FCal 1 FCal 2 FCal 3
9. Analyses at Different
9.1. Cross Section Analysis at √
Table 9.1.: Sample cross sections for the cross-section analysis at√
s=14 TeV.
Process k-factor calculation
Ref. sample cross sample size
order section [pb] [pb−1]
tt¯MC@NLO1 1.00 approx. NNLO [243] 450.0 964
W t-channel 1.14 NLO + 29.1 571
s-channel 1.50 NLO [71] 3.5 2826
t-channel 0.98 NLO ∗ 79.7 271
Z →e+e−+np 1.22 NLO [206] 1727.2 279
Z →µ+µ−+np 1.22 NLO [206] 1808.5 103
Z →τ τ+np 1.22 NLO [206] 95.5 1851
W →eν+np 1.22 NLO [206] 10900 14
W →mν+np 1.22 NLO [206] 11946 28
W W 1.57 NLO [244] 39.1 1280
ZZ 1.29 NLO [244] 2.8 19577
W Z 1.89 NLO [244] 13.9 3600
+References: [76, 75, 205]
∗References: [71, 245, 246]
9.1.1. Differences Between the Analysis at √
s =14 TeV and
√ s =10 TeV
The reconstruction algorithms are following the description in Chapter 5, but some object requirements are different:
• The jet-muon overlap cut used a ∆R < 0.2 cut to reject muons that overlap with a reconstructed jet.
• Muons withη <0.1 and between 1.0<|η|<1.3 were not used, since the muon chambers are inefficient in this regions.
The detector geometry that was used is an early description of the misaligned, as-built detector geometry. Additional material had been added in the inner detector and in front of the electromagnetic calorimeter.
The event cuts were unchanged compared to the event cuts used for the cross-section analysis at √
s=7 TeV except for the following points:
• The trigger requirement was dropped for this study. A combination of single lepton and dilepton trigger is expected to have >98% trigger efficiency.
• No data-driven methods were employed here and also no difference is made between background from real and fake leptons.
• The results of the single sub-channels were not combined with the likelihood method, but instead a combined selection that is flavour-blind (ll final state, with l =e or l =µ) was used with a lower E/T cut of E/T >30 GeV.
9.1.2. Event Yields for the Event Selection at √
s =14 TeV
Table 9.2 shows the number of expected events for each sub-channel and the com-bined selection and Table 9.3 summarises the expected uncertainty on the cross-section measurement and significance for different integrated luminosities. Fig-ures 9.1 show the E/T distribution after the event selection for each sub-channel.
The number of selected events is similar to the number of selected events for the analysis at √
s =10 TeV. The acceptance is somewhat lower due to the older re-construction algorithms and especially for the channels with muons, fiducial cuts were applied. Fake dilepton events were not properly studied here. Also the sample sizes used here were smaller, so that the uncertainty on the background numbers are larger.
The main tendency that Z → ℓ+ℓ− events are the dominating background is also true here. The second largest background are single top-quark events. The problem with the large tails in the E/T distribution for Z → µ+µ− events and thus a larger contribution from this background remains, although the relative fraction of events is small in the µµselection. A signal-to-background ratio between 3.4 and 6.3 was achieved, the S/B in the muon channel is lower than in the ee channel, since fiducial cuts removed a large amount of the signal muons. The acceptances are between 14.7% and 20.2%.
9.1.3. Systematic Uncertainties for the Analysis at √
s =14 TeV
Systematic uncertainties that were considered here are the following:
• The uncertainty of the luminosity was taken as 5%.
• The jet energy scale uncertainty was taken as ±5% and the correlation to E/T
is 100% as described in Section 7.3. The overlap of jets with electrons was not used nor the doubling of the jet energy scale for forward jets.
• ISR/FSR systematic uncertainties were taken into account with the use of PYTHIA simulated samples. The parameters such as the ΛQCD scale or the pT cut-off for the shower evolution were changed such as the resulting sample has increased/decreased ISR/FSR individually. The uncertainty was quoted as the largest uncertainty in each positive and negative direction.
• PDFuncertainties were taken into account withCTEQ6.1 andMRST2001E PDF sets at NLO.
MissingET [GeV]
50 100 150 200 250
Events
0 2 4 6 8 10 12 14 16 18 20
signal t t
lepton+jets t t
→ e e Z →µµ Z
τ τ
→ Z WW (Herwig) ZZ (Herwig) WZ (Herwig)
50 100 150 200 250
0 2 4 6 8 10 12 14 16 18 20
50 100 150 200 250
0 2 4 6 8 10 12 14 16 18 20
50 100 150 200 250
0 2 4 6 8 10 12 14 16 18 20
MissingET [GeV]
50 100 150 200 250
Events
0 5 10 15 20 25
signal t t
lepton+jets t t
→ e e Z →µµ Z
τ τ
→ Z WW (Herwig) ZZ (Herwig) WZ (Herwig)
50 100 150 200 250
0 5 10 15 20 25
50 100 150 200 250
0 5 10 15 20 25
50 100 150 200 250
0 5 10 15 20 25
MissingET [GeV]
50 100 150 200 250
Events
0 5 10 15 20 25 30
35 t t signal
lepton+jets t t
→ e e Z
µ µ
→ Z
τ τ
→ Z WW (Herwig) ZZ (Herwig) WZ (Herwig)
50 100 150 200 250
0 5 10 15 20 25 30 35
50 100 150 200 250
0 5 10 15 20 25 30 35
50 100 150 200 250
0 5 10 15 20 25 30 35
50 100 150 200 250
0 5 10 15 20 25 30 35
Figure 9.1.: E/T distribution for the different sub-channels (eetop left,µµtop right and eµbottom) after the event selection at √s=14 TeV.
Figures 9.2 show, as an example for a systematic uncertainty, the PDF uncer-tainties with the CTEQ6.1 and MRST2006 PDF sets at NLO that were used for Table 9.4.
The results from the systematic studies are summarised in Table 9.4. All the investigated systematic uncertainties have similar sizes.
9.1.4. Expected Sensitivity for the Analysis at √
s =14 TeV
The sensitivity of the cut-and-count analysis at a centre-of-mass energy of√
s =14 TeV and a target integrated luminosity of Lint.=100 pb−1 on the cross-section measure-ment is as follows:
∆σee
σee [%] = 9.8(stat)+4.1−3.1(syst)±5.0(lumi) (9.1)
∆σµµ
σµµ
[%] = 9.0(stat)+5.5−2.9(syst)±5.0(lumi) (9.2)
∆σeµ
σeµ [%] = 5.5(stat)+6.6−3.7(syst)±5.0(lumi) (9.3)
∆σcombined
σcombined
[%] = 4.2(stat)+5.0−2.0(syst)±5.0(lumi) (9.4)
Table 9.2.:√ Number of selected events by the event selection for the analysis at s=14 TeV, scaled to an integrated luminosity ofLint.=100 pb−1.
ee µµ eµ comb.
t¯t dilepton 202±5 253±5 555±7 987±10 acceptance [%] 14.7 18.3 20.2 17.3 t¯t other 12±1 4±1 24±2 39±2 Z →e+e− 9±2 0+0.4−0 0+0.4−0.5 20±3 Z →µ+µ− 0+1−0 50±7 5+3−2 79±9 Z →τ+τ− 4±1 7±1 17±1 25±1 W →eνe 7+10−5 0+8−0 7+10−5 14+13−8 W →µνµ 0+4−0 7+7−4 25+11−9 33+12−10 diboson 2.7±0.4 3.5+0.5−0.4 7±1 14±1 single top 1.3+0.8−0.5 1.1+0.8−0.5 3±1 5.4+1.5−1.2 Total bkg. 36+12−6 73+13−8 88+16−10 228+20−16 S/B 5.6+2.2−2.4 3.4+0.7−0.9 6.3+1.4−1.7 4.3+0.5−0.7
The statistical uncertainties are quite similar to those of the analysis at√
s=10 TeV.
This is mainly because the target luminosity was chosen such that the number of selected events in both cases are similar. Despite the better signal-to-background ratio and the better significance at √
s =14 TeV, the efficiency and purity of the event selection at √
s =10 TeV is improved due to more optimised object selection cuts and improved reconstruction algorithms.
The systematic uncertainties cannot be compared directly, since much more sys-tematic effects were investigated for the analysis at √s =10 TeV. When similar systematic effects, such as jet energy scale uncertainties, PDF uncertainties and ISR/FSR effects, are looked at, the effects are comparable.