University of California at Santa Cruz

University of California at Santa Cruz
Measurement of the Top Quark Pair Production Cross Section with the ATLAS Detector I would like to present a planned measurement of the top quark pair production cross section. This measurement is designed to utilize the first data delivered by the ATLAS detector in 2009. Andrea Bangert University of California at Santa Cruz October 29th, 2008

Overview Large Hadron Collider ATLAS Experiment
Standard Model Top Quark Pair production mediated by strong interaction Top decay mediated by weak interaction Theoretical cross section Cross Section Measurement Luminosity Event Selection and efficiencies Reconstructing top Backgrounds Summary I am going to begin by introducing the LHC and the ATLAS detector. I will continue by introducing the main character in this drama, the Standard Model top quark. Top quark pair production is mediated by the strong interaction. However, the top quark decays weakly to produce a W boson and a b quark. The pair production cross section can be calculated using perturbative QCD. A measurement of the cross section is intended to verify this prediction and therefore provides a test of the Standard Model. When performing a measurement of a cross section it is essential to measure the luminosity provided by the collider. Because the LHC is a new machine, its operational parameters will not initially be well understood. The relative uncertainty associated with the measurement of the luminosity will at first be quite high. I will show that this quantity will define the uncertainty on the first measurements of the cross section. If one is looking for a top-antitop pair which decayed to produce one lepton and several jets, then production of a W boson accompanied by QCD radiation will be a source of background. Production of single top quarks provides an additional source, as do diboson production, Drell-Yan events, and QCD multijet events. In order to eliminate as much of the background as possible, one requires every selected event to leave a certain signature in the detector. However, by doing this one loses some fraction of the signal events. The selection efficiency encodes the kinematics of the signal events and the performance of the detector and the reconstruction. In other words, the measurement of the luminosity encodes the performance of the hadron collider while the selection efficiency encodes the performance of the detector. I will finish up with a quick summary.

Large Hadron Collider This airial photograph shows a lovely valley which lies between the Swiss Alps and the foothills of the Jura mountains. To the left one can see Lake Geneva. Under this rather idyllic countryside lies the largest machine in the world. The Large Hadron Collider is a superconducting proton-proton collider housed in a tunnel 27 kilometers in circumference, traced here in red. The CERN facility and the ATLAS detector are situated at Point 1. The Alice detector is housed at Point 2, CMS is directly across the ring from ATLAS at Point 5, and LHCb sits at Point 8. The remaining four straight sections are occupied by momentum and betatron collimation systems, the superconducting radiofrequency cavities which focus the protons into bunches and accelerate them, and the beam abort system.

Large Hadron Collider Large Hadron Collider
The tunnel which the LHC occupies was originally excavated in order to house the Large Electron-Positron collider. This ring is 27 kilometers in circumference and lies at an average depth of 150 meters below the surface of the earth. In 1985 when the tunnel was excavated this represented the largest civil engineering project in Europe. The LHC is designed to allow proton-proton collisions at a center of mass energy of 14 TeV and a design luminosity of 1034 cm-2s-1. In addition, it will be possible to collide heavy ions at a center of mass energy of more than one thousand TeV and a luminosity of 1027 cm-2s-1. (5.5 TeV per nucleon gives lead nuclei a center of mass energy of 1138 TeV). 27 km circumference, 150 m depth Proton-proton collisions, ECM = 14 TeV Design luminosity L = 1034 cm-2 s-1 Experiments: ATLAS, ALICE, CMS, LHCb

Components of a Collider Experiment
This diagram represents the various components of a typical collider experiment. The diagram also displays the signatures which the various particles leave in each type of detector. The use of several different types of detectors provides complementary information about the products of the proton-proton collisions. The left-hand line represents the spatial point at which collisions occur. The beam pipe, if it were depicted, would be shown here. The vertical segments represent concentric layers of the experiment, and the products of the collisions move outwards through the various detectors. Massive particles such as the W and Z bosons and the top quark decay almost instantaneously. Only the products of such decays exit the beam pipe and are visible in the detector. The most central component of a collider detector is typically a tracking chamber. The tracking chamber records the tracks of charged particles including electrons and positrons, muons, tau leptons, and charged pions and kaons. Neutral particles such as photons, neutrons, and neutral pions and kaons do not interact in the tracking chamber. The next component in the diagram is an electromagnetic calorimeter. Electrons and photons lose their energy in the electromagnetic calorimeter via bremsstrahlung and pair production, producing an electromagnetic shower. The electromagnetic calorimeter thus provides electron and photon identification and also measures the energy. A fraction of the energy of charged hadrons is deposited in the electromagnetic calorimeter, but most of the hadron energy is deposited subsequently in the hadronic calorimeter. The hadronic calorimeter provides measurements of jet energy and direction of flight. Muons produce tracks in the inner detector but do not interact strongly with the heavy nuclei in the electromagnetic or hadronic calorimeters. Instead muons continue to the muon chambers. Muons are nominally the only particles which continue through all other components of the experiment to reach and be detected by the muon chambers. The ATLAS detector is constructed according to the principles illustrated in this diagram.

The ATLAS Experiment Inner Detector, superconducting solenoid magnet.
Pixel detector, semiconductor tracker, transition radiation tracker Momentum and vertex measurements, electron, tau and heavy flavor identification Lead / liquid argon electromagnetic calorimeter Electron, photon identification Hadronic calorimeter Scintillator-tile barrel calorimeter Copper / liquid argon hadronic end-cap calorimeter Tungsten / liquid argon forward calorimeter Air-core toroid magnet Instrumented with muon chambers Muon spectrometer Muon momentum ATLAS is about 50m in length and 20m in height. It is as tall as a five story building and weighs about 7000 metric tons. ATLAS represents fifteen years of labor by several thousand physicists, engineers, and students from 34 countries. Its construction cost participating nations a total of 1.2 billion Swiss Francs. The beam pipe runs horizontally across the diagram, through the center of the experiment. The various detectors then occupy concentric cylinders which are centered on the beam pipe. The most central portion is a tracking chamber called the inner detector, depicted here in yellow. The inner detector is surrounded by a superconducting solenoid magnet which produces a field of 2 Tesla directed parallel to the beam axis. The presence of a strong magnetic field causes the tracks of charged particles to be deflected, which allows the reconstruction software to quantify the momenta and determine the sign of the charge. The inner detector thus provides momentum and vertex measurements, as well as e-,  and heavy flavor identification. The lead and liquid-argon electromagnetic sampling calorimeter, shown here in green, provides e- and  identification and energy measurements. The hadronic calorimeter is depicted in red, and provides measurements of jet energy, direction of flight, and MET. The hadronic calorimeter is required to contain hadronic showers and to prevent hadrons from continuing through the calorimeter to reach the muon system. The hermetic calorimeter system allows reconstruction of the MET carried by , which do not interact with the detector material. A large superconducting air-core toroid magnet is positioned outside the calorimeters and provides a magnetic field of 4 Tesla for the muon spectrometer. The outermost detector is the muon chamber, depicted here in blue. The muon spectrometer is partially contained within a system of toroid magnets. By measuring the curvature of the  track in a high magnetic field the muon spectrometer determines the  momentum and the sign of the charge.

ATLAS Goals Electroweak symmetry breaking Higgs boson Supersymmetry
Gauge bosons Compositeness mt and mW QCD The most important goal of the ATLAS collaboration is to perform measurements which will lead to an understanding of the mechanism of electroweak symmetry breaking. Detection of the Higgs will be an experimental challenge. However, ATLAS was designed to be sensitive to the Higgs over the full range of permitted masses. If Supersymmetry exists at the electroweak scale, plentiful production of squarks and gluinos is expected. The challenge would not be the discovery of supersymmetric signatures, but would instead consist of determining which of many competing models is favored. ATLAS is also intended to search for undiscovered gauge bosons and for evidence that quarks and leptons are composite objects. Precision measurements of top and W masses will increase constraints on the mass of the SM Higgs. The plot on the right hand side depicts the relationship between the top mass along the horizontal axis, the W mass along the vertical axis, and the Higgs mass. Each of the diagonal lines represent a constant Higgs mass. Precision electroweak measurements of the Z mass peak performed by the LEP and SLD collaborations provided constraints on the top, W and Higgs masses. These constraints are represented by the red ellipse. The LEP and SLC collaborations predict a Higgs mass of about 130 GeV by performing SM fits to electroweak parameters. A direct measurement of the W mass was subsequently performed by the LEP collaboration, and direct measurements of the top and W masses have been performed at the Tevatron. The 68% confidence level ellipse for these measurements is depicted in blue. The direct measurements of the top and W masses suggest that the Higgs has a mass less than 114 GeV. However, a search for the Higgs performed at LEP excludes a SM Higgs with a mass of less than 114 GeV at the 95% confidence level. This conundrum could be resolved by direct observation and measurement of the properties of the Higgs. Until such an observation can be performed it is desireable to increase the precision of the constraints on the Higgs mass by increasing the precision of the measurements of the W and top masses. QCD processes will form the dominant background to searches for new signatures at the LHC. Obtaining a detailed understanding of QCD phenomena is therefore essential to the ATLAS physics program. This will include performing an accurate measurement of the top quark pair production cross section. mH = GeV mW = ± GeV mt = ± 1.2 GeV mH > 114 GeV (95% CL)

Standard Model Top Quark
Discovered at Tevatron in 1995 Completed 3rd generation of fermions Extremely massive: mt = ± 1.2 GeV mt ≈ 185 amu mAg < mt < mAu The top quark 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 because the thing was quite simply 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 July 2008 and is GeV with a relative uncertainty of less than 1%. 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 amu) and slightly less than the mass of a gold atom (197 amu). 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. Top-antitop pairs produced via strong interaction Top decays via weak interaction, t → W b

Top Quark Pair Production
Mediated by strong interaction Rate is proportional to cross section tt and luminosity L L = 1034 cm-2 s-1 L ≈ 36 pb-1 / hour Theoretical cross section is σtt = pb 9 top–antitop pairs / second 2.7 million pairs / week 76 million pairs / year Top quark pair production is mediated by the strong force. At leading order it occurs via quark-antiquark annihilation and also via gluon-gluon fusion. The rate of pair production is proportional to the cross section and the instantaneous luminosity of the accelerator in question. The luminosity is completely independent of the interaction under consideration. Instead, it depends on the properties of the colliding beams and thus characterizes the performance of the accelerator. The design luminosity at the LHC is 1034 cm-2s-1. One can rewrite this luminosity in units of barns per second in order to note that the LHC can provide about 30 inverse picobarns of data to each of its experiments per hour. The NLO top quark pair production cross section including NNLO soft gluon resummation is 920 pb. The uncertainty on this quantity reflects the error obtained by varying the renormalization scale by a factor of two. At design luminosity the LHC is therefore expected to produce 9 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 2.7 million pairs per week. If one assumes that the accelerator runs for six months per year, one would expect to observe 76 million top quark pairs per year. This is why one hears people refer to the LHC as a top quark factory. This is unfortunately not the number of top quark pairs which end up in my plots. First, I am looking for a particular combination of decay products which has a branching ratio of 29%. Second, because the detector is not perfect, the efficiency of my event selection is about 20%. However, at design luminosity about four million top-antitop pairs will survive my selection cuts per year. If one assumes that the initial luminosity will be a factor of ten less than the design luminosity, then one would expect 400,000 top quark pairs to survive the event selection during the first year.

Parton Distributions Partonic cross sections
Short-distance hard scattering Calculated to NLO in perturbative QCD Parton distribution functions Non-perturbative, universal Determined from data CTEQ6.6M g, u, d, ubar The calculation of the theoretical production cross section requires knowledge of two things. These are the partonic scattering cross sections and the parton distribution functions. The partonic cross sections are proportional to the probability for each of the short distance hard scattering processes to occur. The partonic processes occur at very high energies and very short distance scales. At high energies s is small and a quantity which is expanded in powers of s will converge quickly. In this case perturbative QCD provides a reliable calculational tool. The partonic cross sections have been calculated to NLO in perturbative QCD. The second component required in order to compute the cross section is a set of parton distribution functions. A PDF represents the probability density for a parton to carry a fraction x of the p+ momentum. The PDFs are nonperturbative and cannot currently be calculated from fundamental principles. However, they are universal. This means they can be extracted from fits to data delivered by deep inelastic scattering experiments and applied to other interactions as a predictive tool. The PDFs can be extrapolated to higher energies using the DGLAP equations. The plot on the left-hand side shows the PDFs for the gluon and the u, d and ubar quarks as a function of the fraction x of the p+ momentum. The momentum transfer Q has been set equal to the top quark mass. The left-hand side of the x axis represents the regime in which the fraction x of the p momentum carried by the parton in question is very small. The plot shows that a parton which carries a very small fraction of the p+ momentum is highly likely to be a gluon. If one were considering only sea quarks then one would expect the PDFs for u and ubar to be equal. The fact that at large fractions of the p+ momentum the distribution for up is much larger reflects the presence of valence up quarks and the absence of valence antiquarks in p+. In other words, a valence quark will be either a u or a d quark and will tend to carry a large fraction of the p+ momentum. Parton Distribution Functions

Factorization Theorem
ij are partonic cross sections f(x) are parton distributions i, j are incoming partons N. Kidonakis and R. Vogt, 2008 ECM = 14 TeV CTEQ6.6M PDFs mt = 172 GeV tt = pb tt(mt) at the LHC We have established that the partonic cross sections and the PDFs are the necessary ingredients when calculating the hadronic cross section. After one has obtained these quantities, one can perform the calculation of tt. The computation of the hadronic cross section σtt is based on the factorization theorem of QCD. It involves the convolution of short distance, perturbative partonic cross sections ij with non-perturbative, experimentally determined PDFs fi and fj. The indices i and j refer to the incoming quarks, antiquarks and gluons. I did not make the scale dependence in this equation explicit. However, the partonic cross sections are functions of the renormalization scale and the parton distributions are functions of the factorization scale. The partonic cross sections depend upon the center of mass energy of the colliding partons. This in turn depends upon the center of mass energy of the colliding p+ and also on the fractions of the p+ momentum carried by each of the incoming partons. The plot was produced for LHC energies; the center of mass energy was assumed to be 14 TeV. The central value for the NLO calculation as a function of the top quark mass is represented by the solid black line. The variation in the NLO calculation which occurs when the scale is changed from one half the top quark mass to twice the top quark mass is depicted by the dashed black lines. The central value for the ‘approximate’ NNLO calculation is represented by the blue dashed line. The red dotted lines represent the variation in the approximate NNLO calculation which is obtained by changing the scale. One can see that the variation in the NNLO calculation due to the scale is less than the variation in the NLO calculation. In order to make a numeric prediction for the tt at a particular collider the quark mass is needed as input. These authors took the most current experimental top quark mass and obtained a theoretical cross section of 920 pb for top quark pair production at LHC energies. It is apparent that a measurement of tt serves as an experimental test of perturbative QCD. Measurement of σtt serves as experimental test of pQCD

Top Decay Top decay: Γ(t→W+b) = |Vtb|2 = 0.998 t ~ 5  10-25 s
No top hadrons W decay: W → l v Γ ≈ 1/3 W → j j Γ ≈ 2/3 Top-antitop decays: “dileptonic” “semileptonic” “hadronic” Cross section can be measured in dileptonic, semileptonic and hadronic decay channels. tt → W+b W-b → (l+ vl b) (l- vl b) tt → Wb Wb → (l vl b) (j j b) tt → Wb Wb → (j j b) (j j b) Γ ≈ 1/9 Γ ≈ 4/9 The branching fraction for tWb is proportional to the |Vtb|2. This is one of the diagonal elements, which relate quarks of the same generation and are almost unity.  is thus almost one, and the top quark “almost always” decays to produce a W and a b quark. The top lifetime is on the order of s. Since the strong force requires on the order of s in order to form a bound state, no top flavored hadrons or top-antitop bound states form. The top decays as a ‘bare quark’. Wl . Since there are three generations of leptons, there are three leptonic decay channels available to the W. Alternatively, Wjj. The phase space available to the decaying W includes ud and cs quark pairs. It does not include tb quark pairs because top is more massive than the W. Each of the two possible quark pairs can carry any of three color charges, which means that six hadronic decay channels are available. A total of nine decay channels is thus available to the W. Three channels are leptonic, leading to a branching ratio of 1/3 for the leptonic decay. Six are hadronic, leading to a branching ratio of 2/3 for the hadronic decay. Since tWb, the decay of a top quark pair will produce two W bosons, each of which will then decay either leptonically or hadronically. Finally, the top-antitop decays are categorized according to the number of leptons produced during the decay of the two W bosons. The decay products of the various channels consist of leptons, , b jets, and light flavor jets. Energetic e and  are relatively easy to identify. It is possible to identify hadronically decaying . However, it takes a long time to develop and validate the necessary algorithms, and  identification methods will not be suitable for use on initial data.  cannot be observed directly in the detector. However, if one assumes that energy is conserved and that any energy which appears to be missing is due to the departure of a , then one can reconstruct the ET of the . Since every tt decay is expected to produce two b quarks, the identification of b jets will be very useful when searching for top quark events. However, the converse is also true: if one can identify top quark events by other means, then one can obtain a sample enriched in b jets which is ideal for calibrating and validating the b-tagging algorithms. The cross section can technically be measured in each of the three decay channels. The top signature in ttlblb is clean and does not suffer from large backgrounds. However, the cross section is relatively small. Furthermore it is not possible to unambiguously reconstruct either top because both branches produce a , which is not observed in the detector. The cross section for ttlbjjb is larger. The background rates are manageable, and tjjb can be reconstructed completely. This channel is ideal for performing measurements using initial data, and I will discuss in detail a measurement designed to be performed in this channel. The cross section can and will be measured using ttjjbjjb. However, since no l are present it is difficult to distinguish these events from the overwhelming QCD background. Identification techniques which utilize neural nets to select events in this channel have been employed very successfully at the Tevatron.

Why measure the cross section?
Test perturbative QCD Physics not predicted by the Standard Model could increase the cross section significantly 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 We have identified the various signatures produced by top-antitop events. This knowledge will be important when selecting signal events. The question remains, why would one want to measure the top quark pair production cross section at all? 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 in addition to the gluon some unknown gauge boson could 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 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. This would cause the measured cross sections for the various channels to deviate from those predicted by the Standard Model. 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 mass, the mass of the W and the presence of two b jets in each top event 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.

Cross Section Measurement
Estimate background rates QCD multijets Electroweak W+N jet production Single top production Estimate εtt Use Monte Carlo samples Include trigger efficiencies from data Luminosity Relative luminosity measured by LUCID Absolute calibration from LHC machine parameters Uncertainty of 20% to 30% expected initially The next question is, how should one perform the cross section measurement? I am going to claim that the answer to this question will initially be to perform a counting experiment. This is a simple and robust method which is ideal for use on first data. In order to perform such an experiment one needs to count the number of events in a data sample containing events with the desired signature. One then needs to estimate the background rate. This is typically done using a combination of data driven techniques and Monte Carlo generated event samples. One also needs to determine the signal selection efficiency. This will be done using a Monte Carlo model. The final ingredient in the cross section measurement is the integrated luminosity. The relative luminosity for ATLAS will be measured by the LUCID detector. The LUCID detector will be able to monitor changes in the instantaneous luminosity precisely. However, LUCID does not measure the absolute luminosity. During the initial period of LHC operation the absolute luminosity will be calculated from LHC machine parameters. During this initial data-taking period the relative uncertainty on the luminosity measurement will be 20% to 30%. The ALFA detector will use the optical theorem to measure the absolute luminosity precisely. However, the ALFA detector will be installed in 2009 and a period of calibration will be necessary before robust luminosity measurements are possible.

Luminosity Necessary input for cross section measurement.
Calculate L using beam parameters. f = 11 kHz F = 0.9 Np = 1011 protons / bunch Nb = 2808 bunches / beam σ* = 16 m As we have seen, the luminosity is an essential input for any  measurement. The relative uncertainty on  due to the luminosity is equal to the relative uncertainty on the integrated luminosity. The instantaneous luminosity L is equal to the number of particles which cross one unit of transverse area at the IP per unit time. This depends on the properties of the colliding beams and therefore characterizes the performance of the accelerator. The first estimate of this quantity at the LHC will be obtained from machine parameters. For a Gaussian beam profile where both beams are round and the numbers of protons per bunch are assumed to be equal, the luminosity can be calculated from the machine parameters according to this equation. The beam revolution frequency at the LHC is 11 kHz. The factor F accounts for the nonzero crossing angle of the two beams at the IP. The maximum allowable beam size is defined by the apertures of the LHC beam cleaning system. The need to minimize the beam-beam interaction and the maximal allowable beam size limit the number of p+ per bunch to Np = 1.15 * 1011. The number of bunches per beam is Nb = 2808. The nominal transverse bunch width at the interaction point is * = 16 m. The determination of the luminosity from machine parameters is nontrivial. Beam monitors will be used to determine the bunch dimensions and population. The beam profiles cannot be accessed directly at the IP. Instead measurements must be performed at other points along the beam and the results must be extrapolated to the interaction point. The bunch currents are not expected to be uniform; variations of 10% or more are expected. The limit on the accuracy of a luminosity determination performed using machine parameters is L ~ 10%. Eventually the ALFA detector will apply the optical theorem in order to measure the absolute luminosity with a relative uncertainty of 5%. The ALFA detector is scheduled to be installed in 2009. It is obvious that improving the precision of the luminosity measurement is of interest to anyone who would like to measure . Initial uncertainty is 20% to 30% Limit on precision is L ~ 10%

Trigger tt  lb jjb allows use of single lepton trigger
Electron trigger e25i Isolated electron pT > 18 GeV For pT > 25 GeV, trigger= 99% tt → evb jjb After event selection pTe > 10 GeV εtrigger = 84% Muon trigger mu20 Muon with pT > 17.5 GeV tt → μvb jjb pTm > 10 GeV εtrigger = 78% Efficiencies must be estimated from data Level 1 Trigger Event Filter The trigger is a combination of hardware and software. It 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. The event rate at design luminosity is about 1 GHz. This must be reduced to 100 Hz before events are written to tape. The trigger must provide a rejection factor of 107 against minimum bias events. , e and  with high pT tend to indicate interesting events, as do jets with high pT, hadronically decaying , and events with large MET. One of the simplest trigger channels searches for an isolated e-, while a second searches for an isolated . ttlb jjb which produce e- or  allow the use of these particularly simple triggers. The electron trigger requires an e- with pT > 18 GeV. In the upper plot one sees the trigger efficiency as a function of the pT of the e-. The efficiency for the Level 1 trigger is depicted in black, whereas the efficiency for the higher level trigger called the Event Filter is shown in red. The efficiency is very low for soft e- and is high and constant for energetic e- with pT > 25 GeV. For the tt  evb jjb events which were chosen by my event selection the trigger efficiency was 84%. It would be a lot higher if I had required the pT of the e- to be higher before applying the trigger requirement. However, I had to set the pT cut quite low in order to see this turn-on curve. The muon trigger requires a  with pT greater than 17.5 GeV. The lower plot shows the trigger efficiency as a function of the pT of the . Once again the efficiency is low for  with less pT and relatively high and constant for  with pT > 20 GeV. For the tt  b jjb events which were chosen by my event selection the trigger efficiency was 78%. In order to perform an accurate measurement of tt, these efficiencies will have to be determined using real data once data is available. The next step is to incorporate the trigger efficiencies into the signal selection efficiency. Trigger Efficiency in tt→lvb jjb

Backgrounds W + jets QCD multijets
tt → lvb jjb signal Backgrounds W + jets QCD multijets top pair production with dileptonic, hadronic decay single top production diboson production Drell-Yan Z → ll W + 4 jets σ ≈ 100 pb I would like discuss some of the processes which form backgrounds to ttlb jjb. The first diagram represents a signal event. Quark-antiquark annihilation is mediated by a gluon, which splits to produce a tt pair. Each top decays to produce a W and a b quark. One Wl and one Wjj. The signature includes l, , two light flavor jets and two b jets. Let us now consider electroweak production of a W. This diagram represents a special case in which initial state radiation occurs twice. One gqq while the other gbb. The signature of this event is thus l, , 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 necessary that gbb in order to confuse W production with the signal. The third diagram represents electroweak single top production. In the t-channel a W is exchanged between a b quark and a light flavor quark. This diagram shows also that the b quark originated via gbb. We see that it is necessary only for bbg to produce once again the same signature as the signal events, namely the l, , two light flavor jets, and two b jets. The final diagram depicts diboson production. In this case two Ws have been produced and initial state radiation is present. If one Wjj while the other decays via Wl, and if the gbb, 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 isolated energetic lepton and the . However, if the reconstruction or identification of objects in the detector is imperfect, then QCD multijet events may nonetheless be mistaken for signal events. single top production σ ≈ 250 pb diboson production (WW) σ ≈ 24 pb

Event Selection Selection Cuts Before cuts S/B = 0.16
Exactly one e or μ Isolated E∆R=0.20 < 6 GeV Energetic pT > 20 GeV Central, |η| < 2.5 At least four jets pTj > 40 GeV pT j4 > 20 GeV Central, || < 2.5 No b-tagging MET > 20 GeV Before cuts S/B = 0.16 After cuts S/B = 1.56 The diagram in the upper left-hand corner represents ttlbjjb. Each tWb. One Wjj to produce light flavor quarks which are observed in the detector as hadronic jets. The other Wl. The purpose of the event selection is to distinguish signal events from background. The background events which are going to survive the selection process will be those which have a signature very similar to that of the signal. This signature includes exactly one isolated, highly energetic e- or . The lepton is isolated because it is the product of an isolated W. It is energetic because it is the decay product of a real and rather massive boson. The lepton must be central because I would like to have tracking provided by the inner detector and this is available over a range ||<2.5 where η = - ln [tan (θ/2)]. I need at least one lepton because I would like to exclude ttjjb jjb and QCD multijets. I don’t want events with two isolated, energetic leptons because these are highly likely to be Z boson decays or ttlb lb. I require at least four energetic jets. Two of these will be b jets and two will be light quark jets. However, since I do not require b-tagging I cannot a priori identify the b jets. Finally, I require a significant amount of MET. In the ideal case this MET will be due solely to the undetected escape of the energetic . In the plot the number of signal events is depicted in blue together with the contributions due to the various backgrounds. The first column represents the Monte Carlo generated “data” before any cuts have been made. The second depicts the number of events which contain exactly one lepton, and the third contains events which produced the required numbers of jets. The final column represents the “data” sample after the requirement has been placed on the MET. During this process I have lost 75% of my signal events. However, I have lost a great deal more of the background. S/B has increased from 0.16 before cuts to 1.56 after all cuts. Number of events, L = 100 pb-1

Invariant Masses t  jjb W  jj tt → Wb Wb → lvb jjb
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 Possible to cut on mjjb, mjj W  jj After the event selection it is desireable to test events for compatibility with the hypothesis that one top decays to produce a b jet and two light flavor jets. Each event contains N jets. N is at least four but may be of the order of ten. Using these N jets one constructs all possible three jet combinations by taking the vector sum of each set of three four-momenta. 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. One then selects that trijet combination with the highest pT to represent the tjjb. If I plot the invariant mass of the selected trijet combinations, I obtain the uppermost distribution, which peaks at the top quark mass. One then has a set of three jets which were used to reconstruct tjjb. Using these three jets one can construct three dijet combinations. One can then select the dijet combination with the highest pT to represent the Wjj. If one plots the invariant mass of this W boson candidate one obtains the plot on the lower right. The invariant mass of the selected dijet combination peaks very nicely at the W mass. The shoulder represents combinatorial background, ie instances in which I selected incorrect jets. 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 which selects the region directly under the mass peak. In this way it is possible to obtain a signal to background ratio of S/B = 4 without the application of b-tagging. However, this cut would be extremely sensitive to uncertainties in the JES, and the JES will not be well understood during the first period of data-taking. L = 100 pb-1, tt → evb jjb

Transverse Masses t  Wb  lb W  l L = 973 pb-1 W+jets, tt lb jjb
Two variables which could help to discriminate against QCD multijet events are the transverse masses of Wl and tlb. In the plot on the left is shown the transverse mass of Wl. The histograms are superimposed. The black histogram represents the distribution of the transverse mass in W+jet events. The histogram in red represents the distribution observed in ttlb jjb. It is not surprising that these two distributions are very similar, because the events in each contain a legitimate Wl candidate. It is unfortunate that it was not possible to include the background due to QCD multijet events in this plot, because these are the events which this distribution is expected to discriminate against. If one looks at data from CDF one sees that the QCD multijets tend to result in the reconstruction of W boson candidates with very low mT, because they tend to have very little MET. CDF applies a cut requiring mT(W)> 20 GeV in order to exclude QCD multijets. In the plot on the right-hand side is shown the transverse mass of the leptonically decaying top quark candidate. Again, these histograms are superimposed. If one were to implement a cut on one of the transverse masses I would suggest using the mT of the W boson. Adding in the b quark in order to calculate the transverse mass of the parent top increases the possibility of making a combinatoric error, especially in an analysis which does not employ b-tagging. The mT of the top quark would also be dependent on the JES whereas the transverse mass of the W boson is dependent only on the successful reconstruction of the lepton and the MET.

Selection Efficiencies
Small selection efficiencies: dileptonic ttbar hadronic ttbar single top W→τv Large selection efficiencies: W→ev plus 5 partons W→μv plus 4 partons At the moment the event selection ends with the cut on the MET; no cuts on the masses of any top or W candidates have been imposed. A certain percentage of events of each type survive the event selection; this is the selection efficiency. This plot depicts  for the signal and several different types of backgrounds. The blue points represent the signal efficiencies. These include ttebjjb and ttbjjb. The turquoise points represent efficiencies for selection of ttbjjb and ttlblb. One can see that the selection efficiency for ttjjb jjb is quite small because these events do not produce either an isolated lepton or an energetic . The yellow points represent the selection efficiencies for single top events, including Wt production, s channel and t channel. Selection efficiencies for W+N jets samples are represented by stars. These are divided into We, W, and W. Each sample is then further split according to how many partons are produced via QCD radiation. One can see that if only two or three partons are produced then  remains quite low. However, if four or five partons are produced  becomes rather formidable. The statistical uncertainties on the efficiencies are very small. The uncertainty on the Jet Energy Scale is estimated by the ATLAS collaboration to be 5%. A first estimate of the uncertainty on the selection efficiencies due to the JES has been made by varying the cuts on the pT of the jets by the same amount. The error bars seen in the plot were obtained in this way. It makes sense that events producing a large number of jets should be quite sensitive to uncertainties on the JES. The subleading jets are likely to have a momentum which is close to the threshold for the cut. Changing this threshold by a small amount is thus likely to change the number of suitable jets in the event, which will affect the number of events which produce the required four jets. A first estimate of δε due to Jet Energy Scale was performed by varying cuts on jet pT by 5%. For ttlb jjb, / ~ 8% which implies / ~ 8%.

W + N Jets Background Most dangerous background.  is large
CERN-PH-TH/ Electroweak production of W+jets is the most dangerous background to ttlb jjb. After determining  one uses the theoretical cross section and the integrated luminosity in order to determine the expected number of background events. The relative uncertainty on the theoretical cross section is quite large. This will produce a large relative uncertainty on the background rate. In the plot on the right-hand side one sees the systematic uncertainty on calculations of the cross section for production of a W+ together with N jets. The authors considered the performance of five leading order Monte Carlo event generators, including Alpgen, Ariadne, Helac, MadEvent and Sherpa. The bins along the horizontal axis represent the inclusive number of jets. The cross sections in each bin are normalized to the average value of the default settings for all codes. If one discounts the predictions made by Ariadne, then the variation within an individual generator is the same order of magnitude as the discrepancies between the generators. The dipole cascade in Ariadne does not employ DGLAP evolution. Instead it allows evolution which is ordered in  rather than ordered in pT. This allows for a greatly increased phase space for jet production as compared to that allowed by the other generators. The same effect is seen in deep inelastic scattering data delivered by HERA. In this case the DGLAP based parton showers fail to correctly reproduce the final state properties whereas Ariadne does a fairly good job. What one should note qualitatively is that all of the event generators and in particular Ariadne must be tuned to data from HERA and the Tevatron before accurate predictions can be made for the LHC. The authors report that the largest variation is obtained by changing the scale used to evaluate αs.  is large σ is large N is large Significant source of uncertainty for tt Systematic Uncertainty on σ(W+)+Njets

W + N Jets tt / tt  8% Alpgen: Assign uncertainties:
W+2j = 2032 pb W+3j = 771 pb W+4j = 273 pb W+5j = 91 pb Assign uncertainties: W+2j = 20% W+3j = 30% W+4j = 40% W+5j = 50% Events in 100 pb-1: NW+2j = 53 ± 10 NW+3j = 271 ± 81 NW+4j = 775 ± 310 NW+5j = 800 ± 400 The first column records the cross section predicted by Alpgen for production of a W boson in association with 2, 3, 4 and 5 partons. A rough estimate of the relative uncertainty was assigned to each cross section. This produced both a low and a high estimate of the number of background events expected in a data sample of 100 pb-1. The plots depict the invariant mass of tjjb. On the left hand side one sees the low estimate for the number of expected W+N jets background events; on the right-hand side one sees the high estimate. These assumptions for the uncertainty on the W+jets background are very rough. It should be noted that measurements of these cross sections will be performed once data is available. The relative uncertainties associated with the measurements will be less than 50%, so this assignment of the uncertainties represents an overestimate. Once measurements of the cross sections are available it will also become apparent how good the predictions delivered by the Monte Carlo event generators are. Given the very rough assumptions made about the uncertainty associated with the prediction for the background rate, the relative uncertainty on the ‘measured’ cross section is about 8%. tt / tt  8% Low and high estimates of W+N jets contribution in 100 pb-1

QCD Multijet Background
Reducible background MET is due to b→Wc→lνc Mismeasurement Leptons are Non-prompt “Fake” Not isolated Fake Rate R~10-5 (ATLAS TDR) R = R(pT, η) Difficult to model QCD multijet background adequately using Monte Carlo samples, detector simulation Contribution will be measured from data MET 10,000 events Distributions normalized to contain 10,000 events. Electron Isolation The  for QCD at the LHC will be huge. However, QCD represents a reducible background. In the SM an isolated, energetic l or  must result from the decay of a massive W, Z or H. Top is more massive than W, so top decays are a good source of real Ws and therefore of isolated, energetic l and . Light flavor jets produce W bosons, however these tend to be highly virtual and are not a very successful source of energetic leptons. If QCD multijets tend not to produce energetic, isolated l or  then one can require the presence of these objects in order to discriminate against multijet events. In the ideal case, the MET represents the ET carried by the unobserved . The upper plot shows the distribution of the MET. The samples shown here include QCD, tt decays which produce at least one lepton, and W+N jets events where Wl. One can see that multijets tend to have less MET than events which produce a real Wl. The MET observed in multijet events is due to semileptonic heavy flavor decays as well as mismeasurement. The selection cuts for the analysis require MET > 20 GeV. A lepton in a multijet event may be the product of the semileptonic decay of a heavy flavor quark, in which case it is a true, non-prompt lepton. Alternatively a jet may ‘fake’ the signature of a reconstructed lepton. Neither non-prompt nor ‘fake’ leptons will be isolated. On the lower right-hand side is a plot of the amount of energy contained within a hollow cone of ∆R<0.2 centered on each e- candidate. An e- accompanied by very little energy in the surrounding cone is “isolated”. An e- accompanied by a significant amount of energy in this surrounding cone is not “isolated”. One can see that the signal events and the W+N jets contain a large number of isolated e, whereas multijets do not. One of the selection cuts requires ET < 6 GeV within the hollow cone about the electron. The rate at which a jet can fake the electron signature is estimated to be about In particular, the fake rate is not a constant but will depend on the pT and  of the jet. Because the fake rate is so low it is difficult to model QCD using Monte Carlo generated samples and the simulation of the detector response. The contribution from QCD will have to be measured from data. ∆R = 0.2 Hard cuts placed on jets. No cuts on leptons.

Consistency Check tjjb σ·Γ = 246.0 ± 3.5 (stat) pb
Sample contains ttlbjjb, ttlblb ~10% of sample used as “data” ~90% of sample used as model Ldata = 97 pb-1, Ndata ~ 45,000 LMC = 970 pb-1, NMC ~ 450,000 Efficiencies calculated using model Assume εdata = εMC Number of background events in “data” predicted by model tjjb Even when only Monte Carlo samples are available, a consistency check can be performed by using a small portion of the sample as “data” and using the remaining portion of the sample as the model. In the plot on the right-hand side, 100 pb-1 of “data” is represented by the red points. The error bars represent the statistical uncertainty on the number of entries in each mass bin. The “data” is superimposed over the model. The model predicts which portion of the observed events are tteb jjb, ttb jjb, ttb jjb, or ttlb lb. No ttjjb jjb or W+jets are included. One uses the Monte Carlo model to obtain  for each decay channel. One then makes the assumption that  for the “data” is the same as that for the Monte Carlo. In this instance this is a highly valid assumption because our “data” consist of Monte Carlo generated events produced by the same event generator as the events which compose the model. If one were to use two different event generators this would become a more courageous assumption and the consistency check would become more meaningful. After real data becomes available in 2009 this will be a dangerous but essential premise. The success of the measurement will then depend upon how well the Monte Carlo model describes the data. Armed with the number of events observed in the “data”, the expected number of background events, the efficiency for the signal channel, and the integrated luminosity, one can then perform a pseudomeasurement of the cross section. The counting experiment described here produced a result for the partial pair production cross section which was quite close to the cross section reported by the Monte Carlo event generator. All this really means is that the analysis was counting the number of initial and final events correctly. However, the measurement which will be performed using data in 2009 is at heart a counting experiment. This exercise therefore indicates that the skeletal version of the analysis is working properly. σ·Γ = ± 3.5 (stat) pb From Monte Carlo: σ·Γ = pb

Next Steps Implement analysis in Athena 14.2.23
Run over signal Monte Carlo Perform “consistency check” W+Jets Monte Carlo Implement trigger decision Optimize selection cuts Consider a cut on invariant or transverse masses Compare different methods of reconstructing tjjb and Wjj Jet Energy Scale Prepare analysis for data 10,000 events The next step is to implement the event selection and the calculation of efficiencies in the current version of the ATLAS reconstruction software. One ascertains that the analysis is functional by running over a Monte Carlo sample containing signal events. A cross check such as the one I just described provides a useful exercise. It will be essential to run over a Monte Carlo W+Jets sample as well. If samples of ttjjb jjb, single top production, diboson production and Drell-Yan events are available, those will be included in the analysis. It will be vital to implement the trigger decision into the analysis. The selection cuts are not necessarily optimal. In particular, one might consider implementing a cut on the invariant mass of tjjb or Wjj or on mT of the tlb or Wl candidates. One can see in the plot that the semileptonic top-antitop signal allows reconstruction of a nice peak in the invariant mass of the hadronically decaying W boson. In the W+jets sample, the W boson decayed leptonically and no mass peak can be reconstructed using light flavor jets. The QCD multijets produced only virtual W bosons and could not produce a mass peak. One can see that this invariant mass might offer a means of discriminating against the W+jet and multijet backgrounds. If one were going to utilize the invariant mass of tjjb or Wjj then one would need to compare different methods of reconstruction. One would also need to consider the uncertainty introduced by the lack of knowledge of the JES. The most immediate goal is to prepare the analysis so that it is robust enough to run on data. I tend to believe that moving from analysis of Monte Carlo simulations to analysis of data is going to be a shock. tt  lb jjb, W  l, QCD

Conclusion Measurement of tt
Test of perturbative QCD Use to calibrate detector performance Prerequisite to observation of new signatures Observation of tt lb jjb will utilize all components of the detector Counting experiment using L=100 pb-1 W+N jets will be most significant background QCD multijet contribution determined from data Uncertainty tt determined by L ~ 20% - 30% Looking ahead to data Observation of tt pair production will be one of the most immediate goals of the ATLAS experiment once LHC operation begins. tt is interesting because it offers a test of theoretical predictions made using perturbative QCD. In addition, top quark events can be used to calibrate the detector performance. In particular these can be used to calibrate the JES, b-tagging performance, and the measurement of MET. Finally, it will be essential to perform a precise measurement of the top quark pair production cross section before an observation of many more exotic signatures is possible. We have seen that the observation of ttlb jjb will utilize all components of the detector. The tracking detector will be needed to measure the momenta of charged leptons and later to identify b jets. The calorimeters will be essential to measure jet and e- energy and to provide the MET. The muon spectrometer will be needed to identify and measure the momenta of muons. An observation of top quark production will therefore represent a small victory for the ATLAS collaboration. My goal is to perform a counting experiment using the first 100 pb-1 of integrated luminosity delivered by the LHC. Production of a W accompanied by several jets will be the most significant source of background. We have seen that the uncertainty due to a lack of knowledge of this background rate will be about 8%. The contribution from the QCD multijet background is highly uncertain and will have to be estimated from data. The uncertainty on the initial measurement of the pair production cross section will be determined by the uncertainty on the measurement of the absolute luminosity. The first measurement will be obtained using machine parameters which will not be well understood during the initial phase of operation. This source of uncertainty will decrease dramatically as new methods of measuring the luminosity become available. In summary, there is a lot which must be done before the analysis is ready for the first data. I think the advent of data will provide a moment of truth.

Backup Slides

References “The Large Hadron Collider”, Lyndon Evans, New Journal of Physics 9 (2007) “LHC Machine”, L. Evans, P. Bryant, JINST (2008) “Collider Physics”, Dieter Zeppenfeld (1998), hep-ph/ “The ATLAS Experiment at the CERN LHC”, JINST (2008) ATLAS Technical Design Report (1999) “ATLAS Forward Detectors for Measurement of Elastic Scattering and Luminosity”, ATLAS TDR 18 (2008) “The theoretical top quark cross section at the Tevatron and the LHC”, N. Kidonakis and R. Vogt (2008), hep-ph/ “Top Quark Physics at the LHC”, W. Bernreuther (2008), hep-ph/ “The Top Priority at the LHC”, Tao Han (2008), hep-ph/ “Top Studies for the ATLAS Detector Commissioning”, S. Bentvelsen, M. Cobal, ATL-PHYS-PUB (2005) Particle Data Group, “Precision Electroweak Measurements on the Z Resonance”, LEP and SLD (2006), hep-ex/ “Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions”, CERN-PH-TH/

Units 1 amu = GeV 1 barn = m2

Theory

Electroweak Precision Measurements
EM, GF, mZ → sin2θW  1 - (mW / mZ)2 mW2 ~ 1 / GF sin2 θW (1-▲r) ▲r contains all one-loop corrections to mW. (▲r)top ~ GFmt2 / tan2 θW To leading order in the SM all electroweak quantities depend on 3 parameters. The three best measurable electroweak quantities can be used to determine these three parameters: αEM, the Fermi constant GF, and the mass of the Z boson mZ. The electroweak mixing angle can thus be written in terms of the W boson mass. The mass of the W boson can then be expressed as a function of the electroweak mixing angle, the three electroweak parameters αEM, GF and mz, and a term ▲r which contains all one-loop corrections to the W mass. Contributions to ▲r from virtual top quark loops are proportional to the top mass squared. Contributions to ▲r due to Higgs boson loops are proportional to the logarithm of the Higgs mass. Because the loop corrections are proportional to mt2 and to ln(mH2), constraints on the top mass derived from electroweak precision measurements are much stronger than constraints on the Higgs mass. Beginning in 1995 the top quark mass has been measured directly at the Tevatron. The measured masses of the top quark and the W boson can now be used to constrain the mass of the SM Higgs. (▲r)Higgs ~ GF mW2 ln (mH2 / mZ2) 32

CKM Matrix The charged current W± couples to quarks q and q’ with coupling given by CKM matrix element Vqq’. The diagonal elements are close to unity,  = |Vus| = ± Branching ratios for decays which do not mix generations are thus close to unity. Vtb ≈ Γ(t→Wb) = |Vtb|2 = 0.998

Branching Ratios (W  e) = (10.80 ± 0.09)%
(W  jj) = (67.60 ± 0.27)% (tt → Wb Wb → lvb lvb) = 10.3% (tt → Wb Wb → lvb jjb) = 43.5% (tt → Wb Wb → jjb jjb) = 46.2% [Particle Data Group, C. Amsler et al; T. Liss and A. Quadt, 2008]

Single Top Production t channel exchange of W boson
s channel exchange of W boson associated production of real W and top

Luminosity and Machine

LHC Machine Parameters
Circumference: 26.7 km Operating temperature: 1.9 K Dipole field at 7 TeV: 8.33 Tesla Stored energy in magnets: 600 MJ Proton energy during injection: 0.45 TeV Proton energy during collisions: 7 TeV Protons per bunch: Number of bunches: 2808 Bunch crossing rate: 40 MHz Orbit frequency: kHz Beam current: 0.58 A Nominal bunch spacing: ns Design luminosity: 1034 cm-2s-1 Kinetic energy per beam: 362 MJ Power radiated per beam: 3.8 kW Inelastic events per crossing: 23 Nominal bunch width at interaction point: 16 m Total bunch length: 1.0 ns Normalized transverse emittance: 3.75 m Total longitudinal emittance: 2.5 eV s  at interaction point: 0.5m Crossing angle at interaction point: 320 rad

ATLAS Forward Detectors
LUCID “Luminosity measurement Using Cherenkov Integrating Detector” Array of Cherenkov tubes located 17 m from interaction point Detects inelastic p-p scattering in forward region Measures integrated luminosity Provides online monitoring of instantaneous luminosity Initial calibration based on machine parameters, L ~ 20% - 30% Later calibration provided by ALFA, L ~ 5% ALFA “Absolute Luminosity for ATLAS” Scintillating fibre trackers inside Roman pots Located 240 meters from interaction point Measures elastic Coulomb scattering at small angles Measurements performed under special beam conditions Final installation and first measurements in 2009

Measuring Luminosity Methods of measuring luminosity:
Measure rate of process with large, well-known cross section . R = dN / dt = L σ More applicable to e+e- colliders than to hadron colliders. Example: QED Babha scattering. Calculate luminosity using beam parameters. 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%

Uncertainty on Luminosity

Reconstruction

Selection Cuts Inclusive kT algorithm, E scheme, D=0.4. Hard Jet Cuts
No cuts are applied to lepton quantities Require at least four jets: |η| < 5.0 Lead jet must have pT(j1)>80 GeV Three subsequent jets must have pT(j)>40 GeV Selection Cuts Exactly one isolated, high-pT e or  E∆R=0.20 < 6 GeV pT(l) > 20 GeV, |η| < 2.5 Muons are reconstructed by Staco Electron candidates must: Be reconstructed by eGamma Fulfill (isEM==0) Exclude crack region in liquid argon calorimeter, 1.37<|η|<1.52 At least four jets |η| < 2.5 First three jets have pT(j) > 40 GeV Fourth jet has pT(j4) > 20 GeV Jets are removed if ∆R(j,e)<0.4 MET > 20 GeV.

Jet pT

Missing Transverse Energy
Neutrinos do not interact with the detector. Initial pT of colliding proton-proton system is zero. Conservation of momentum requires net pT of all decay products to be zero. Assumption: ET and pT of any object except  are measured perfectly. Then Σi ET + ET = 0 where sum is over all visible particles. Conclusion: “Missing Transverse Energy” (MET) is ETn ET = MET = -Σi ET Events which produced an energetic  have significant MET. Events which did not produce a  have little MET. Caveat: If two  were present, information is lost. Caveat: no measurement is perfect. Instrumental effects can result in energy imbalance and can ‘fake’ the  signature. Use known mass of W boson and W → l data to calibrate and test performance of MET reconstruction.

isEM: Quality Control for Electrons
Flag designed to identify electrons and reject jets Represents combinations of cuts imposed on reconstructed quantities Electromagnetic and hadronic calorimeters: Very little hadronic leakage (1st bit). Energy deposit in electromagnetic calorimeter is narrow in width (2nd bit). Energy deposit in electromagnetic calorimeter has one narrow maximum, no substructure (3rd bit). Inner detector: At least nine precision hits from pixel detector and semiconductor tracker; small transverse impact parameter. η and φ of track are extrapolated to calorimeter cluster; extrapolated and measured values are required to match. Energy measured in electromagnetic calorimeter is required to match momentum measured in inner detector. isEM == 0 demands that each electron candidate pass all cuts. An electromagnetic shower may deposit a small amount of energy in the hadronic calorimeter. This is termed ‘hadronic leakage’ and is defined to be the ratio of the transverse energy reconstructed in the first compartment of the hadronic calorimeter to the transverse energy reconstructed in the electromagnetic calorimeter. If the particle in question is an electron, the hadronic leakage will be small. If the particle in question is an energetic pion, the hadronic leakage will be much larger than that of an electron. An electromagnetic shower will deposit most of its energy in the second compartment of the electromagnetic calorimeter. An electron will exhibit very little lateral leakage and a narrow lateral width, whereas a jet may exhibit significantly more lateral leakage and a wider lateral width. Jets in which a 0 decays often exhibit a substructure consisting of two or more maxima in the energy deposited in the first compartment of the electromagnetic calorimeter. Jets exhibiting this substructure are discarded. Only very narrow showers containing exactly one reconstructed maximum are likely to be produced by an electron. Background produced by photon conversion and jets containing energetic 0 mesons can be reduced by requiring the presence of a high-quality track through the inner detector pointing to an electromagnetic cluster which provides an energy measurement consistent with the momentum measurement from the tracker. 4th bit imposes all restrictions derived only from quantities measured in calorimeter. 5th bit imposes only track-based cuts. 6th bit imposes all cuts except those derived from measurements performed by Transition Radiation Tracker.

Fake Leptons Electrons Muons
QCD multijet event is background if jet fakes electron Require isolated electrons ET (∆R < 0.2) < 6 GeV Muons QCD multijet event 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 QCD multijet events provide a source of background for semileptonic top-antitop decays if one of the jets fakes an isolated lepton. 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 QCD mutijet events 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.

Invariant Mass

Transverse Mass

HT The quantity called HT is the scalar sum of the transverse momenta of all high-pT objects in the event, including the missing transverse energy. HT relies upon the measurement of missing transverse energy and is highly dependent on the jet energy scale.

mT(W) and HT at CDF QCD multijets tend to have very low mTW
CDF: hep-ex/ A Tevatron plot of the transverse mass distribution of the leptonically decaying W boson is shown on the left. Note that b-tagging is used in this CDF analysis. In the Tevatron analysis a cut is implemented requiring mTW > 20 GeV. This eliminates the “Non-W” background, which is QCD multijets. On the right is shown a Tevatron plot of HT. At Tevatron energies this is a useful observable because top quark events tend to have a higher HT than background events. One of the selection cuts for top-antitop events at the Tevatron is HT > 200 GeV. QCD multijets tend to have very low mTW Cut at mTW > 20 GeV helps to eliminate QCD Top-antitop decays tend to have large HT Cut at HT > 200 GeV helps to select top pairs

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 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

Trigger L1 trigger L1_em25i requires
4x4 matrix of calorimeter towers 2x2 central core is “Region of Interest” 12 surrounding towers measure isolation L1_em25i requires ET>18 GeV in ROI in EM calorimeter ET<2 GeV in ROI in hadron calorimeter Isolation: ET<3 GeV in EM calorimeter ET<2 GeV in hadron calorimeter Event Filter requires ET>18 GeV εtrigger = 99% for electrons with pT>25 GeV. L1_mu20 requires ET>17.5 GeV. Sample 5200, tt→evbjjb events Event selection with pT(e) > 10 GeV

Trigger Trigger Efficiency in tt→evb jjb events
The trigger is a combination of hardware and software. It 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. Muons, electrons, and photons with high transverse momenta tend to indicate interesting events, as do jets with high transverse momenta, hadronically decaying tau leptons, and events with large missing transverse energy. One of the simplest trigger channels searches 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. I would now like to move on to present the results of trigger studies underway at the MPI. The lepton triggers relevant to the selection of semileptonic ttbar events are e25i and mu20. e25i searches for an isolated electron with transverse momentum pT>25 GeV whereas mu20 searches for a muon candidate with pT>20 GeV. The four plots shown here contain semileptonic and dileptonic events from ATLAS sample The events were selected using the standard cuts listed in the backup slides with a modified requirement placed on the transverse momentum of the lepton. The plots on the left-hand side represent the efficiency for the electron trigger as a function of the transverse momentum and pseudorapidity of the electron. The plots on the right-hand side represent the efficiency of the muon trigger as a function of the pseudorapidity and transverse momentum of the muon. The efficiency of each Level 1 Trigger is depicted in black, the efficiency of the corresponding Event Filter in red. The efficiency for the trigger system to observe an electron in a selected semileptonic ttbar event with electron is 84%. The efficiency for the trigger system to observe a muon in a selected semileptonic ttbar event with muon is 78%. The next step is to incorporate these results into our signal selection efficiency.

Backgrounds

Uncertainty on σW+Njets
“Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions” CERN-PH-TH/ Systematic Variation at Tevatron Systematic Variation at LHC Proton-antiproton collisions, 1.96 TeV, W±, Cone7 jets, ET(j)>10 GeV, |η|<2 Proton-proton collisions, 14 TeV, only W+, Cone4 jets, ET(j)>20 GeV, |η|<4.5

Matrix Method Method of estimating W→lv, QCD multijet contributions
Combines use of data, Monte Carlo Calculate efficiencies; obtain final numbers of events Use Monte Carlo to obtain εW lW is the number of events in the Monte Carlo sample which pass loose cuts lW’ is number of events which also pass tight cuts εW = lW’ / lW Use data to obtain εQCD MET < 10 GeV lQCD is number of events in QCD sample which pass loose cuts lQCD’ is number of events in QCD sample which pass tight cuts εQCD = lQCD’ / lQCD Matrix Method The Matrix Method provides a means of estimating the contributions due to the two main sources of background. In this analysis these main sources of background are events in which a W boson is produced in association with QCD radiation and also QCD multijet events in which a jet fakes the isolated lepton signature. The method applies the familiar algorithm of first calculating a selection efficiency then using the initial number of events to determine the final number of selected events. One would typically use a Monte Carlo generated sample in order to obtain the selection efficiency for W boson events. Let lW be the number of events in the Monte Carlo sample which contain at least one lepton which passes a set of loose selection cuts. lW’ is the number of events which contain at least one lepton which also passes a more stringent set of cuts. The efficiency for an event with a lepton which passed the loose cuts to also pass the tight cuts is then W. Because it is difficult to model the lepton fake rate accurately, one needs to use a data sample in order to obtain the efficiency for QCD multijet events. One can obtain a data sample which contains primarily QCD multijet events by requiring that the missing transverse energy be quite small. This tends to eliminate any events such as leptonic W boson decays which produce an energetic neutrino. lQCD represents the number of events in the QCD multijet sample which contain at least one lepton which passes the loose selection cuts. lQCD’ is the number of QCD multijet events which contain a lepton which also passes the more stringent cuts. The efficiency for a QCD multijet event which passed the loose cuts to also pass the tight cuts is then QCD. The leap of faith which I need to make here lies in assuming that an efficiency calculated using a sample with very low missing transverse energy will still be valid in a sample with higher missing transverse energy. Given enough data one could test this assumption by calculating the efficiency in several samples with various amounts of missing transverse energy.

Matrix Method S contains N events which passed loose lepton cuts
N = NQCD + NW S’ contains N’ events which passed tight lepton cuts N’ = NQCD’ + NW’ N’= εQCD NQCD + εW NW The number of W→lv events in S’ is NW’ = εW NW NW’= εW (εQCD N – N’) / (εQCD – εW) The number of QCD multijets in S’ is: NQCD’ = εQCD NQCD NQCD’ = εQCD (N’ – εW N) / (εQCD – εW) Matrix Method The initial data sample S contains a total of N events, each of which contained at least one lepton which passed the loose cuts. These initial events consist of QCD multijet events and W boson production. The selected data sample S’ contains N’ events, each of which contains at least one lepton which passed the more stringent set of cuts. We also know that the final number of events of each type is equal to the initial number of events of that type, multiplied by the selection efficiency. If I solve this system of equations for NW and insert the result into the equation for the final number of W decays, I obtain the above equation. Since we know the initial number of events N, the final number of events N’ and the selection efficiencies, we now know the final number of W decays. If instead I solve the system of two equations for NQCD and insert the result into the equation for the final number of QCD multijet events, I obtain the following equation. Once again all quantities on the right hand side are known and I have solved for the number of QCD multijet events in the final sample.

Samples

Samples Semileptonic and dileptonic ttbar events: MC@NLO and Herwig.
Sample 5200, TID 8037. Filter requires prompt lepton, σ*f = 461 pb. Hadronic ttbar events: Sample 5204, TID 6015. Filter forbids prompt lepton, σ*f = 369 pb. Single top samples: AcerMC and Pythia. Wt Production: sample 5500, TID 6958. σ*f = 25.5 pb, W→lv plus W→jj s channel: sample 5501, TID 6959. σ*f = 2.3 pb, filter requires W→lv. t channel: sample 5502, TID 6960. σ*f = 81.5 pb, filter requires W→lv.

Samples W+Njets events Alpgen and Herwig. Samples 8240-8250
Filter requires 3 jets pT>30 GeV, |eta|<5. QCD multijet events Samples 5061, 5062, 5063, 5064. σ*f=21188 pb, σ*f=53283 pb, σ*f=9904 pb, σ*f=6436 pb. Generated in , reconstructed in Filter requires 4 jets with |η|<6. Lead jet must have pT(j1)>80 GeV. 3 subsequent jets must have pT>40 GeV.

Samples for Consistency Check
Semileptonic and dileptonic ttbar events csc11 #5200, σ = 461 pb, mt = 175 GeV. Used ~10% of sample as “data”. Used remaining ~90% of sample as “Monte Carlo”. Ldata = 97 pb-1, Ndata ~ 45,000 LMC = 973 pb-1, NMC ~ 450,000. Reconstructed with Athena

Theoretical uncertainty on σ [pb]
Top Samples Process sample Cross section [pb] Theoretical uncertainty on σ [pb] εfilter σ*f [pb] L [pb-1] Weight (100 pb-1) Initial events Final events Efficiency [%] stat. uncertainty Wtd final events ttbar tt→(evb)(jjb) 5200 833 100 0.54 461 770.7 0.130 94304 17932 19.02 0.13 2327 tt→(μvb)(jjb) 94489 27975 29.61 0.15 3630 tt→(τvb)(jjb) 95292 4049 4.25 0.07 525 tt→(lvb)(lvb) 70324 6072 8.63 0.11 788 tt→(jjb)(jjb) 5204 0.46 369 190.6 0.525 65742 237 0.36 0.02 133 Single top Wt production 5500 25.5 421.6 0.237 10750 744 6.92 0.24 176 s channel 5501 2.3 5652 0.018 13000 159 1.22 0.10 3 t channel 4402 81.5 152 0.657 12400 437 3.52 0.17 287

W + N Jets Process Cross section [pb] Relative uncertainty on σ
MLM match rate εfilter σ*f [pb] L [pb-1] Weight (100 pb-1) Initial events Final events Efficiency [%] stat. uncertainty Wtd final events W→ev 2 partons 2032 0.20 0.402 0.262 214 593.0 0.1686 126916 102 17 3 partons 771 0.30 0.301 0.534 124 556.8 0.1796 69006 479 0.694 0.032 86 4 partons 273 0.40 0.252 0.78 53.7 232.3 0.4306 12463 680 5.456 0.203 293 5 partons 91 0.50 0.264 0.929 22.3 165.8 0.6032 3700 423 11.432 0.523 255 W→μv 0.020 16.3 260.1 0.3844 4250 82 1.929 0.211 32 0.304 0.276 64.7 185.5 0.5391 12000 304 0.253 0.143 164 0.229 0.576 36.0 446.4 0.2240 16073 1859 11.566 416 0.84 20.2 173.4 0.5766 3500 837 23.914 0.721 483 W→τv 0.415 0.104 87.7 233.2 0.4289 20450 9 0.044 0.015 4 0.303 0.373 87.1 149.2 0.6703 13000 0.246 0.043 21 0.245 0.686 45.9 119.9 0.8342 5500 79 1.436 0.160 66 0.866 20.8 525.4 0.1903 10930 328 3.001 0.163 62

Estimated Uncertainty on W+Jets
Process Alpgen cross section [pb] Relative uncertainty assigned to σ Nexp, low estimate central value high W+2 partons 2032 20% 42 53 63 W+3 partons 771 30% 190 271 352 W+4 partons 273 40% 465 775 1085 W+5 partons 91 50% 400 800 1200

Selection Efficiencies
Process Efficiency pT(j) > 42 GeV pT(j4) > 21 GeV pT(j) > 40 GeV pT(j4) > 20 GeV pT(j) > 38 GeV pT(j4) > 19 GeV Uncertainty due to ∆pT Relative uncertainty ttbar tt→(evb)(jjb) 0.175 0.190 0.206 0.015 0.081 tt→(μvb)(jjb) 0.272 0.296 0.321 0.025 0.084 tt→(τvb)(jjb) 0.0388 0.0425 0.0461 0.0036 0.085 tt→(lvb)(lvb) 0.0772 0.0863 0.0950 0.009 0.103 tt→(jjb)(jjb) 0.0034 0.0038 0.0002 0.061 Single top Wt production 0.0603 0.0692 0.0799 0.01 0.14 s channel 0.0101 0.0122 0.0142 0.002 0.17 t channel 0.0321 0.0352 0.0396 0.004 0.11 W→ev 2 partons 0.28 3 partons 0.25 4 partons 0.0468 0.0546 0.0627 0.008 5 partons 0.104 0.114 0.125 0.09 W→μv 0.0136 0.0193 0.0264 0.007 0.33 0.0208 0.0253 0.0323 0.23 0.0996 0.1157 0.1318 0.016 0.219 0.239 0.258 0.019 0.08 W→τv 0.0001 0.0022 0.0025 0.0033 0.0008 0.22 0.0124 0.0143 0.0173 0.003 0.0275 0.0300 0.0325

Efficiencies (L = 973 pb-1) Depicted here are the selection efficiencies derived from the Monte Carlo. In the left-hand plot are shown the selection efficiencies for semileptonic events with electron; in the right-hand plot are shown the selection efficiencies for semileptonic events with muon. Each of the three points along the horizontal axis represents a different cut on the momentum of the fourth jet. Because the luminosity was 900 pb-1, the statistical uncertainties on the efficiencies are too small to be visible on the plots. In general the efficiency for events reconstructed with the Cone4 algorithm is less than the efficiency for events reconstructed with the kT algorithm with D=0.4. This indicates a difference in the transverse momentum distributions of jets reconstructed with Cone4 versus those reconstructed with kT.

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