4.7 REFERENTE CONTEXTUAL
5.1 TIPO DE INVESTIGACIÓN
8.2.1 Z→
ττ
-background EstimationThe decay of theZ boson into twoτ-leptons and the further decayτ →µν is understood very well in theory, since it is an electroweak process and higher order calculations of perturbation theory are available. Moreover, this process was studied in detail in the different LEP ex- periments [13]. Modern event generator programs likePythiamodel this process with good precision. It was shown in section 8.1.2 that the background ofZ →ττ is mainly reduced by kinematic constraints and hardly affected by the isolation requirements. The impact of the detector response is therefore also small. Hence, we can estimate the background contribu- tion due to this process with fully simulated Monte Carlo events. We expect a background contribution of
fZ→ττ ≈0.0018±0.0006(stat.).
8.2.2 tt¯-background Estimation
As already mentioned in section 8.1.2, the remaining tt-background is due to two muons,¯ which stem from the decay of the two opposite chargedW bosons. They appear isolated and highly energetic in the ATLAS detector. Their background contribution is limited by the kinematic cuts on the pT of the muons, their invariant mass and the muon isolation criteria.
The decay of a top-quark pair into twoW bosons is understood theoretically very well. This also applies for the further decay of the W boson into one muon and one neutrino. The cross section of this process is known with a precision of∼15%, which is mainly due to the uncertainties of the parton distribution functions of the proton at these high energies. The tt-background contribution is based on the Monte Carlo simulation predictions. The¯ muon reconstruction and trigger efficiencies for muons originating from tt¯ decays can be assumed to be equivalent to Z boson events. This does not apply for the isolation requirement, sincett¯events are expected to have a significant larger hadronic activity. It can be assumed, that the hadronic activity in a Z boson event with at least two reconstructed jets with a transverse energy above 50 GeV is comparable to a tt¯ event with full leptonic decay. The isolation efficiency for these selected Z boson events can be determined in data (see section 8.3.6) and hence also be estimated for tt¯ events. The probability for a tight isolated muon in the selected Z boson events is 0.858 while the full Monte Carlo simulation of tt¯ events predicts an isolation probability of0.765. The difference of roughly10%is treated as further systematic uncertainty. This leads to an overall systematic uncertainty of ∼ 20% on the expected background contribution due tott¯events. Hence, a tt¯background contribution of
ft¯t ≈0.0043±0.0004(stat.)±0.0010(sys.).
is expected.
8.2.3 QCD-background Estimation
A precise theoretical and experimental description as for the previoustt¯two background pro- cesses is not available for the QCD background. Hence, another method had to be developed to estimate this background contribution.
8.2. BACKGROUND ESTIMATION 73 The main idea of the QCD background estimation is to use a sub-sample of the triggered data which is enriched of QCD events. Using a Monte Carlo prediction of the ratio between the size of the sub-sample and the number of expected QCD events in the signal-sample allows an indirect calculation of the QCD background contribution. The big advantage of this method is that it is independent of cross section assumptions of QCD processes which are not known with sufficient precision. Only a ratio between data samples based on the same physics process but different selection cuts must be predicted correctly by the full Monte Carlo simulation.
Two examples of possible choices of an QCD enriched data sample are shown in Figure 8.11 and Figure 8.12. Two reconstructed muons, passing the kinematic cuts but not being isolated, have been required. A further like-sign charge requirement on the two muons leads to a nearly pure QCD sub-sample.
DiMuon Mass (0Iso,LS) [GeV]
50 60 70 80 90 100 110 Number of Entries 1 10 2 10
DiMuon Mass (0Iso,LS) [GeV]
50 60 70 80 90 100 110 Number of Entries 1 10 2 10 µ µ → * γ Z/ µ µ → b b WW → t t ν µ → W τ τ → * γ Z/
Figure 8.11: Expected invariant mass spectrum for signal and background process with two non- isolated, like-sign muons passing all kinematic cuts
DiMuon Mass (0Iso,OS) [GeV]
50 60 70 80 90 100 110 Number of Entries 1 10 2 10
DiMuon Mass (0Iso,OS) [GeV]
50 60 70 80 90 100 110 Number of Entries 1 10 2 10
non-isolated, opposite-sign muons
non-isolated, opposite-sign muons Z/γ*→µµ µ µ → b b WW → t t ν µ → W τ τ → * γ Z/
Figure 8.12: Expected invariant mass spectrum for signal and background process with two non- isolated, opposite-sign muons passing all kine- matic cuts
Tevatron data suggests that the charges of muons coming from an bb¯ decay are described in general reasonably well by Monte Carlo generator programs like Pythia. The situation becomes more complicated in the case of the isolation probability of these muons, since isolation is defined within the detector response which might not be modeled to high precision in the ATLAS detector simulation for the first phase of LHC. Hence it would be preferable to have a QCD enhanced data sample which does not depend on the detector simulation itself. One solution would be to require two muons which have passed all cuts but are like-sign. Monte Carlo studies suggest, that the sub sample defined with these cuts contains all types of background and signal events. In order to enhance the QCD background in the sub sample it is advantageous to apply looser isolation cuts and a like-sign requirement.
Cut name loose cut tight cut
Number of inner track isolation ≤ISF×6 ≤ISF×4 Inner Track pT isolation <ISF×15GeV <ISF×8GeV
Jet isolation <ISF×15GeV <ISF×25GeV Electro Calorimeter isolation <ISF×6GeV <ISF×20GeV
Table 8.5: Impact of theIsolation Safety Factor (ISF) on the choosen isolation cuts.
A quantity calledIsolation Safety Factor (ISF)is defined to describe the tightness of isolation cuts, as shown in Table 8.5. An ISF of1.0 corresponds to the usual cuts, ISF =2.0 relaxes all cuts by a factor of two. For example, a muon must have less than 12reconstructed inner
74 CHAPTER 8. CROSS-SECTIONσ(PP→Z/γ∗ →µ+µ−) MEASUREMENT tracks within a halo to pass the loose cut requirement for ISF =2.0 instead of less than 6 reconstructed inner tracks as it was the case forISF =1.0.
As a first cross-check, the impact of the ISF is tested for single muons stemming from bb-¯ events. Figure 8.13 and 8.14 shows the fraction of loosely and tightly isolated bb-muons¯ vs. different ISFs. As expected, both distributions reach 0 for small values of ISFs and a saturation value for large ISFs. The distributions can be parameterized by
fISF =A·
e−x·B
1+e−C·(x−D), (8.9)
where A,B,C and D are fitting variables. The fitted function fISF is also shown in Figures
8.13 and 8.14.
Isolation Safety Factor
0 0.5 1 1.5 2 2.5 3 3.5 4
-events
b
from b
all muon
loosely isolated muons
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 χ 0.002928 / 5 p0 0.003931± 0.0186 p1 -3.586 ± 0.1857 p2 1.042 ± 0.0439 p3 -3.652 ± 0.1903 / ndf 2 χ 0.002928 / 5 p0 0.003931± 0.0186 p1 -3.586 ± 0.1857 p2 1.042 ± 0.0439 p3 -3.652 ± 0.1903
Figure 8.13: Fraction of loosely isolated muons stemming from bb¯-events for different Isolation Safety Factors
Isolation Safety Factor
0 1 2 3 4 5 6 7 8
-events
b
from b
all muon
tightly isolated muons
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 / ndf 2 χ 0.002508 / 7 p0 0.04442± 0.6039 p1 1.632 ± 0.1386 p2 2.477 ± 0.0858 p3 0.01087± -0.05937 / ndf 2 χ 0.002508 / 7 p0 0.04442± 0.6039 p1 1.632 ± 0.1386 p2 2.477 ± 0.0858 p3 0.01087± -0.05937
Figure 8.14: Fraction of tightly isolated muons stemming from bb¯-events for different Isolation Safety Factors
A similar behavior as seen for the single muons, is also expected for the number of selected QCD background events. Figure 8.15 shows the number of selected events for several pro- cesses, predicted by full Monte Carlo simulation, for different values of ISF. Two things can be noted: First of all the QCD processes seem to dominate for ISF > 2.5. Secondly, Monte Carlo simulation predicts a similar behavior between the number of QCD events and the chosen ISF as shown in Figure 8.14 for single muons. These facts suggest the following procedure for QCD background estimation from data:
• Count the number of events, which pass all kinematic cuts for Isolation Safety Factor values of2.5 to10.0. It is expected that these samples are largely dominated by QCD- background
• Fit a function fISF to the measured values and extrapolate to ISF =1. This will give
an estimate of the number of QCD-events NLSQCD which have passed all cuts, but are like-sign.
• Multiply NLSQCD by the Monte-Carlo ratio rMCLS,OS to get an estimation of the number of opposite-sign QCD-events NOSQCD.
It is crucial to note thatNLSQCD does not depend on the simulation of the isolation probability but is determined exclusively within data. The ratio
8.2. BACKGROUND ESTIMATION 75
rMCLS,OS= Number of opposite-sign QCD events Number of like-sign sign QCD events
for events which pass all kinematic and isolation cuts must be determined within the Monte Carlo simulation. The limited statistics of the available QCD-sample forbids a direct cal- culation. Figure 8.16 shows the ratio for different values of ISF and two different invariant mass-ranges. Isolation Safety Factors below 2.5 lead to a background contribution from other processes and hence cannot be used. A linear extrapolation of the fitted function toISF=1.0 leads to an expected ratiorMCLS,OS≈11±6. The error on the ratio includes statistical and a con- servative estimation of systematic uncertainties. The uncertainty will decrease significantly as soon a higher statistic sample of the QCD background is available.
The dependence of rMCLS,OS on the isolation can be explained on physics grounds: A direct decay of bb¯ would lead to two opposite charged muons. Like-sign bb¯ muons come from the decay of a bb-mixing state or from the cascade decay of one¯ b-quarks
− W µ µ − W b c ν b W c s ν + µ µ
The probability of the second process has a stronger correlation with the isolation requirement than the direct decay of bb.¯
Applying this method to the available Monte Carlo samples, we expect a QCD background contribution of fbb¯ ≈0.002. A systematic uncertainty of this method is the choice of Equa- tion (8.9) as parameterization of fISF, since the structure of the function is not physically
motivated. To get an estimation of the systematic uncertainty due to this special choice, it was also tested to use a simple parabola
fISF =Ax2.
as a parameterization. The extrapolated value at ISF=1 using the parabola differs by 20% from the value using Equation (8.9), which should be treated as further systematic uncer- tainty. No bb-events survives the selection cuts within the available Monte Carlo sample.¯ As an estimation it can be assumed that one bb-event survives the selection cuts, which¯ corresponds to an uncertainty of 68 %. This would lead to a background contribution of fbb¯ ≤0.0019, which is in agreement with the above estimated value and is used in the follow- ing discussion.
8.2.4 W →
µν
-background EstimationThe decay ofW → µν and Z → µµ are relatively similar from a theoretical point of view. The only large difference between the two processes is the ten times larger cross section of W production. It can be assumed that the probability having a high energetic, additional muon, resulting from a QCD interaction, is equal in both processes6
. Hence, the number of 6
It should be noted, that the QCD interaction responsible for the additional muon, is the reason, why this background contribution is also estimated from data and not from Monte Carlo prediction
76 CHAPTER 8. CROSS-SECTIONσ(PP→Z/γ∗ →µ+µ−) MEASUREMENT
Isolation Safety Factor
0 2 4 6 8 10
Number of expected LS Events
µ µ → b b WW → t t ν µ → W µ µ → * γ Z/ Parabola Fermi-Func.
Figure 8.15: Comparison of expected events passing all cuts with like-sign requirement for dif- ferent processes vs. the isolation Safety-factor is shown.
Isolation Safety Factor
1 1.5 2 2.5 3 3.5 4 4.5
# Opposite Sign / # Like Sign
0 2 4 6 8 10 12 14 16
Isolation Safety Factor
1 1.5 2 2.5 3 3.5 4 4.5
# Opposite Sign / # Like Sign
0 2 4 6 8 10 12 14 16 60 GeV < Mµµ < 120 GeV < 60 GeV µ µ 30 GeV < M
Figure 8.16: All cuts have been applied on re- constructed muons within the bb¯-sample except the opposite-charge requirement. The ratio of events passing a like-sign requirement to events passing the opposite-sign requirement is shown for different isolation Safety-factors.
Z→ µµ with Z→ µµ with W →µν with W →µν with two tight and one loose three tight isolated one tight and one two tight isolated candidate muons muons loose isolated muon isolated muons
4±2 0 60±24 0
Table 8.6: Overview a W → µν- andZ → µµ-events, with more than one or two isolated muons, respectively. The number of events are normalized to the same integrated luminosity.
W → µν events, which pass all selection cuts should be ten times higher, than the number of Z→ µµ events, where three instead of two muons pass all cuts, i.e. two Z boson candidates are found.
A possible systematic uncertainty of this approach are di-boson events. These events could have also a third muon which passes all selection cuts. All muons resulting from a di-boson event are expected to fulfill the tight isolation requirement, while it is more probable for an additional muon from QCD process to pass only the loose isolation requirement. Hence, the number of events with three tightly isolated muons must be subtracted.
This method was tested on simulated data with results shown in Table 8.6. As expected, no events with three tight isolated muons were found within the Z → µµ sample, but four events with two tight and one loose isolated muon. Considering the statistical uncertainty, the prediction ofW → µν background contribution agrees well with the direct Monte Carlo measurement. The difference of the number of predictedW events and the true number ofW events is treated as systematic uncertainty, which is expected to get smaller with increasing size of the relevant Monte Carlo simulation samples. Hence, the background contribution in this channel is expected to be fWµν ≈0.002±0.001(sys).
8.2.5 Cosmic Muons
High energetic cosmic ray muons are also expected to fake the signal process, when traversing the ATLAS detector. The problematic issue about a cosmic muons track is that it appears as two opposite charged and isolated tracks in the detector. Obviously only those cosmic muons might fake the signal which are reconstructed by the Muon Spectrometer and the
8.3. IN-SITU DETERMINATION OF DETECTOR EFFICIENCIES 77