The identification efficiency is measured withW →eν and Z →ee tag-and-probe on data in order to derive data/MC scale factors, as was presented in chapter 5. The
final medium and tight efficiency scale factors from the combined W and Z results were shown in Figure 5.11 above.
The data/MC scale factor for medium has been found to be slightly lower than unity with littleη dependence and approximately 1% total uncertainty per bin. It is therefore of fundamental importance to propagate this to theZ selection in simulated data, in order to not estimate an incorrect number ofZ candidates in MC. The tight identification SF is on the other hand greater than unity overall. It also suffers from a large η dependence, and larger uncertainties of about 1-3% total per bin.
Since the final cross section results used MC@NLO as signal MC rather than Pythia, with which the data/MC scale factors have been deduced, the MC true efficiencies were re-computed with MC@NLO. An overall difference below per mille level was concluded and no difference was seen in theηdistribution of the efficiencies.
The official data/MC scale factors can therefore be directly applied to the MC@NLO distributions.
Medium + b-layer hit + isolation efficiency
For the final differential cross section analysis, tight identification is replaced by medium + b-layer hit + isolation requirements. After the efficiency of different isolation variables had been studied (some of which are included in Appendix B), the “caloIso98” [111] was chosen. caloIso98 applies a cut on the distribution of the calorimeter isolation within a η-φ cone of 0.3 normalized to the electron ET
(ETcone(0.3)/ET), which was optimized on release 15 MC to yield a 98% efficiency throughout the electron ET and η phase space. For the remainder of this chapter
“isolation” impliescaloIso98 if not otherwise specified.
The combination of medium + b-layer + isolation was found to increase the effi-ciency by nearly 10% in comparison with the tight selection, with only a small loss in background rejection. The overall efficiency of the b-layer and isolation requirement with respect to a medium electron, measured with Z → ee tag-and-probe is shown in Table 6.7. The background contribution at medium level for Z tag-and-probe is sufficiently low to obtain the efficiencies without applying background subtraction.
The W →eν differential cross section measurement as a function ofηe, is carried out in a finer binning than the medium efficiency scale factor measurement described above and separately for positive and negative electrons. Since the W tag-and-probe method can directly measure the efficiencies from the positively and negatively re-constructed electrons originating from theW (directly accounting for the fraction of charge mis-identified electrons) this method alone is used to derive the charge de-pendent medium and b-layer efficiencies. W tag-and-probe also has higher statistics than the Z tag-and-probe method, which facilitates obtaining the efficiency in the
Efficiency [%] Data/MC scale factor
b-layer hit Data 96.94 ±0.14
1.0066 ± 0.0015 wrt medium ID MC truth 96.29 ±0.01
Isolation requirement Data 96.83 ±0.14
0.9902 ± 0.0015 wrt medium + b-layer MC truth 97.80 ±0.01
Table 6.7: Overall b-layer hit and caloIso98 isolation identification efficiency with respect to electrons passing medium and medium + b-layer respectively, obtained withZ →eetag-and-probe. Data-driven and MC true efficiencies together with their data/MC scale factors are included. No background subtraction has been applied and the errors are statistical only.
finer binning. The medium + b-layer efficiencies are presented in Figure 6.4 for pos-itive and negative electrons as a function of η. The results for data and MC as well as their corresponding ratio (scale factor) are shown.
Table B.13 in Appendix B explicitly documents the medium identification + b-layer hit efficiency and data/MC scale factor, extracted in data withW tag-and-probe for each η bin. The table includes statistical and systematic errors separately for the scale factors, which are propagated to the final differential cross section results. An advantage with this new selection is thus the decreased uncertainties and fluctuations in η for the data/MC scale factors, as well as the smaller charge dependence, in comparison with the tight selection.
Since theW tag-and-probe method uses calorimeter isolation as the discriminating variable for the background subtraction, the efficiency of the the W → eν isolation cut itself cannot be obtained with this method. Instead, Z tag-and-probe is used to derive the isolation efficiency with respect to electrons passing medium + b-layer cuts.
Due to the small background (per mille level) remaining after medium identification has been applied, no background subtraction is applied. This reduces the statistical and systematic uncertainty significantly, which is a great advantage for obtaining the scale factors in the fine differential η binning. Figure 6.5 shows the resulting data and MC isolation efficiencies as well as their scale factor, measured withZ →ee tag-and-probe. The isolation scale factor only displays small fluctuations as a function of η.
The scale factor of the isolation cut is deduced without separating the negative and positive probes and the opposite sign cut in the Z tag-and-probe methodology removes the charge mis-identified electrons, that are otherwise included in the W → eν analysis. The fraction of charge mis-identified events at medium identification level is however very small (see section 6.3.3). To assure that there is no large charge dependence of the isolation efficiency, the ratio of positive and negative efficiency is investigated after the opposite charge requirement between the tag and the probe
(a)
-2 -1 0 1 2
Medium ID + b-layer efficiency
0.75
Medium ID + b-layer efficiency
0.75
Figure 6.4: Medium + b-layer efficiency of (a) positive and (b) negative electrons as a function of ηfor data and MC. The data efficiencies are measured with W →eν tag-and-probe and the MC values reflect true efficiencies. The binning in η is equivalent to that of the W → eν differential cross section measurement. Errors are statistical only.
has been removed. The results are shown in Figure 6.6 displaying no visible charge dependence as a function of η.
The nominal method of assessing the systematic uncertainty of the efficiency scale factor by varying the background subtraction method, described in [81], is not ap-propriate for the isolation efficiency measurement since no background subtraction is applied. Instead, the systematic uncertainty is evaluated by investigating the stability of the result after varying the amount of background, applying the standardηbinned background subtraction as well as relaxing the opposite sign requirement. In addi-tion, the scale factors are re-evaluated after scaling and smearing the electron energy as described below. The methodology is also modified by choosing one tag and probe pair in the event by selecting the pair with the invariant mass closest to the Z mass, rather than selecting all possible tags and probes. The impact of these variations on the method is small and adding the effect on the scale factor in quadrature yields a systematic uncertainty which is below the statistical error. Figure 6.7 presents the relative uncertainty of the isolation efficiency scale factor, from the different variation of the Z tag-and-probe method as well as the total systematic and statistical errors.
The fluctuations seen in the systematic uncertainty as a function of η are primarily due to the relatively large statistical error.
Table B.12 in Appendix B explicitly states the isolation efficiency with statistical uncertainty estimated with Z tag-and-probe in data, as well as the data/MC scale
-2 -1 0 1 2
Efficiency
0.75 0.8 0.85 0.9 0.95 1
Data MC truth
η
-2 -1 0 1 2
Data/MC SF
0.9 0.95 1 1.05 1.1
Figure 6.5: Calorimeter isolation efficiency with respect to medium identification + b-layer hit requirement as a function ofη for data and MC. The data efficiencies are measured withZ →eetag-and-probe and the MC values reflect true efficiencies. The binning in η is equivalent to that of the W differential cross section measurement.
Errors are statistical only.
η
-2 -1 0 1 2
positive/negative eff
0.85 0.9 0.95 1 1.05 1.1 1.15
data MC truth
Figure 6.6: Isolation efficiency ratio of positive and negative electrons after relaxing the opposite sign requirement in the Z → ee tag-and-probe methodology. The MC values reflect true efficiencies and errors are statistical only.
η
-2 -1 0 1 2
Relative uncertainty
-0.01 0 0.01
Total stat Total syst
Bgd sub OS+SS
Energy scale Best mass
Figure 6.7: Statistical (red) and systematic uncertainty of the data/MC scale factor for isolation efficiency with respect to medium ID + b-layer as a function ofη. The to-tal systematic uncertainty is shown (black) together with the individual components;
applying background subtraction, relaxing the OS requirement, applying energy scal-ing/smearing and choosing the tag and probe pairs with the best mass rather than all tags and probes in the event.
factor with resulting statistical and systematic error, for each η bin.
Efficiency scale factors in the cross section evaluation
The data/MC efficiency scale factors are applied to the W →eν and Z → ee cross section analysis to correct the MC. This is performed at the level of identifying the electron(s) originating from theW or the Z.
The statistical and systematic uncertainties of the scale factors are accounted for when computing the total systematic uncertainties of the measurements, i.e. the correction factors CW and CZ. Specifically the systematic uncertainty of the SF is treated as fully correlated between η (and charge) bins, while the statistical com-ponent is uncorrelated and may average out partially when combining the different bins into an inclusive cross section measurement. The propagation of the statisti-cal uncorrelated component is performed by generating 1000 random samples with Gaussian distributions according to the given uncertainty. The uncertainty applied to the CW and CZ factors is then determined as the RMS of these 1000 measurements.
The systematic uncertainties of the inclusive and differential CW and CZ factors are further discussed in sections 6.3.8 and 6.3.9.
Charge misID rate [%] Data MC
Container 2.17±0.25±0.29 2.74
Track quality 1.12±0.20±0.18 1.27
Medium 1.04±0.11±0.14 1.19
Medium + b-layer + caloIso98 0.63±0.08±0.11 0.81
Tight 0.37±0.07±0.11 0.5
Table 6.8: Charge mis-identification probability for different levels of electron iden-tification with statistical and systematic error for data. The corresponding values derived in MC are included for comparison [81, 103].