20.4
Figure 5.13: Distributions of the leading-jet pT (top left), leading-jet η (top right), second-leading-jet pT (bottom left), and second-leading-jet η (bottom right) in the muon
“2 jets, 0 btags” category.
The leading-jet pT and η distributions for jets from tt in the “≥ 4 jets, 1 btag” category are shown in figure 5.14. Events with electrons (left column) and muons (right column) are sep-arately shown, since events in both lepton categories are selected with varied criteria. All kinematic distributions are also shown for the second-leading jet in figure 5.15.
The observed jet-pT spectrum is softer than predicted by the simulation. The same trend is observed for W-boson-plus-jets events. However, W-boson-plus-jets events are a minor contri-bution to events in the “≥ 4 jets, 1 btag” category, and W-boson-plus-jets events only partially explain the disagreement. Furthermore, the Q2-scale variations have a smaller effect on the jet-pT spectra of tt processes. The same is true for the jet-energy-scale variations, since jets from tt production mostly are central in the detector, in which the jet-energy-scale uncertainties are small. Thus, the disagreement is expected to be a “real” effect of the event simulation. It is correlated to the description of the top-quark-pT spectrum and is discussed in more detail in
one of the following paragraphs. The altered selection efficiency of tt events between data and simulation is covered by the normalization uncertainties.
Jets from tt production are more central in the detector than jets from W-boson-plus-jets production. The predicted jet-pseudo-rapidity distributions well agree with the observed dis-tributions, except for residual corrections to the tt normalization (or other systematic uncer-tainties that affect the process normalization, e.g. jet-flavor-tagging efficiencies). The excess of jets around|η| ≈ 3.5, which is observed for W-boson-plus-jets events, cannot be confirmed for tt production, but the statistical precision is low in that region.
Events / 10 GeV
400 KS-test prob.: 0.01
= 7 TeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
(GeV) leading jet pT
50 100 150 200 250 300
MCData - MC -0.4-0.200.20.4
Events / 10 GeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
(GeV) leading jet pT
50 100 150 200 250 300
MCData - MC -0.4-0.200.20.4
Events / 0.4
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.4
600 KS-test prob.: 0.82
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Figure 5.14: Distributions of the leading-jet pT (top row) and leading-jet η (bottom row) in the
“≥ 4 jets, 1 btag” category for events with electron (left) or muon final states (right).
150
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space
600 KS-test prob.: 0.01
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 10 GeV
800 KS-test prob.: 0.0
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.33
400 KS-test prob.: 0.34
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.33
500 KS-test prob.: 0.05
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Figure 5.15: Distributions of the second-leading-jet pT(top row) and second-leading-jet η (bot-tom row) in the “≥ 4 jets, 1 btag” category for events with electron (left) or muon final states (right).
ETmissand transverse W-boson mass The ETmissis shown in both W-boson-plus-jets-enriched and tt-enriched control regions in figure 5.16. An overall good agreement of the ETmissresponse is observed. The observed ETmiss distribution is slightly broader than predicted by simulation and the tails of the ETmiss distribution are overestimated by simulation. The low-ETmiss region (top plot in fig. 5.16) is sensitive to both normalization and ETmiss-distribution shape of QCD-multijet events. The QCD-QCD-multijet model is estimated from data with large uncertainties and might explain the observed discrepancies in the left tail of the distribution.
The EmissT is an important input to the reconstruction of the transverse W-boson mass, whose distributions are shown in figure 5.17 for W-boson-plus-jets events and in figure 5.18 for tt events. The reconstructed W-boson mass is shown either before (left figure) or after (right figure) applying the neutrino-reconstruction algorithm. The QCD-multijet yield is underes-timated at low transverse-W-boson-mass values (both plots in fig. 5.17), but covered by the uncertainties of the QCD-multijet prediction.
The tails of the MT(W boson) distributions (MT(W boson)≥ M(W boson)) show an excess of data w.r.t. the prediction (right plot in fig. 5.17). The data excess originates from residual cor-rections as observed in the ETmiss-response distribution (fig. 5.16). The reconstructed transverse-W-boson mass can be larger than the invariant-transverse-W-boson mass if the ETmissis mismeasured. If the ETmiss is mismeasured, complex solutions for the z-component of the neutrino momentum arise while applying the neutrino-reconstruction algorithm. These complex solutions are then resolved by varying ETmiss(cf. sec. 4.4.2).
As a result of the neutrino-reconstruction algorithm, events with values MT(W boson) >
M (W boson) obtain a reconstructed transverse-W-boson mass that is equal to the invariant-W-boson mass MT(W boson) = M (W boson) = 80.4 GeV/c2. Figure 5.17 (right) shows that a reasonable description of the observed transverse W-boson mass is obtained after applying the neutrino-reconstruction algorithm. Small residual differences of about 7% remain due to the ETmiss resolution. Uncertainties are covered by jet-energy-scale and Q2-scale uncertainties within 1.5σ. However, both ETmissand MT(W boson) are not a direct input to the BDT-classifier training.
152
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet
450 KS-test prob.: 0.41
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 5 GeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Figure 5.16: Distributions of the ETmiss in the muon “2 jets, 0 btags” category (top plot) and
“≥ 4 jets, 1 btag” category for events with electron (bottom left) or muon (bottom right) final states. Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
reco. (GeV) ν
(W boson), before MT
0 50 100 150 200
MCData - MC -0.4-0.200.20.4
Events / 5 GeV Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
transverse W-boson mass (GeV)
0 20 40 60 80 100 120 140
MCData - MC -0.4-0.200.20.4
Figure 5.17: Reconstructed transverse-W-boson mass distributions before (left) and after (right) applying the neutrino reconstruction algorithm. The distributions are shown in the
“2 jets, 0 btags” category for events with a muon final state.
Events / 5 GeV
300 KS-test prob.: 0.02
= 7 TeV
W/Z + jets, Diboson QCD Multijet
(W boson), before MT
0 50 100 150 200
MCData - MC -0.4-0.200.20.4
Events / 5 GeV
450 KS-test prob.: 0.92
= 7 TeV
W/Z + jets, Diboson QCD Multijet
(W boson), before MT
0 50 100 150 200
MCData - MC -0.4-0.200.20.4
Events / 5 GeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
transverse W-boson mass (GeV)
0 20 40 60 80 100 120 140
MCData - MC -0.4-0.200.20.4
Events / 5 GeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
transverse W-boson mass (GeV)
0 20 40 60 80 100 120 140
MCData - MC -0.4-0.200.20.4
Figure 5.18: Reconstructed transverse-W-boson mass distributions in the “≥ 4 jets, 1 btag” cat-egory for events with electron (left) or muon final states (right). Distribu-tions are shown before (top row) and after (bottom row) applying the neutrino-reconstruction algorithm.
154
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space
5.3.2 Top-Quark Reconstruction
The distributions of the transverse momentum (pT) of the top quarkin tt events are shown in figure 5.19 (top row). The top-quark pT is significantly lower in data than predicted by the simulation. Variations of jet-energy scale and Q2 scale only have minor effects on the pre-dicted top-quark-pTdistribution. The observed disagreement is confirmed in dedicated mea-surements of the differential top-quark-pair production cross sections [167]. About 15% more events are observed at a top-quark pTbelow 50 GeV/c, and about 15% less for a top-quark pTof about 225 GeV/c. The observed difference remains stable against the choice of the event gener-ator (MADGRAPH+PYTHIA,POWHEGBOX+PYTHIA, and MC@NLO +HERWIG). In particular, the observed data are compatible with approximate NNLO predictions [79].
The softer top-quark-pTspectrum translates into softer jet-pTspectra, which explains that the observed jet-pTdistributions are softer than predicted by the simulation (cf. fig. 5.14 and 5.15).
The simulation is not reweighted according to the observed top-quark-pTspectrum, since the top-quark-pTis only weakly correlated to the BDT output as it is not directly used for the BDT training.
The distributions of the top-quark pseudo rapidity (η) show a good agreement between data and simulation (fig. 5.19, bottom row). A disagreement between simulation and data is observed at−4 < ηtop quark<−3 for events with electrons, but cannot be confirmed in events with muons.
The reconstructed top-quark mass in tt events is shown in figure 5.20 (top row). A good agreement between data and simulation is obtained.
Figure 5.20 (bottom row) shows the mass of the top-quark-reconstruction hypothesis (“pseudo-top quark”) in W-boson-plus-jets events, which do not contain a top quark. The dis-tribution peaks at significantly lower mass values as for tt events. In general, a good agreement between data and simulation is observed. The observed distribution of the pseudo-top-quark mass is slightly higher compared to simulation due to discrepancies in the basic-physics objects (leptons, jets, ETmiss). Mainly the uncertainties of the Q2scale, W-boson-plus-jets normalization, and QCD-multijet normalization cover these differences.
An alternative top-quark reconstruction is the combination of the four-vectors of recon-structed W boson with one of the jets, but independent of jet-flavor-tagging algorithms. Here, the jet is chosen such that the mass of the top-quark candidate is close to 172.0 GeV/c2. The mass distribution of the “best-top-quark hypothesis”, which is also used as an input for the BDT discriminator, is shown in figure 5.21. The best-top-quark-mass distribution has a signifi-cantly larger width for W-boson-plus-jets events than for tt events. A reasonable agreement is observed both in W-boson-plus-jets-enriched and tt-enriched phase space.
Events / 15 GeV
400 KS-test prob.: 0.02
= 7 TeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 15 GeV
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.27
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Events / 0.27
W/Z + jets, Diboson QCD Multijet
MCData - MC -0.4-0.200.20.4
Figure 5.19: Transverse-momentum distributions (top row) and pseudo-rapidity distribu-tions (bottom row) of the b-tagged-top-quark reconstruction hypothesis in the
“≥ 4 jets, 1 btag” category for events with electron (left) or muon final states (right).
156
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space
700 KS-test prob.: 0.64
= 7 TeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
btagged-top-quark mass (GeV)
100 200 300 400 500 600
MCData - MC -0.4-0.200.20.4
Events / 20 GeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
btagged-top-quark mass (GeV)
100 200 300 400 500 600
MCData - MC -0.4-0.200.20.4
Events / 20 GeV Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
btagged-top-quark mass (GeV)
100 200 300 400 500 600
MCData - MC -0.4-0.200.20.4
Figure 5.20: Mass distributions of the b-tagged-top-quark reconstruction hypothesis in the
“≥ 4 jets, 1 btag” category for events with electron (top left) or muon (top right) final states. Furthermore, the top-quark-reconstruction hypothesis is evaluated for events in the muon “2 jets, 0 btags” category, which do not contain a top-quark (bottom).
Events / 15 GeV Muon, 2 jets, 0 btags
Data t-channel
; s-channel, tW t
t
W/Z + jets, Diboson QCD Multijet W + jets rate unc.
best-top-quark mass (GeV)
100 200 300 400 500 600
MCData - MC -0.4-0.200.20.4
Events / 20 GeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
best-top-quark mass (GeV)
100 200 300 400 500 600
MCData - MC -0.4-0.200.20.4
Events / 20 GeV
W/Z + jets, Diboson QCD Multijet
rate unc.
t t
best-top-quark mass (GeV)
100 200 300 400 500 600
MCData - MC -0.4-0.200.20.4
Figure 5.21: Reconstructed best-top-quark mass, i.e. the mass reconstructed with the jet that yields a mass closest to 172.0 GeV/c2, for events in the muon “2 jets, 0 btags” cate-gory (top), and for events with electron (bottom left) or muon (bottom right) final states in the “≥ 4 jets, 1 btag” category.
158
5.3 Top-Quark-Pair- and W-Boson-plus-Jets-Enriched Phase Space