5.4 Systematic uncertainties
5.4.3 Impact of pile-up
5.4 Systematic uncertainties
Number of b-tagged jets
0 1 2 ≥ 3
1 / events
0 0.2 0.4 0.6 0.8 1
WWbq template
Nominal IFSR up, derived IFSR down, derived
Number of b-tagged jets
0 1 2 ≥ 3
1 / events
0 0.2 0.4 0.6 0.8 1
WWqq template
Nominal IFSR up, derived IFSR down, derived
Figure 5.17: The tt → WWqb (left) andtt → WWqq(right) templates and their derived ISR/FSR “up” and
“down” variations.
experiments are performed. Results obtained using the original ISR/FSRtt → WWbbtemplate (tt → WWqbandtt → WWqqare taken from Protos), results obtained with only thett → WWbbtemplate derived, including the symmetrisation procedure (tt→WWqbandtt→WWqqare taken from Protos) and results where all derived templates tt → WWbb, tt → WWqb and tt → WWqq are used, are compared and the resulting ISR/FSR uncertainty are shown in table5.6.
Setting ∆Rb ∆σdilepton
Varied sample (tt→WWbbonly) 0.016 0.15 pb
Derivedtt→WWbbtemplate 0.018 0.16 pb
Derivedtt→WWbb,tt →WWqb,tt→WWqq 0.018 0.16 pb
Table 5.6: Uncertainty onRbandσdileptonin different scenarios concerning the variation of thett→WWbb,tt→ WWqbandtt→WWqqtemplates obtained from pseudo-experiments withRb=0.99830 andσdilepton=11.33 pb.
No significant discrepancy is observed when comparing the results forRbandσdilepton for the three different approaches.
Measurement ofRbandσtt¯
µ>
<
0 2 4 6 8 10 12 14 16 18 20
Fraction of events
0 0.02 0.04 0.06 0.08 0.1 0.12
ATLASInternal
= 7 TeV,
s
∫
Ldt= 4.66 fb-1µ +µ ee+eµ
data (MC@NLO) t t
Number of primary vertices
0 2 4 6 8 10 12 14 16 18 20
Fraction of events
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
ATLASInternal
= 7 TeV,
s
∫
Ldt= 4.66 fb-1µ +µ ee+eµ
data (MC@NLO) t t
Figure 5.18: Distributions of the average number of interactionshµiand the number of primary vertices in data and simulation after re-weighting the simulation byhµiand applying all selection criteria from section3.
weighting the simulation sample byhµialso aligns its distribution of number of primary vertices with data.
To verify the impact of pile-up on the measurement ofRb andσdilepton, the data is split into 26 sub-samples byhµivalue (every sub-sample covered a 0.5 range from 3.5 to 169) and a fit is performed separately for each sub-sample. For each of these measurements a distribution of the number of b-tagged jets in data, as well as the selection efficiencies fortt →WWbb tt →WWqbandtt → WWqq processes from simulation, are obtained. The templates for signal and background are not changed, i.e.
they are obtained from the events from the entirehµispectrum in simulation. The results are presented in figure5.19. There is a small effect observed on the measured value ofRband a linear dependence of σdileptononhµi.
µ>
<
4 6 8 10 12 14 16
bR
0.6 0.8 1 1.2 1.4
1.6 χ2 / ndf 15.86 / 23
Prob 0.8613
p0 1.055 ± 0.020 p1 -0.003849 ± 0.002132
/ ndf
χ2 15.86 / 23
Prob 0.8613
p0 1.055 ± 0.020 p1 -0.003849 ± 0.002132
ATLASInternal
= 7 TeV,
s
∫
Ldt= 4.66 fb-1µ +µ ee+eµ
>
<µ
4 6 8 10 12 14 16
dileptonσ
8 10 12 14 16 18 20 22 24 26
/ ndf
χ2 35.32 / 23
Prob 0.04832
p0 9.712 ± 0.554 p1 0.1668 ± 0.0612
/ ndf
χ2 35.32 / 23
Prob 0.04832
p0 9.712 ± 0.554 p1 0.1668 ± 0.0612
ATLASInternal
= 7 TeV,
s
∫
Ldt= 4.66 fb-1µ +µ ee+eµ
Figure 5.19: Measured values ofRbandσdileptonfor average number of interactions 3.5 < hµi < 16. The error bars represent the sum of statistical uncertainties returned by the fit and the statistical uncertainty on the selection efficiency for thett → WWbbprocess. The black line in the distribution ofσdilepton shows the value measured with the entire dataset.
A similar test is repeated for the numbers of primary vertices: a series of measurements is performed for sub-samples of events with number of primary vertices between 2 and 16. The results are presented in figure5.20. There is a linear dependence observed on the measured value of bothRbandσdilepton.
9There are not enough events withhµi<3.5 orhµi>16 to build templates forhµioutside of this range, as can be observed in figure5.18(left).
94
5.4 Systematic uncertainties
Number of primary vertices
2 4 6 8 10 12 14
bR
0.6 0.8 1 1.2 1.4
1.6 / ndf
χ2 13.26 / 12
Prob 0.3504
p0 1.096 ± 0.020 p1 -0.01055 ± 0.00257
/ ndf
χ2 13.26 / 12
Prob 0.3504
p0 1.096 ± 0.020 p1 -0.01055 ± 0.00257
ATLASInternal
= 7 TeV,
s
∫
Ldt= 4.66 fb-1µ +µ ee+eµ
Number of primary vertices
2 4 6 8 10 12 14
dileptonσ
8 10 12 14 16 18 20 22 24 26
/ ndf
χ2 13.95 / 12
Prob 0.3037
p0 8.977 ± 0.521 p1 0.3278 ± 0.0733
/ ndf
χ2 13.95 / 12
Prob 0.3037
p0 8.977 ± 0.521 p1 0.3278 ± 0.0733
ATLASInternal
= 7 TeV,
s
∫
Ldt= 4.66 fb-1µ +µ ee+eµ
Figure 5.20: Measured values ofRb andσdilepton for events with number of primary vertices between 2 and 16.
The error bars represent the sum of the statistical uncertainties returned by the fit and the statistical uncertainty on the selection efficiency for thett→WWbbprocess. The black line shows the value measured with the entire dataset.
The impact of a possible mismodelling of pile-up in the simulation samples is evaluated by re-calculating the values ofRbandσdileptonusing the found linear dependencies on the number of primary vertices and hµi and the distribution of those two variables for data and simulated samples shown in figure5.18in the following way
x= Pnbins
i=1 ni·(p0+p1·yi) Pnbins
i=1 ni (5.5)
wherexis eitherRborσdilepton,p0andp1are parameters describing the dependence ofRbandσdilepton on hµior the number of primary vertices from fits in figures5.19and5.20, which are summarised in table5.7. ni is the number of events andyi is the central value ini-th bin of the respective distribution shown in figure5.18.
p0 p1 hµi
σdilepton 9.7 0.17
Rb 1.055 -0.004
number of primary vertices
σdilepton 9.0 0.33
Rb 1.10 -0.01
Table 5.7: p0 and p1 parameters of linear functions fitted to the distributions ofRbandσdilepton in figures5.19 and5.20.
The resulting values ofRbandσdileptonmeasured in data and simulation are presented in table5.8. The higherδ(data-sim.) is treated as the uncertainty resulting from the pile-up mismodelling in simulation.
As the sub-samples from data have a limited size, both measurements are repeated using generated pseudo-data to check if the dependencies described above are not an effect of statistical fluctuations. No dependence onhµior number of primary vertices are observed for neitherRbnorσdilepton, which could indicate that pile-up does not impact these measurements, but more data would be needed for a definite conclusion. The results of the studies with pseudo-experiments are described in appendixE.
Measurement ofRbandσtt¯
data simulation δ(data-sim.) hµi
σdilepton 11.1797 11.154 0.0257
Rb 1.0211 1.0217 -0.0006
number of primary vertices
σdilepton 11.2854 11.2257 0.0597
Rb 1.0217 1.0236 -0.0019
Table 5.8: Values ofRbandσdileptoncalculated with equation5.5.