9. Results 153
9.6. Discussion of Uncertainties
Uncertainties play a crucial role in this measurement. They limit the precision of the result and and can give a clear hint to further improvements. This section concludes the chapter of results by discussing the dominating uncertainties and explaining their effects.
9.6.1. Dominating Uncertainties Uncertainties From Ensemble Testing
A summary of all uncertainties evaluated via ensemble tests is listed in Table8.6. The dominating uncertainties are the renormalization/factorization scale, the top quark pT (all affecting both down-type quark and b-quark analysers), the PDFs, as well as the parton showering and the initial and final state radiation (affecting the b-quark a lot more than the down-type quark).
9.6. Discussion of Uncertainties
Parameter Name
p0 1
2(NSM t¯t+Nunc.t¯t)
p1 1
2(NSM t¯t−Nunc.t¯t)
p2 Nrem. backg.,e+jets+Nrem. backg.,µ+jets
p3 NW+jets,njets=4,e+jets
p4 NW+jets,njets≥5,e+jets
p5 NQCD,njets=4,e+jets
p6 NQCD,njets≥5,e+jets
p7 NW+jets,njets=4,µ+jets
p8 NW+jets,njets≥5,µ+jets
p9 NQCD,njets=4,µ+jets
p10 NQCD,njets≥5,µ+jets
p11 Jet Multiplicity Correction p12 JES/EffectiveNP Stat1 p13 JES/EffectiveNP Model1 p14 JES/EffectiveNP Det1 p15 JES/EffectiveNP Mixed2 p16 JES/Intercal TotalStat
p17 JES/Intercal Theory
p18 JES/RelativeNonClosureMC11b
p19 JES/PileUpOffsetMu
p20 JES/PileUpOffsetNPV
p21 JES/Closeby
p22 JES/FlavorComp
p23 JES/FlavorResponse
p24 JES/BJES
p25 btag/break5
p26 btag/break6
p27 btag/break8
p28 ctag/break0
p29 ctag/break1
p30 ctag/break3
p31 ctag/break4
p32 mistag
p33 JVF
p34 el/Trigger
p35 mu/Trigger
p36 el/ID
p37 mu/ID
p38 el//Reco
p39 el/E scale
p40 mu//Reco
p41 WJets/bb4
p42 WJets/bb5
p43 WJets/bbcc
p44 WJets/c4
p45 WJets/c5
Table 9.5.: List of all fit parameters.
All these uncertainties affect the kinematic configuration of the t¯t pair and the spin analysers. Hence, the impact of the measured spin correlation is expected to be large.
This is confirmed in both the measurements of CMS [188,189] and ATLAS [180]. The PDF uncertainty can be highlighted as it affects not only the kinematics but also the initial state composition and the production mechanism. The relation of gluon fusion to quark/antiquark annihilation directly changes the spin configuration. In Figure 9.9 the effect of varied PDFs is illustrated. Two default PDF sets (CT10 and HERAPDF) are compared as well as their spread due to evaluation of the error sets. Both sets are plotted at the scale of the top quark mass (Q2 =m2t).
Q2 = mt2
(a) (b)
Figure 9.9.:(a)PDF distribution as a function of the momentum fraction xfor gluons.
For both the CT10 and the HERPDF set the variations within the error sets are indicated by the two lines. (b) Relative deviations to the central value of the CT10, caused by the variations of the CT10 and the HERAPDF error sets.
Two of the uncertainties should be emphasized as they have large effects which do not cancel in the combination. The first one is the initial / final state radiation. As seen in Table8.6, the b-quark is affected to much larger extent. In Figure9.10the effect on the ISR/FSR variation on the ∆φ distributions is shown.
The down-type quark is not affected while theb-quark shows a slope in the ISR/FSR up/down ratio. This slope is interpreted by the fit as a deviation in the spin correlation and leads to a large uncertainty. It is expected that the b-quark is affected by the FSR to a much larger extent. The reason is the larger phase space available for FSR radiation due to theb-quark’s largerpT (see Figure7.4).
Next to ISR/FSR, the modelling of the parton shower has a large impact on the measured fSM using the b-quark. The compared showering generators, HERWIG and PYTHIA, base on different showering models (cluster fragmentation vs. string model).
Not only kinematics are affected, but also the flavour composition of theb-jets. Figure 9.11 shows the number of b-tagged jets for POWHEG+HERWIG and POWHEG+PYTHIA. A
9.6. Discussion of Uncertainties
Figure 9.10.:(a) ∆φ(l, d) distribution in the µ+ jets channel for the samples with in-creased and dein-creased initial and final state radiation. (b) ∆φ(l, b) distri-bution in theµ+ jets channel for the samples with increased and decreased initial and final state radiation.
(l, b)
Figure 9.11.: Number of b-tagged jets for POWHEG+PYTHIA and POWHEG+HERWIG in the µ+jets channel. Events containingτ leptons were vetoed and both samples were reweighted to the same top quark pT spectrum.
clear difference is visible. For this plot, the distributions of the different generators are reweighted to the same top quark pT spectrum. Also, τ leptons are vetoed as their polarization was not properly handled by the generators.
Uncertainties From Nuisance Parameters
There are different ways of classifying the most significant nuisance parameters. The five most significant NPs are presented. In the first type of ranking, shown in Table 9.6, the NPs with the largest effect on the measured value offSM are listed for the full combination fit. The ranking is created by performing the fit with all NPs included. After that, each NP under test is taken out of the fit. The differentfSM values are compared.
The sign of the value represents the relative change when taking the nuisance parameter out of the fit.
NP relative change of fSM
JES/BJES +2.4 %
JES/EffectiveNP Stat1 +1.7 % JES/EffectiveNP Model1 +1.6 %
btag/break8 +1.2 %
JES/EffectiveNP Det1 −1.0 %
Table 9.6.: Most significant nuisance parameters (in terms of change offSM) for the full combination fit.
Another ranking can be created by evaluating the effect on the total uncertainty, not the central value. Table9.7shows the NPs with the largest effect on the total uncertainty (which might become either larger or smaller) for the full combination fit. The most
NP relative change of ∆fSM
JES/FlavorComp −7.6 %
btag/break8 −4.6 %
JES/FlavorResponse −3.4 % JES/EffectiveNP Det1 +1.5 % JES/EffectiveNP Model1 −1.4 %
Table 9.7.: Most significant nuisance parameters (in terms of change of the fit uncer-tainty) for the full combination fit.
significant uncertainties for the individual combinations of the down-type quark and b-quark analysers can be found in the AppendixI.
As the measurement depends a lot on the modelling of jets, the large contribution of the JES components is expected. The large impact of the b-tagging uncertainty is a
9.6. Discussion of Uncertainties consequence of the utilization of the b-jets as analysers as well as of the dependence of the down-type quark reconstruction on theb-tag weight.
9.6.2. Expected Deviations
The title of this section might be misleading. In case a deviation is really expected, it can be calibrated. To allow for reweightings and calibrations, the preceding measurements must have sufficiently high precision. Until changes in the top quark modelling are established, indications can be noticed. Such indications are listed in the following, concluding this chapter. The question is: Where did independent measurements indicate a preference of the data to a different modelling than the one implemented in this analysis? And if such deviations are observed: What would be the effect on the current measurement? Would it cause further tension between the down-type quark and the b-quark analysers? Or would it bring the results closer together?
Top Quark pT
As shown in Figure8.4(a), the top quarkpTseems to be modelled imperfectly inMC@NLO.
The data prefers a softerpT spectrum, shifted to lower values. As shown in Figure8.11, this would lead to a flatter ∆φdistribution. The fit templates based on a harder toppT spectrum will interpret this as a higher spin correlation for the down-type quark and a lower spin correlation for theb-quark, respectively (see Figure7.1). This is exactly what was observed in data by measuring fSM: For the down-type quark, the measured fSM is higher than the SM prediction and for the b-quark it is lower.
During the discussion of the PDF uncertainties their large impact and opposite effect on down-type quark and b-quark analysers was stressed (Section 8.1.6). The question is: Does the data have a preferred PDF? In the ATLAS measurement of the differential top quark cross section [301] the impact of the PDF on the top quark pT is checked. As shown in Figure 8.4(b), HERAPDF is preferred by the data. In particular, this is the case for large values of top quarkpT. Furthermore, the worst modelling seems to be given by the CT10 PDF. This motivated to check how HERAPDF would affect the measured values of fSM. To answer this question, the LHAPDF reweighting was repeated using HERAPDF. The results are shown in Figure 9.12. The shown fit values correspond to pseudo data created with distributions that are reweighted to a modified PDF.
In case the data was modelled with HERAPDF, a larger value offSM was fitted for the down-type quark and a smaller value for the b-quark. This means that if the data prefers HERAPDF – and the indications for that were shown in Figure8.4(b) –fSM is expected to be fitted with fSM >1.0 for the down-type quark and with fSM <1.0 for theb-quark. Indeed, this is what is measured.
PDF set
Figure 9.12.: Fit results forfSMusing pseudo data reweighted to different PDF sets and error sets. (a) Combined fit using the down-type quark. (b)Combined fit using theb-quark.
Generator Variation
Concerning the uncertainties assigned to thet¯tgenerator, effects coming from the parton showering, the renormalization/factorization scale, the underlying event, the ISR/FSR variation and the colour reconnection are evaluated. There has been no direct comparison ofMC@NLOto other t¯tgenerators. The reasons are the following:
• The spin correlation is different for LO and NLO generators. Thus, only NLO generators should be used for comparison.
• Samples usingPOWHEG+HERWIGsuffer from a bug in the τ lepton polarization.
• All availablePOWHEGsamples suffer from an additional bug concerning spin corre-lation in the antiquark-gluon and gluon-antiquark production channel.
• Samples with uncorrelatedt¯tspins are not available for any generator other than MC@NLO.
However, it should be mentioned that fitting pseudo data created usingPOWHEG+HERWIG leads to values offSMdeviating from the expectation offSM= 1.0. The results are shown in Table9.8.
One of the main differences between POWHEG+HERWIG and MC@NLO is the top quark pT spectrum. Hence, POWHEG+HERWIG is reweighted to match the top pT spectrum of MC@NLO.
Reweighting the toppT spectrum reduces the deviations to the expected fit values of fSM = 1.0, but does not fully remove them. One aspect is the non-perfect reweighting.
Reweighting techniques are not expected to replace event generations with a modified modelling. Furthermore, thePOWHEG+HERWIGsample is known to suffer from bugs affect-ing the τ polarization and a small part of the spin correlation. To eliminate the effects
9.6. Discussion of Uncertainties
Sample fSM
down-type quark b-quark Combination
MC@NLO 1.00 0.99 1.00
POWHEG+HERWIG(nominal) 1.26 0.64 1.02
POWHEG+HERWIG(top pT reweighted) 1.15 0.73 0.99
Table 9.8.: Results from ensemble tests for pseudo data created with MC@NLO, POWHEG+HERWIG (nominal) and POWHEG+HERWIG reweighted to the top pT spectrum ofMC@NLO.
of these bugs and the effects coming from the reconstruction, an additional comparison on parton level is done.
Figure9.13shows the differences in the shape of the ∆φdistributions for both gener-ators. Additional comparisons of the ∆φdistributions on parton level before and after reweighting in top quark pT are shown in AppendixJ.
0.042 PowHeg+Herwig (top pT rew.) full phase space, parton level
(l, dQ) PowHeg+Herwig (top pT rew.) full phase space, parton level
(l, bQ)
Figure 9.13.: Comparison of the ∆φ distribution between MC@NLO (black) and POWHEG (red) using (a) the down-type quark and(b)theb-quark as analyser. The dashed distribution shows the POWHEG spectrum reweighted to match the top pT distribution of MC@NLO.
The ∆φdistribution is flatter forPOWHEG+HERWIG. As shown in Figure7.1, this results in different interpretations of a fittedfSM: higher values offSMfor the down-type quark and lower ones for the b-quark analyser. Reweighting POWHEG+HERWIG to the top pT
spectrum ofMC@NLOleads to good agreement for the down-type quark distribution, but not for the b-quark distribution. However, an improvement is observed. The reason for the remaining difference lies in theb-quark energy spectrum. This difference is still present after reweighting, even though theW kinematics of the two generators do agree.
To conclude,POWHEG+HERWIGandMC@NLOlead to different toppTand b-quark energy spectra, both affecting the fitted value offSM. In the case thatPOWHEG+HERWIGis able to describe the data better thanMC@NLO– and Figure8.5 as well as the jet multiplicity distribution give indications for this assumption – it could replaceMC@NLOfor the fit to data. In this case the measuredfSM is expected to be fitted lower using the down-type quark and higher using the b-quark. This would lead to a better compatibility of the down-type quark andb-quark combinations.