8 Systematic Uncertainties
8.2 Uncertainties in Detector Modelling
is adopted bin-by-bin as done for the nominal fit validation studies. The resulting pseudo-data distributions are fitted to the corresponding decay width templates. Sets containing 2,000 of such pseudo-experiments are used for each systematic variation.
For systematic uncertainties having dedicated up and down variations, the differences between the means of the histograms of fitted Γt values using the nominal distributions and the up and down variations are quoted as the - usually asymmetric - systematic uncertainty from the respective source. Systematic uncertainties with a solely one-sided variation are determined in the same way based on the differences between the nominal distributions and the available variation. The uncertainty value is then symmetrised, i.e. taken as both the positive and negative uncertainty from this systematic source.
8.2 Uncertainties in Detector Modelling
Detector modelling uncertainties consist of the object reconstruction of the charged leptons, jets and missing transverse momentum. Also, uncertainties in the tagging of bjets,cjets and light jets are included.
8.2.1 Charged Lepton Uncertainties
Systematic uncertainties arising from charged leptons have the following origins: They are due to the trigger and reconstruction efficiencies, the lepton identification or originate from the lepton momentum and energy scales as well as their resolutions.
Since reconstruction, trigger and identification efficiencies differ between data and MC, scale factors are applied to correct for such discrepancies, as described in Sec. 4.2 for muons and Sec. 4.3 for electrons. These scale factors are varied within their uncertainties to derive the required variation samples for the estimation of the related uncertainties in the efficiencies according to the procedure in Sec. 8.1.
In a similar fashion, the uncertainties for corrections of the lepton momentum or energy scales and of the lepton momentum resolutions are employed to determine variation samples used for the evaluation of resulting systematic uncertainties caused by the lepton resolution and scales.
The given five categories lead to five components of uncertainties for electrons but six for muons because resolution uncertainties from the muon spectrometer and the ID tracking system are de-termined independently of each other.
8.2.2 Missing Transverse Momentum Uncertainty
The missing transverse momentumETmiss, as introduced in Sec. 4.6, is reconstructed from the vector sum of terms which are associated with other reconstructed objects. As a result, uncertainties coming from energy scales and resolutions for charged leptons and jets are propagated into the ETmiss uncertainty estimate. The systematic uncertainty of the ETmiss soft term is calculated using Z→µ+µ−events exploiting the transverse momentum balance of this soft term and the different
physics objects after calibration. Furthermore, the impact of the MC generator and the underlying event modelling in addition to pile-up effects which cause further energy deposits [239] is also considered.
The above sources of uncertainty are combined into two ETmissuncertainty components, namely a resolution and a scale component, possessing up and down variations each.
8.2.3 Jet Reconstruction Efficiency
Systematic uncertainties related to jets are due to the reconstruction efficiency, the jet vertex requirement, the jet energy scale and the jet energy resolution. The latter three are described in more detail in the following subsections.
The jet reconstruction efficiency is not simulated correctly by MC generators but instead overes-timated. This is taken into account by a dedicated systematic uncertainty. In order to match the efficiency reached in data, jets are randomly chosen and dropped from the selection. In total, 0.2% of jets having pT < 30 GeV are removed and the steps to obtain observable distributions are repeated based on the reduced amount of jets. The difference between this variation and the nominal setup is used to compute the systematic effect due to the jet reconstruction efficiency.
8.2.4 Jet Vertex Fraction
The requirement on the JVF variable implies that all jets used in the analysis must satisfy|JVF|>0.5.
The efficiency per jet to pass this jet vertex fraction cut is estimated usingZ→`+`−+1 jet events in both simulation and data [233], which is sufficient to properly account for pile-up jets. The underlying procedure is a comparison between events enriched with jets from the hard-scattering process and events enriched with pile-up jets. The JVF uncertainty is thus determined by increasing or decreasing the cut value by 0.1 to values of 0.6 and 0.4, respectively. Observable distributions are derived for these two alternative values acting as up and down variations to specify this systematic effect.
8.2.5 Jet Energy Scale
The jet energy scale constitutes the largest detector modelling uncertainty in the measurement of Γt. The JES and its uncertainty are calculated using the results from LHC collision data, test-beam data and MC simulations[229]. The JES calibration, as delineated in Sec. 4.4, and its uncertainty estimate rely on dijet, multijet or vector boson+jets events, depending on the detector region and thepTrange of the jets. These measurements are then combined[230, 231]. The jet energy scale uncertainty itself is split into 26 individual components which are treated independently in the analysis. These components depend on underlying jet transverse momentum and pseudorapidity.
The components comprise the in-situ calibration of jets (15 components), pile-up effects (five components), the η intercalibration (two components), the jet flavour composition and the jet flavour response, the bjet energy scale and, finally, one component for high-pTjets.
8 . 2 U N C E RTA I N T I E S I N D E T E C T O R M O D E L L I N G
An eigenvector decomposition is conducted to obtain these components of the JES uncertainty by retaining their correlations. Correlations between transverse momentum and pseudorapidity are accounted for by a correlation matrix defined as a function ofpTand|η|. An eigenvector reduction leads to 26 uncorrelated so-called nuisance parameters which are able to cover and describe all of these correlations and effects relevant for the JES uncertainty.
In order to estimate the underlying systematic uncertainty values, the energy of the jets in MC simulation is smeared by the uncertainty associated with each nuisance parameter variation. This method of propagating uncertainties is repeated for all nuisance parameters and leads to the 26 variations of the observable distribution with respect to the nominal configuration.
The so-called flavour composition is one of the dominant sources of the JES uncertainty. This component induces a variation of the jet energy scale with respect to the fraction of jets initiated by gluons as a function of the transverse momentum and the pseudorapidity of jets. In the default configuration of the object reconstruction software, the fraction of gluon-initiated jets is set to 50% and a conservative value of the uncertainty is applied: 0.5±0.5, equivalent to a fraction of 50%±50%. The flavour composition components propagate this uncertainty in the fraction of gluon-initiated jets to theΓt measurement.
To reduce the corresponding JES uncertainty, the fraction of gluon-initiated jets and its associated uncertainty value were evaluated separately in this analysis. The implemented procedure relies on events passing the selection criteria given in Sec. 6.2 which are matched to parton level truth events. Reconstructed jets of the selected events are matched to parton level truth jets within a cone of∆R=0.3. Based on the information in the truth record of the simulated events, reconstructed jets are classified according to the flavour of the parton that initiated the jet. The fraction of gluon-initiated jets was determined from this classification as a function ofpTand|η|of the jets. Applying this procedure to the nominalt¯tMC sample yielded the nominal fraction of gluon jets. In the pT and|η|regions with most jets the fraction is around 30%-40% with an uncertainty around 5%-10%.
In order to obtain the corresponding uncertainty value, this method was repeated for alternative t¯tMC samples, namely a sample with a different amount of ISR/FSR jets, a sample using a different parton shower generator (PO W H E G+HE RW I G) and a sample with an alternative matrix element generator (MC@NLO). These alternative samples are also used to derive systematic uncertainties in the signal model, as described in more detail in Sec. 8.4. Due to their large impact on top quark measurements this approach can be regarded as a justified estimate of uncertainties. The values for the fraction of gluon jets obtained from these alternative samples were compared to the results from the nominal setup. Differences were summed in quadrature and constitute the required uncertainty in the fraction of gluon jets. The two dimensional distributions of this fraction and its uncertainty representing the dependence on pTand|η|of the jets can be found in Fig. 8.1.
To quantify the effect of this modified treatment of the flavour composition component, the resulting JES uncertainty in the flavour composition component is presented in Table 8.2 for the default calculation (0.5±0.5) and for the new setup resting on the actual fraction of gluon jets in the selected event sample. The corresponding JES uncertainty is considerably reduced by the new
(a) (b)
Figure 8.1:Fraction of gluon-initiated jets: (a) nominal central value and (b) associated uncer-tainty as a function of the jet pseudorapidity and the jet transverse momentum used to evaluate the JES flavour composition uncertainty.
approach with respect to the default setup. Despite this reduction, the JES uncertainty is still the largest systematic uncertainty related to detector modelling underlining the relevance of such additional studies to minimise the impact of systematic effects.
Flavour composition Uncertainty inΓt
Default treatment +0.34 GeV −0.22 GeV New implementation +0.04 GeV −0.02 GeV
Table 8.2:Impact of the modified treatment of the JES flavour composition component on the top quark decay width compared to the default configuration.
8.2.6 Jet Energy Resolution
Another important systematic uncertainty for the measurement ofΓt is the jet energy resolution.
It is estimated separately in simulated events and data employing two in-situ techniques [229]. These are complemented by additional in-situ measurements based on dijet, photon+jet andZ+jets decay processes. The JER uncertainty is mainly driven by pile-up effects for jets having low trans-verse momentum. This relevant contribution is measured pursuant to the nethod of Ref. [230]. Mathematically, the JER can be expressed by three terms:
σ(pT) pT = N
pT ⊕ S ppT⊕C.
The first parameter N describes the effect of electronic noise and pile-up contributions, and S parametrises stochastic effects which are due to the sampling nature of the calorimeter system.
The last parameterC is a constant term. Based on in-situ measurements involving additional noise
8 . 2 U N C E RTA I N T I E S I N D E T E C T O R M O D E L L I N G
studies, values for N, S and C including parameter uncertainties are extracted. The expected pT resolution for a particular jet is obtained as a function of its transverse momentum and its pseudorapidity.
An eigenvector decomposition is conducted to reduce the related sources of the JER uncertainty as applied for the JES uncertainty. The above described method of propagating uncertainties is conducted for all nuisance parameters and leads to eleven variations of the observable distribution with respect to the nominal configuration.
These up and down variations affecting shape and normalisation of the observables are summed in quadrature and the resulting systematic uncertainty value is symmetrised at the end.
8.2.7 Heavy and Light Flavour Tagging
Systematic uncertainties also arise from the tagging of band mistagging ofc jets, summarised as heavy flavour tagging, and from the mistagging of the light jets,u,d ands. Principles ofb-tagging and the related efficiencies including scale factors are discussed in Sec. 4.5.
As mentioned in that chapter, data is used to calibrate efficiencies of the utilisedb-tagging algorithms which depend on the jet flavour. The probability density function calibration method[236, 237] corrects the b-tagging efficiency to match the value observed in data. This technique rests on a combinatorial likelihood applied to dileptonic t¯t data events. On the contrary, the mistag rate for cjets is obtained usingD∗mesons while the one for light jets relies on measured jets characterised by secondary vertices and impact parameters that conform to a negative lifetime[234, 237]. Scale factors which depend on the transverse momentum correct the efficiencies measured in simulated samples for both bandcjets. The scale factors derived for light jets depend on the jet pseudorapidity in addition. The b-tagging efficiency is affected by six independent sources of scale factor uncertainties, four need to be considered for the tagging ofcjets[236]. Twelve uncertainty components which depend on different regions of pTandηdescribe the uncertainty related to the mistagging of light jets[237].
All these components can be associated with an eigenvector belonging to the matrix which contains uncertainty information about the transverse momentum per bin and about correlations between bins. This complies again with the procedure described above for the JES and JER uncertainty. The systematic uncertainties are regarded as uncorrelated between the different types of jets, i.e. b,c and light jets.