5.4 E T dependent efficiencies
5.4.2 Efficiency vs E T measured by fitting the E T distribution
As an alternative to using the invariant mass distribution as the discriminating vari-able to subtract the background from the probe sample, one can fit theETdistribution directly in order to obtain the background as a function of ET. The results can then be used as a cross check for the ET binned efficiencies derived through fitting the invariant mass of the Z boson. The background estimation using the ET spectrum is performed with the template method using TFractionFitter. Tag and probe pairs with opposite sign electrons outside the crack region and with an invariant mass of
[GeV]
ET
20 30 40 50 60 70 80
Background fraction
0 0.1 0.2 0.3
0.4 container
loose
Figure 5.15: The background fraction as a function ofET, at container and loose level, estimated by fitting the invariant mass of the tag and the probe for each ET bin.
80-100 GeV are used for the efficiency extraction.
The background template is extracted from probes in the data. In order to min-imize signal contamination in the background distribution, the tag requirement is relaxed to loose identification and only events where the probe has same sign as the tag are used. No invariant mass requirement is applied here. The trigger require-ment for the background template must be altered from the standard EF e15 medium to EF e20 loose due to the relaxation of the tag requirement from tight to loose.
EF e20 loose has a small inefficiency for lower ET values (20-25 GeV), which intro-duces a bias on the ET shape for the background template. Another caveat is that the background shape at container level is also applied for the loose fit, since ac-quiring a background template at loose level is prevented by the significant signal contamination. The distribution used as background template is shown in Figure 5.17.
The different shapes used as signal templates are taken from signal MC at con-tainer, loose, medium and tight level after having applied loose truth matching to the probe in order to avoid any combinatorial background. The signal templates at the different levels are presented in Figure 5.18.
Due to the low statistics together with the minimal background fraction, the fit does not converge at the medium and tight level. Instead, rejection factors are ap-plied to the estimated loose background. Background rejection factors are calculated by estimating the fraction of background events passing the electron identification criteria. The jet rejection factors applied to the estimated loose background are Rloosemedium= 0.1286±0.0004(stat) and Rtightloose = 0.0313±0.0001(stat).
[GeV]
ET
20 30 40 50 60 70 80
isEM efficiency
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
MC truth loose medium tight
Figure 5.16: The efficiency as a function of ET for loose, medium and tight identi-fication, in MC truth (black) and estimated in data (color) by fitting the invariant mass for each ET bin in order to subtract the background at each level.
The resulting fits at container and loose level are shown in Figure 5.19. A total of 9.2±0.6% background at container level and 0.6±0.6% at loose level are measured.
The χ2/DoF of the fits are low; 1.2 for the container fit and 1.1 for the loose fit.
Comparing with the method of fitting the invariant mass as background estimation method (see section 5.4.1 above), these results show a 0.8% smaller background at container and loose level.
The background fraction is then computed separately for each ET range in the efficiency binning presented in Table 5.2. The background fraction in the desired binning for container and loose level can be found in Figure 5.20. Comparing with the background estimation with the previously described method of fitting the invari-ant mass (Figure 5.15) shows that even though the ET fit finds smaller amounts of background at loose and container level, there is a fair agreement of the behavior of the background as a function of ET.
The background fraction at tight and medium level are estimated by applying the jet rejection factors on the result from the fit on the loose probes and results in 0.1±0.1% and 0.0±0.0% for the total medium and tight background respectively. For an overview of the amount of estimated background in each ET bin at the different levels consult Table B.7 in Appendix B.
The efficiencies are then calculated through subtracting the estimated background at each level and for each ET bin. The overall efficiencies obtained are 97.1±0.8%
for loose, 91.6± 0.6% for medium and 78.4± 0.5% for tight identification. The
[GeV]
ET
20 30 40 50 60 70 80
Entries
0 200 400 600 800 1000
Background probes
Figure 5.17: Background template extracted from data; container probes in events with a loose tag. A same sign requirement on the tag and probe is applied.
results are compatible with the efficiencies estimated using the method of fitting the invariant mass (see Table 5.13). The efficiencies as a function of ET in data together with MC true efficiencies are shown in Figure 5.21. The behavior of the efficiency for low ET follows the one observed with the main fitting method even though the two methods are largely uncorrelated. What is common between the methods is that the lower ET bins suffer from a large uncertainty due to low signal statistics and increasing fraction of background, especially at container level. The inconsistency with MC is however larger for this method. One possible explanation is that the background template is acquired with the EF e20 loose trigger which has a few percent inefficiency for the 20-25 GeV range. Except for the two bins at lower ET, the method provides a reasonable efficiency estimate, which follows the shape in the MC. Table B.8, Appendix B, documents the data efficiencies together with the data/MC scale factors for each ET range.
An evaluation of the systematic uncertainty is performed through altering the method and the fit conditions in different ways. One variation and cross check is to apply the electron energy scaling in data and energy smearing in MC. This has little effect on the data/MC SFs (see Table 5.14). Larger effects are seen if the histograms are re-binned before performing the fit. Another method is to widen the invariant mass spectrum from 80-100 GeV to 75-105 GeV, which also has a notable impact, especially on the loose scale factor.
To summarize, the efficiency scale factors as a function of electronET, from fitting theET spectrum directly, are in reasonable agreement with, and provide a cross check for, the main method of fitting the invariant mass spectrum of the Z. This method is, however, less stable than the Mee fitting method. A few of the concerns are:
[GeV]
Figure 5.18: Signal templates obtained from MC; theET distribution of loosely truth matched probes at the different identification levels.
(a) ET [GeV]
Figure 5.19: Resulting ET fits at (a) container and (b) loose level. The QCD and signal templates are stacked and normalized to the data that is fitted.
• The method shows unstable results in the lowerETregion (20-30 GeV), possibly due to the trigger used for the background template (EF e20 loose), which may bias the shape at lower ET.
• Monte Carlo is used as the signal template and may not perfectly model the data distribution.
• The method suffers from instability due to low statistics, e.g. no background is found at medium and tight level and must be extrapolated from the loose fit.
This can induce a bias since the background shape as a function of ET might not be compatible at loose and medium/tight level.
[GeV]
ET
20 30 40 50 60 70 80
Background fraction
0 0.1 0.2 0.3
0.4 container
loose
Figure 5.20: Fractional QCD background in the desired efficiency binning as a result of the ET fit at container and loose level.
Efficiency Nominal Energy re-binning the 75< Mee <105 SFs [%] selection scaling/smearing histogram GeV
Loose SF 98.6±0.8 −0.1 +1.1 +1.1
Medium SF 97.9±0.7 −0.1 +1.2 +0.4
Tight SF 102.1±0.7 −0.3 +1.2 +0.1
Table 5.14: Estimated overall loose, medium and tight efficiency through fitting the ET spectrum to assess the amount of background to subtract. The method is varied by applying energy scaling and smearing, re-binning the template histograms before the fit as well as altering the invariant mass region of the tag and the probe pair.
This method provides a cross check for the Mee fit method, which is used to derive the official e/γ ET dependent efficiency scale factors [81].
5.4.3 Official e/γ ID efficiency scale factors
The ET dependent identification efficiency scale factors, provided by the e/γ group, uses the method of fitting the invariant mass for the Z tag-and-probe [57, 81]. The computed scale factors are estimated with different variations of the standard RooFit method described above, also including a template method for fitting the invariant mass distribution. As for the η dependent scale factors, the e/γ efficiencies are mea-sured with respect to track quality rather than container in order to combine the
[GeV]
ET
20 30 40 50 60 70 80
isEM efficiency
0.65 0.7 0.75 0.8 0.85 0.9 0.95 1
MC truth loose medium tight
Figure 5.21: Loose, medium and tight identification efficiencies from MC truth (black) and data (color), fitting the ET spectrum as QCD background estimation method.
results with W tag-and-probe. Variations are made on the signal region, fit range and tag requirements to obtain a distribution of scale factors where the mean yields the central value and the spread the systematic uncertainty. The estimated system-atic uncertainty increases towards lower ET, as expected, since these bins have less signal events and a larger background contamination. In addition, a systematic un-certainty from a MC closure test, showing a bias of the estimated number of signal events from the fits, is added linearly.
The resulting Z andW tag-and-probe efficiency scale factors are shown in Figure 5.22 for medium and tight identification. As for theηdependent scale factors,Z tag-and-probe yields higher values than theW tag-and-probe results. Another difference is that W tag-and-probe displays a stronger ET dependence with decreasing scale factors for lower ET. The 15-20 GeV ET range is also included in the W tag-and-probe results due to the more abundant statistics.
The final combined W and Z tag-and-probe results for medium and tight iden-tification scale factors are shown as a function of ET in Figure 5.23. The statistical and total uncertainties are indicated.