1. Measuring the Top Quark Pair Production Cross Section
I am going to present planned measurements of the top quark pair production cross section using the ATLAS detector at the Large Hadron Collider.
These measurements will be performed using the first data delivered by ATLAS and should take place within the next year.
The most important concept in this lecture is represented by this Feynman diagram. What we see here is quark antiquark annihilation although the incoming partons might alternatively be gluons. This process is mediated by a gluon, and a top-antitop pair is produced.
A cross section is a quantity with units of area which represents the probability for a certain process to occur. In this case, we are interested in the probability for top quark pair production to occur.
Andrea Bangert, Max Planck Institute of Physics, June 3rd 2008
CSC Note: “Determination of Top Pair Production Cross Section in ATLAS”, May 15th, 2008

2. Overview The Standard Model top quark Why measure the cross section?
Top quark pair production
Top-antitop decay
The single lepton trigger
b-tagging
Hadronic decay: tt → jjb jjb
Semileptonic decay: tt → lvb jjb
Backgrounds
Counting experiment
Jet multiplicity
Dileptonic decay: tt → lvb lvb
Summary and Conclusion
I shall begin by introducing the Standard Model top quark and discussing the reasons why we are interested in measuring its cross section.
I shall discuss top quark pair production and decay. The three different decay channels are categorized according to the number of leptons produced, namely zero, one, and two leptons. The single lepton trigger is therefore a very important tool for identification and collection of certain subsets of top quark events.
One can see that the decay products of a top-antitop pair contain a number of b quarks. For this reason b-tagging is a very important tool in the selection of top quark events. Conversely, the selection of top-antitop pairs provides a sample which is ideal for b-tagging performance studies.
I shall finish up with a summary and conclusion.

3. Standard Model Top Quark
Discovered at Tevatron in 1995
Completed 3rd generation of fermions
Extremely massive:
mt = ± 1.4 GeV
mt ≈ 185 u
mAg < mt < mAu
Top-antitop pairs produced via strong interaction
Top decays via weak interaction, t → W b
Top was discovered at the Fermilab Tevatron in It is the weak isospin partner of the b quark and completed the third generation of fermions.
Physicists had been waiting for this discovery since the advent of the b quark in It took twenty years to actually observe the top at a collider experiment because the thing was more massive than anyone had expected. It is, in fact, the most massive known elementary particle.
The most current result for the top quark mass was reported by the Tevatron experiments in March 2008 and is about 170 GeV.
If one recalls that one atomic mass unit is just a bit less than one GeV, then one realizes that the mass of a top quark is slightly more than the mass of a silver atom (108 u) and slightly less than the mass of a gold atom (197 u).
The production of top quark pairs is mediated by the strong interaction while the top decays via the weak interaction. In the Standard Model the channel in which top decays to produce a W boson and a b quark is overwhelmingly preferred.
1 u = g = 931 MeV/c2 = GeV/c2

4. Why is the cross section interesting?
Measurement of cross section provides a test of perturbative QCD.
Non SM physics could increase the cross section significantly.
Non SM physics could affect the branching ratios for the various top decay channels. (t → H+b)
Top production is a “standard candle”.
Measurements involving known top properties will allow us to calibrate the ATLAS detector.
Top pair production will be a significant
background for other measurements.
The question remains, why are we interested in measuring the top quark pair production cross section?
The partonic cross section can be calculated in perturbative QCD. A measurement of the cross section therefore provides a test of predictions made by QCD and thus challenges the Standard Model itself.
If the total cross section observed at the LHC is not equal to the predicted cross section, this will indicate that the Standard Model fails to provide an adequate description of the production process.
For example, if instead of a gluon some unknown gauge boson were to mediate pair production, this would increase the observed cross section with respect to that predicted by the Standard Model.
If the branching ratios which we observe for the various decay channels are different than those predicted by the Standard Model this will also indicate that the model is inadequate.
For example, if the top were to decay to produce a charged Higgs boson and a b quark, then the signature would depend on the decay channels available to the Higgs as well as those available to the W boson.
Top quark pair production is a “standard candle” of hadron collider physics. Top production at the LHC will be plentiful and known properties such as the top quark mass, the mass of the W boson and the presence of b jets in top events can be used for calibration and performance studies.
Finally, top quark pair production will be a significant background to measurements of Standard Model processes such as electroweak single top production as well as possible observations of supersymmetric processes. In order to observe such events it is mandatory that we measure the pair production cross section as precisely as possible.

5. Top Quark Pair Production
Mediated by strong interaction
Rate of pair production is proportional to cross section and luminosity:
dN/dt = σ L
LHC design luminosity is
L = 1034 cm-2 s-1
Theoretical cross section is
σtt = 833 ± 100 pb
8 top–antitop pairs per second
2.5 million pairs per week
70 million pairs per year
Top quark pair production is mediated by the strong force. The rate of pair production is proportional to the cross section and the luminosity of the accelerator in question.
The luminosity is a quantity which characterizes the performance of an accelerator; it is determined by design parameters such as the revolution frequency of the proton beams, the number of protons which the engineers manage to pack into the colliding beams, and the width of the beams at the interaction point.
The design luminosity at the LHC is 1034 cm-2s-1.
The NLO top quark pair production cross section including NLL soft gluon resummation is 833 pb. The uncertainty on this quantity reflects the error obtained by varying the renormalization scale by a factor of two.
By recalling that 1 barn = m2, one can calculate the number of top quarks N produced per unit time T via N = σ L T.
At design luminosity the LHC is expected to produce 8 top-antitop pairs per second.
If one assumes that collisions occur for half the time that the accelerator is actually running, this implies that we will see 2.5 million pairs per week. If one then assumes that the accelerator actually runs for six months per year, one would expect to observe 70 million top quark pairs per year.

6. Top Quark Decay W → l v Γ ≈ 1/3 W → j j Γ ≈ 2/3
Top decay: t → W b
W decay:
W → l v Γ ≈ 1/3
W → j j Γ ≈ 2/3
Top-antitop decays:
“dileptonic” tt → W+b W-b → (l+ vl b) (l- vl b) Γ ≈ 1/9
“semileptonic” tt → Wb Wb → (l vl b) (j j b) Γ ≈ 4/9
“hadronic” tt → Wb Wb → (j j b) (j j b) Γ ≈ 4/9
Decay products:
Leptons, neutrinos (MET), b jets, light quark jets.
Cross section can be measured in dileptonic, semileptonic and hadronic decay channels.
The top quark almost always decays to produce a W boson and a b quark.
The W boson can decay to produce a lepton and the corresponding neutrino. Alternatively, it can decay hadronically to produce a pair of light flavor quarks.
The top-antitop decays are then categorized according to the number of leptons produced.
In a dileptonic top-antitop decay both W bosons decay leptonically. Two leptons are produced and the branching ratio is 1/9.
In a semileptonic event one W boson decays leptonically, while the other decays to produce light quark jets. Exactly one lepton is produced and the branching ratio is 4/9.
In a hadronic top-antitop decay both W bosons produce light quark jets. Zero leptons are present, and the branching ratio is 4/9.
The decay products of the various channels consist of leptons, neutrinos, which are visible in the detector as missing transverse energy, b jets, and light quark jets.
The cross section can technically be measured in each of the three decay channels.
I am going to present two measurements performed in the semileptonic channel using a very small data set with an integrated luminosity of 10 pb-1. This represents one day of successful data-taking, and these will be among the first measurements performed after the LHC startup.
I will also present one measurement performed in the dileptonic channel using 100 pb-1 of data. This represents about a week of data-taking after the LHC startup.
The cross section can and will be measured in the hadronic channel. However, since no leptons are present it is difficult to distinguish these events from the overwhelming QCD multijet background. An analysis in the hadronic channel will have to wait until a larger data set has been collected.

7. Trigger
Trigger Efficiency in tt→evb jjb Events
tt decays which produce a lepton allow the use of a single lepton trigger.
Electron trigger “e25i”
Requires isolated electron with pT > 25 GeV.
εtrigger = 52.9% in tt → evb jjb
Muon trigger “mu20”
Requires single isolated muon with pT> 20 GeV
εtrigger = 59.9% in tt → μvb jjb
Trigger efficiencies must be estimated from data.
I would like to discuss some experimental techniques which are useful for the selection of top-antitop events.
The first of these is the trigger. The trigger is a combination of hardware and software which uses information delivered by the detector to decide which events are interesting and should be saved for analysis and which events are uninteresting and can be discarded.
One particular trigger looks for an isolated electron, while a second searches for an isolated muon.
The electron trigger requires an electron with transverse momentum greater than 25 GeV. In the plot on the left one sees the trigger efficiency as a function of the transverse momentum of the electron. The efficiency is very low for soft electrons and is high and relatively constant for very energetic electrons.
The lower plot shows the trigger efficiency as a function of the electron pseudorapidity. One can observe the effect of the segmented geometry of the detector in this plot. The efficiency is high in the barrel region of the detector, low in the cracks between the barrel and the endcaps, and is high again in the endcaps.
η = - ln [tan (θ/2)]
The efficiencies for the electron and muon triggers as determined using Monte Carlo generated events are 50% to 60% in semileptonic top-antitop decays.
In order to perform an accurate measurement of the cross section, these efficiencies will have to be determined using real data once data is available.

8. b-tagging Purpose Importance Top quark events produce b quarks
Top-antitop
Single top
W + jets
Purpose
Identification of heavy flavor jets (b)
Suppression of light flavor jets (u, d, s)
Importance
Top quark events produce b quarks
Most W + jets, QCD multijet events produce only light quark jets
Use b-tagging to suppress significant sources of background
Caveat
Requires precise alignment of inner detector
Several months of data-taking necessary
Interplay between tt sample, b-tagging:
In a pure sample of tt events, every event contains two b jets
Use to test b-tagging performance
tt → evb jjb
L = 100 pb-1
W > 7.05
Top-antitop
Single top
W + jets
A second concept of interest is b-tagging.
The purpose of b-tagging is to identify heavy flavor jets and to suppress light flavor jets.
This is useful because the decay of a top quark pair produces plentiful b quarks whereas most W boson and QCD multijet events contain only light quark jets. One can thus use b-tagging to remove significant sources of background from the top quark analysis.
The uppermost plot shows the number of b-tagged jets in semileptonic top-antitop events, single top events and the W+jets background. One can see that at least one b jet can be identified in most top events, whereas the W boson events tend to produce zero b-tagged jets.
If I require at least one b-tagged jet, then plot the invariant mass of the hadronically decaying top quark candidate, I obtain the lower distribution. One should note that after the application of b-tagging the signal to background ratio is very large.
The caveat is that identification of a secondary vertex resulting from the delayed decay of a B meson requires very precise alignment of the inner detector. Several months of data taking will be necessary in order to understand the ATLAS b-tagging capabilities.
There is a certain amount of interplay between the top-antitop sample and b-tagging. If one were to select signal events without requiring b-tagging and if one were nonetheless able to achieve a high purity, then one would have an ideal sample in which to test the b-tagging performance because one would know that every event contains two b jets.
Nb-jets > 1
t → jjb

9. Semileptonic Decay tt → Wb Wb → lvb jjb Selection:
One lepton with pT > 20 GeV
MET > 20 GeV
At least four jets
No b-tagging
Selection efficiency: ε ≈ 20%
Reconstruct t → Wb → jjb
Each event contains N jets
Create all possible trijet combinations
Choose combination with highest pT to represent t → jjb
Reconstruct W → jj
t → jjb contains three jets
Three dijet combinations are possible
Choose dijet combination with highest pT to represent W → jj
Use selected tt sample to study b-tagging, MET, jet energy scale
L = 100 pb-1
Monte Carlo tt → evb jjb events
L = 100 pb-1
I am now going to discuss measurements of the cross section performed in the semileptonic decay channel.
The first step is to collect a large sample of events using the single lepton triggers.
One then requires exactly one energetic lepton, missing transverse energy, which is the signature of the departing neutrino, and at least four jets.
In the initial analyses no b-tagging will be required.
Including the effect of the trigger, the efficiency for the event selection is about 20%.
After the event selection it is desireable to test events for compatibility with the hypothesis that one top quark decays to produce a b jet and two light flavor jets.
The number of possible trijet combinations is C(N, 3) = N! / 3! ∙ (N-3)! Where N is the number of jets in the event. If there are four jets in the event, there are four possible trijet combinations. If there are five jets in the event there are ten possible trijet combinations. If there are six jets in the event there are twenty possible trijet combinations.
If I plot the invariant mass of the selected trijet combinations, I obtain the uppermost distribution, which peaks at the top quark mass.
If I plot the invariant mass of the selected dijet combination I obtain a distribution which peaks at the W boson mass.
These mass peaks will not be visible in the main sources of background. In order to increase the purity of the selected sample one can introduce a cut in order to select the region directly under the mass peak. In this way one can obtain a purity of 80% even without application of b-tagging.

10. Backgrounds W + jets QCD multijets
tt → lvb jjb signal
Backgrounds
W + jets
QCD multijets
top pair production with dileptonic, hadronic decay
single top quarks
diboson production
Drell-Yan Z → ll
W + 4 jets
σ ≈ 100 pb
I would now like to mention some backgrounds to a measurement in the semileptonic decay channel.
The first diagram represents a signal event. Quark-antiquark annihilation is mediated by a gluon, which splits to produce a top-antitop pair. Each top quark decays to produce a W boson and a b quark. One W decays leptonically and the other hadronically; the signature includes a lepton, neutrino, two light flavor jets and two b jets.
Let us now consider electroweak production of a W boson. This diagram represents a special case in which initial state radiation occurs twice. One of the gluons splits to produce a pair of light flavor quarks while the other splits to produce a pair of b quarks. The signature of this event is thus a lepton, neutrino, two light flavor jets, and two b jets and mimics exactly the signature of the signal events. If the analysis does not require b-tagging it is not even necessary that one of the gluons split to produce a pair of b quarks in order to confuse W boson production with the top-antitop signal.
The third diagram represents electroweak single top production. In the t-channel a W boson is exchanged between a b quark and a light flavor quark. This diagram shows also that the b quark originated via gluon splitting. We see that it is necessary only for one of the heavy quarks to radiate a gluon in order to produce once again the same signature as the signal events, namely the lepton, neutrino, two light flavor jets, and two b jets.
The final diagram depicts diboson production. In this case two W bosons have been produced and initial state radiation is present. If one W decays hadronically while the other decays leptonically, and if the gluon from the QCD radiation splits to form a b quark pair, then we have once again an irreducible background.
The above processes are all examples of irreducible backgrounds because they produce exactly the same signature as the signal events.
One source of instrumental background is provided by QCD multijet events. These produce a signature which differs from that of the signal because it lacks both the energetic lepton and the neutrino. However, if the reconstruction or identification of objects in the detector is imperfect, then QCD multijet events may nonetheless be mistaken for signal events.
The semileptonic decay of a b quark can produce both electrons and muons, and hadronic objects can simply be mistaken for an electron.
single top production
σ ≈ 250 pb
diboson production (WW)
σ ≈ 24 pb

11. Counting Experiment
Ndata = 311 events
Cross section “measurement” using streamtest “data”
L = 18 pb-1
Standard Model processes
Monte Carlo generated events
Full simulation of ATLAS detector
Simulation of triggers
Data reconstruction
Test analysis in “realistic” setting
tt→ evb jjb
Apply selection cuts to “data”
Count number of (signal and background) events
Estimate number of background events
Using Monte Carlo samples
Using theoretical cross sections
Compute trigger and selection efficiencies
A pseudomeasurement of the cross section was performed using the ATLAS streamtest “data”. This dataset was about 18 pb-1 and included an admixture of Standard Model processes. The event samples were created using various Monte Carlo event generators. A full simulation of the ATLAS detector response was performed, including a simulation of the trigger response, and the reconstruction intended for use with real data was performed.
This exercise gave the collaboration a chance to test analyses in a realistic setting.
The measurement was performed in the semileptonic decay channel and the selection cuts discussed previously were applied to the “data”.
The first step is to count the number of events observed in the selected sample.
It is then necessary to estimate how many of the observed events are due to background processes. To do this one can consider Monte Carlo samples, one can use the theoretically predicted cross sections, and one can employ data-driven methods.
Finally one needs to compute the trigger and selection efficiencies. This is typically done using Monte Carlo samples.
After all the necessary input quantities have been determined one enters them into this equation in order to obtain the measured value for the cross section.
The cross section determined using this counting method was 771 pb, which agrees with the theoretical value of 833 pb to within the calculated uncertainties.
Ndata = 311 events
NBG = 93 events
Branching ratio Γ = 5/9
Luminosity L = 8.74 pb-1
Selection efficiency εtt = 5.8%
σtt = 771 ± 133 pb

12. Jet Multiplicity Cross section “measurement” using Monte Carlo “data”
Signal: tt → evb jjb
Require one electron and MET to collect W → ev
Select signal: Njets > 4
Selection efficiency εtt = 5.3%
Fix diboson and single top cross sections to theory.
Select background sample by requiring Njets < 2
Use relative cross sections for W / Z production to extrapolate from Njets < 2 to signal region
σtt = 717 ± 158 pb
Njets > 4
Ndata = 486 ± 22
NBG = 167 ± 37
Signal: tt → evb jjb
Signal has high jet multiplicity
Main background: W → ev + jets
W → τv + jets
Z → ee + jets
Diboson production: WW
Single top quarks, single top quarks
A second measurement was performed in the same channel, again using the streamtest data.
An inclusive sample of events containing a real, leptonically decaying W boson was collected by requiring an energetic electron and missing transverse energy.
All events in this inclusive sample are shown in the plot on the right, which depicts the number of events as a function of the jet multiplicity.
The pink and brown blocks represent single top production; the blue and green are W bosons which decay to produce a tau lepton or an electron. One can see that these events tend to produce fewer jets.
The top-antitop signal is shown in turquoise, and one can see that the signal events tend to have a high jet multiplicity.
One selects the signal phase space from this inclusive sample by requiring at least four jets. One then needs to estimate how many of these selected events are indeed background events and how many events can be attributed to the signal.
The cross sections for diboson and single top production were fixed to agree with the theoretical values.
A sample containing only background events was then selected by collecting only events with less than two jets. The contributions due to diboson and single top production were then subtracted from this sample. The relative cross sections for W and Z boson production were then used in order to extrapolate the prediction for the background rate from the phase space with low jet multiplicity to the signal phase space. This method will deliver the expected number of background events due to production of a single W boson in association with jets.
Finally one enters the calculated quantities into the equation in order to obtain the central value for the cross section. The “measured” value of 717 pb agrees with the theoretical value of 830 pb within the given uncertainties.

13. Differential Cross Sections
d2N / dpT dy
dN / dmtt
Least squares fit
4 jets, lepton, MET used as input, mW and mt used as constraints.
Alternative reconstruction
Lepton, MET and mW used to reconstruct W→lv. W and four jets used to reconstruct tt system.
It is also interesting to consider differential cross sections.
The distribution on the left-hand side represents the invariant mass of the top-antitop system.
Unknown heavy resonances which decay to form a top-antitop pair would appear as a bump in this distribution.
The plot compares the true invariant mass of the top-antitop system, which is known from the Monte Carlo sample, to the invariant mass of the system as obtained using two different methods to reconstruct the top quarks.
The four leading jets, the lepton, the missing transverse energy were used as input to a least squares fit. The known W boson and top quark masses were used as constraints.
In the second method the four-momentum of the lepton, the MET and the known W mass were used to reconstruct the leptonically decaying W boson. This W boson was then combined with the four leading jets in order to reconstruct the top-antitop system.
The plot on the right-hand side represents the number of hadronically decaying top quarks observed in bins of transverse momentum and rapidity. One can see that there is a highly favored region of phase space.
It is interesting to note that sources of background are included in the plot. In order to obtain a clean signal, the analysis required two b-tagged jets. This cuts the number of selected events dramatically such that this analysis will necessitate a larger luminosity and is not suitable for the very first data.
Created W→jj candidates by forming all possible dijet combinations using only light jets.
Assigned closest b-jet to each dijet combination to create t → jjb candidate.
Took trijet combination with highest pT to represent t → jjb.
tt → lvb jjb (t → jjb)
2 b-tagged jets
L = 1000 pb-1
Background included
Rapidity:
y = ½ ln [E + pz / E – pz]

14. Dileptonic Decay Electron, muon triggers Selection
tt → W+b W-b → l+vb l-vb
Electron, muon triggers
Selection
Two leptons of opposite charge
No tau leptons
MET > 30 GeV
At least two jets
No b-tagging
Drell Yan Backgrounds
Z → l+ l-
Veto Z boson mass
85 GeV < mll < 95 GeV
I will now move on to discuss a different decay channel, namely the dileptonic channel in which both W bosons decay to produce leptons.
The events are collected by requiring either the electron or the muon triggers to fire.
It is important to note that the two leptons produced when the top and the antitop decay are of opposite charge. This requirement helps to eliminate backgrounds due to fake leptons.
For example, if a jet in a semileptonic top-antitop decay fakes the signature of a lepton, it is as likely to fake a lepton of positive charge as it is to fake a lepton of negative charge. In half of such cases the two observed leptons would not be of opposite charge.
Tau leptons are not considered because their identification is difficult.
One can expect large quantities of missing transverse energy because two neutrinos are produced.
The uppermost plot shows the distribution of the missing transverse energy. One can see that background events do indeed tend to have less MET than do the signal events. The cut is placed at 30 GeV.
One should remember that this plot contains Monte Carlo simulated events and that the missing transverse energy is difficult to model correctly using Monte Carlo techniques. Once data is available it will be important to check whether the distributions predicted by the Monte Carlo agree with those observed in the data.
At least two jets should be present. The analyses which will be performed on first data do not require b-tagging.
Drell Yan production of a Z boson which decays to two oppositely charged leptons is the most significant source of background in this channel. In order to cut as many of these events as possible, one discards events where the dilepton mass falls within the Z mass peak.
The lower plot shows the dilepton invariant mass distribution. One can see that the signal events do not have a peak at the Z mass, whereas Drell-Yan events do. One simply discards the events which fall within this range.

15. Fake Leptons Electrons Muons
tt → lvb jjb is background if jet fakes electron
Require isolated electrons
ET (∆R < 0.2) < 6 GeV
Muons
tt → lvb jjb is background if b-jet produces μ
Distinguish between:
Hard process:
t → Wb → μvb
b decay:
b → Wc → μvc
Require separation between μ and jet
∆R(μ, j) > 0.2
Semileptonic top-antitop decays can provide a source of background for the dileptonic signal if one of the jets in the event suceeds in faking the signature of an energetic electron.
The way to minimize this effect is to require isolated electrons. One considers the amount of energy deposited in a hollow cone about the trajectory of the electron candidate. If there is a lot of energy in this cone, then the electron is not “isolated”; if there is very little energy in the cone, the electron is “isolated”.
As one can see from the uppermost plot, prompt electrons resulting from the decay of the top quark tend to be isolated, while all the unwanted electrons tend not to be.
Prompt electrons: ∆R(reco electron, true electron) < 0.1
Unwanted electrons: ∆R(reco electron, true electron) > 0.1
Semileptonic top-antitop decays can also provide a source of background if a b-jet decays to produce a muon. As one might expect, it is difficult to distinguish between a muon produced during the decay of the top quark and a muon produced during the decay of a b quark. The way to avoid this problem is to require that any acceptable muon be a reasonable distance away from any jet.
In the lower plot the distance between the muon and the closest jet is shown along the horizontal axis. One sees that muons from the top quark decay tend to be rather far away from the nearest jet, whereas the unwanted muons tend to be rather close to the nearest jet.

16. Measuring the Cross Section
Counting experiment
tt → lvb lvb
εtt = 11.05%
L = 100 pb-1
Ndata = NS + Nbg
Ndata = 1216
Nbg = 229
NZ→ll = 124
NW+jets = 47
Ntt bg = 39
Ndiboson = 14
Nsingle top = 5
σtt = 804 ± 47 pb
B(x)
G(x)
S(x)
Maximum Likelihood Method
Ndata = Ns + Nbg
S(x) describes signal distribution
B(x) describes background distribution
G(x) = Ns ∙ S(x) + Nbg ∙ B(x)
Maximize the log likelihood
L = -Σ ln G(x) + Ndata
Obtain NS and Nbg
The efficiency for selection of dileptonic top-antitop events using the cuts just described was 11%.
The collaboration used Monte Carlo samples to estimate the number of signal and background events which would be observed in a data set of 100 pb-1.
If one uses the estimated number of events to “measure” the cross section one obtains a central value and an uncertainty of about 6%.
One should note that this uncertainty does not include the effect of the uncertainty on the luminosity measurement, which will be 20% to 30% during the initial period of data taking.
A simple counting experiment is not the only option. One can also perform a maximum likelihood fit in order to determine the number of excess signal events with respect to the background.
Ndata represents the number of events observed in the data. This is of course the sum of the signal and background events.
A discriminant variable is used to define the functions S(x) and B(x). S(x) is the distribution which describes the behavior of the signal events and B(x) is the distribution which describes the behavior of the background events.
The discriminatory variable pictured here is the azimuthal angle between the trajectory of the leading lepton and the missing transverse energy.
The function G(x) is then expected to describe the distribution observed in the data. G(x) is a superposition of S(x) and B(x) with weights Ns and Nbg.
The correct weights, ie the numbers of signal and background events, are determined by numerically maximizing the log likelihood function L.

17. Conclusion
Measurement of σtt will be one of the first analyses performed after LHC comes online
Test of perturbative QCD
Calibration of detector
b-tagging performance, MET, jet energy scale
Background to future measurements
Top-antitop pairs produced via strong force
Top decays via weak force
Dileptonic channel (tt → lvb lvb)
L = 100 pb-1, δσtt ≈ 6%
Semileptonic channel (tt→ lvb jjb)
L = 100 pb-1, δσtt ≈ 17%
Single lepton trigger
Reconstruct t → jjb and W → jj
Reconstruct invariant mass of top-antitop system
Hadronic channel (tt → jjb jjb)
The future looks promising!
A measurement of the top quark pair production cross section will be one of the first analyses performed after the LHC comes online.
This measurement offers a test of perturbative QCD. It also provides various useful ways of calibrating the detector. Finally, it will be essential to understand top quark pair production as a background to future measurements of more exotic processes.
Top-antitop production is mediated by the strong force, while the top decay is mediated by the weak force.
Top pairs decay in a variety of channels, producing a variety of signatures. The pair production cross section can and will be measured in all three decay channels. However, the presence of energetic leptons is particularly helpful because it provides a useful trigger.
The semileptonic channel is interesting because one can reconstruct the hadronically decaying top quark from the jets which are its decay products.
We have also seen that one can reconstruct the invariant mass of the top-antitop system.
In conclusion, there are a lot of interesting measurements waiting to be made, and the future looks promising.

18. Backup Slides

19. References ATLAS CSC Notes: Analysis references:
“Determination of Top Pair Production Cross Section in ATLAS”, May 15th, 2008
“Triggering top quark events in ATLAS”, April 22nd, 2008
“Light jets in tt events”, May 15th 2008
“Flavor tagging calibration with tt events in ATLAS”, March 31st, 2008
Analysis references:
“Top Studies for the ATLAS Detector Commissioning”, S. Bentvelsen, M. Cobal, July 2005
“Commisisioning ATLAS using top quark pair production”, W. Verkerke, I. van Vulpen
Analysis using streamtest “data”:
“A pre-commissioning tt cross section measurement at ATLAS”, December 14th, 2007
MET:
“On the missing transverse energy in semi-leptonic tt events using a kinematic fit”, E. van der Kraaj
Top quark at LHC:
“Heavy quarks and leptons”, ATLAS Technical Design Report, May 25th, 1999
“Top Quark Physics”, M. Beneke, I. Efthymiopoulos, M. Mangano, J. Womersley

20. Γ(t→Wb)
The charged current W± couples to quarks q and q’ with coupling given by CKM matrix element Vqq’.
Vtb ≈
Γ(t→Wb) = |Vtb|2 = 0.998

21. Luminosity Necessary input for any cross section measurement.
Quantity which characterizes performance of accelerator.
At the LHC design luminosity is L = 1034 cm-2 s-1
Necessary input for any cross section measurement.
Methods of measuring luminosity:
Measure rate of process with large, well-known cross section.
R = dN/dt = L σ
More easily applicable to e+e- colliders than to hadron colliders.
Example: QED Babha scattering.
Calculate luminosity using beam parameters.
L = F f ΣN1N2 / 4πσx*σy*
Beam revolution frequency at LHC is f = 11 kHz.
F = 0.9 accounts for nonzero crossing angle.
N1 and N2 are the number of protons in colliding bunches.
Caveat: bunch currents will not be very uniform.
σx* and σy* are transverse bunch widths at interaction point.
Caveat: beam profile measurements are necessary.
Typical precision is 5% - 10%.
Use the optical theorem (ALFA, 2009).
Measure total rate of pp interactions Rtotal.
Measure rate of forward elastic scattering dRelastic/dt |t=0.
Protons scatter with very small momentum transfer t.
L ∙ dRelastic/dt |t=0 = Rtotal2 (1 + ρ2) / 16 π
ρ is ratio of real to imaginary part of elastic forward amplitude.
Typical precision is 5% - 10%

22. Missing Transverse Energy
Neutrinos do not interact with the detector.
The initial transverse momentum of the colliding proton system is zero.
Conservation of momentum requires that the net transverse momentum of all decay products must be zero.
Assumption: transverse energy and momentum of any object except a neutrino are measured perfectly.
Σi ET + ET(v) = 0 where subscript i runs over all visible particles.
Conclusion: the “missing transverse energy” (MET) is the transverse energy of the neutrino.
ET(v) = MET = -Σi ET
Events which produced a neutrino will have significant MET.
Events which did not produce a neutrino will have little MET.
Caveat: no measurement is perfect. Instrumental effects can result in energy imbalance and can ‘fake’ the neutrino signature.
Use known mass of W boson and W → lv data to calibrate and test performance of MET reconstruction.
Neutrinos do not interact with the material in the detector.
The initial transverse momentum of the colliding proton system is zero. At leading order the initial transverse momentum of the colliding partons is therefore also zero.
Conservation of momentum requires that the net transverse momentum of the top-antitop system and all its decay products must also be zero.
If one assumes that the transverse energy of all particles except neutrinos is measured perfectly and that the sum of the transverse energies of all particles including neutrinos is zero, then the missing transverse energy is the negative of the vector sum of the transverse energies measured in the detector and is equal to the transverse energy of the departing neutrino.
The conclusion is that large quantities of missing transverse energy correspond to the presence of a neutrino; small quantities mean that no neutrino was present.
However, no measurement is perfect. Instrumental effects can fake the neutrino signature. For example, if a muon is not reconstructed then the transverse momentum of that muon will be interpreted as missing transverse energy. Furthermore energy can be lost in calorimeter cracks or through leakage in the calorimeter or failure of calorimeter cells.

23. Object Definitions Electrons Muons Jets b-tagging
pT > 20 GeV, |η| < 2.5
Exclude calorimeter crack: 1.37 < |η| < 1.52
Isolation based on calorimeter energy: ET(∆R < 0.2) < 6 GeV
Reconstruction efficiency: ε = 67%
Purity: 97%
Muons
Staco algorithn
Best combination of information from muon chambers and tracking detector
pT > 20 GeV, |η| < 2
Isolation: ET(∆R < 0.2) < 6 GeV
Efficiency: 88%
Purity: 100%
Jets
Reconstructed from energy depositions in calorimeter towers
Cone4
Jet is removed if ∆R(j,e) < 0.2
pT(ji) > 40 GeV for I = 1, 2, 3. pT(j4) > 20 GeV
b-tagging
IP3D+SV1 (3 dimensional impact parameter and secondary vertex algorithms)
W > 7.05
εb-tag = 60% for pT(b) > 30 GeV
5% uncertainty on εb-tag is expected after L = 100 pb-1
MET (MET > 20 GeV)
Cells from electron and photon clusters
Cells inside jets
Cells inside topologcal clusters which are outside identified objects
Contribution from muon
Cryostat correction

24. Counting Experiment in Semileptonic Channel
tt → evb jjb
L = 8.74 pb-1
Considered W + jets, Wbb and Wcc, single top production.
NW+light flavor = 58, NW+heavy flavor = 21, Nsingle top = 14
σtt = 771 ± 96 (statistical) ± 93 (MC systematics) pb
Uncertainties expected for L = 100 pb-1
50% uncertainty on normalization of W + jets, 14.7%
5% uncertainty on jet energy scale, 13.3%
Initial and final state radiation, 10.6%
Statistical uncertainty on 100 pb-1, 2.7%
Uncertainty on PDFs, 2.3%
Electron identification efficiency, 1%
Electron trigger efficiency, 1%

25. Jet Multiplicity tt → evb jjb, L = 8.74 pb-1 Cuts: Efficiencies:
e25i single electron trigger
exactly one electron
Electron author is egamma
pT > 25 GeV
|η| < 2.4
No calorimeter isolation required
isEM == 0
Reconstructed electron must match trigger electron, ∆R(ereco, etrigger) < 0.2
Overlap between jets and electron removed, ∆R(jet, e) > 0.3
MET > 25 GeV
Jets have
|η| < 2.5
Transverse mass of W → ev
mT(W → ev) = √ [(ET(e) + MET)2 - (px(e) + METx)2 - (py(e) + METy)2]
mT(W → ev) > 45 GeV
Efficiencies:
Efficiency of electron trigger: εtrigger = ± “measured” using Z → ee
Efficiency of inclusive W → ev selection: εW → ev = ±
Efficiency of signal selection (Njets > 4): εjet multiplicity = ±
(Errors are statistical)
Uncertainties:
5% uncertainty due to jet energy scale
5% uncertainty due to MET
10% uncertainty due to Monte Carlo generator
10% uncertainty due to QCD radiation
Monte Carlo “data”
Generated in Athena
Reconstructed in Athena

26. Estimation of inclusive W+4 jets production for Jet Multiplicity Analysis
Consider W → ev and Z → ee
“Exclusive production of W + 1 jet” refers to production of W boson in conjunction with zero or one jets
“Inclusive production of W + 4 jets” refers to production of W boson in conjunction with four or more jets
Ratio of W production with respect to jet multiplicity in data:
Rdata(W) = N(inclusive W + 4 jets) / N(exclusive W + 1 jet)
Ratio of W production with respect to jet multiplicity in Monte Carlo:
RMC(W) = N(inclusive W + 4 jets) / N(exclusive W + 1 jet)
Ratio of Z production with respect to jet multiplicity in data:
Rdata(Z) = N(inclusive Z + 4 jets) / N(exclusive Z + 1 jet)
Ratio of Z production with respect to jet multiplicity in Monte Carlo:
RMC(Z) = N(inclusive Z + 4 jets) / N(exclusive Z + 1 jet)
Relative cross sections for W and Z production are well understood:
Rdata(W) / Rdata(Z) = RMC(W) / RMC(Z)
Solve to obtain number of background events attributed to W + 4 jets:
N(inclusive W + 4 jets) = RMC(W) / RMC(Z) ∙ Rdata(Z) ∙ N(exclusive W + 1 jet)

27. Counting Experiment in Dilepton Channel
tt → lvb lvb
Efficiency: εtt = 11.05%
Purity = 4.3
L = 100 pb-1
Ntt = 987
NZ→ll = 124
NW+jets = 47
Nsemileptonic tt = 39
Ndiboson = 14
Nsingle top = 5
Uncertainties
Statistical uncertainty: 3.6%
Jet energy scale: %, - 2.1%
PDF uncertainties: 2.4%
Final state radiation: 2.0%