Measurement of the tt̄ production cross section using dilepton events in pp̄ collisions

We present a measurement of the a production cross section sigma((u) over bar) in p (p) over bar collisions at root s = 1.96 TeV using 5.4 fb(-1) of integrated luminosity collected with the D0 detector. We consider final states with at least two jets and two leptons (ee, e mu, mu mu), and events with one jet for the e mu final state as well. The measured cross section is sigma((u) over bar) = 7.36(-0.79)(+0.90)(stat + syst) pb. This result combined with the cross section measurement in the lepton + jets final state yields sigma((u) over bar) = 7.56(-0.56)(+0.63)(stat + syst) pb, which agrees with the standard model expectation. The relative precision of 8% of this measurement is comparable to the precision of the latest theoretical calculations. (C) 2011 Elsevier B.V. All rights reserved.

We present a measurement of the tt production cross section σ tt in pp collisions at √ s = 1.96 TeV using 5.4 fb −1 of integrated luminosity collected with the D0 detector. We consider final states with at least two jets and two leptons (ee, eµ, µµ), and events with one jet for the the eµ final state as well. The measured cross section is σ tt =7.36 +0.90 −0.79 (stat + syst) pb. This result combined with the cross section measurement in the lepton + jets final state yields σ tt =7.56 +0.63 −0.56 (stat + syst) pb, which agrees with the standard model expectation. The relative precision of 8% of this measurement is comparable to the precision of the latest theoretical calculations.

I. INTRODUCTION
The precise measurement of the top quark pair (tt) production cross section (σ tt ) and its comparison with the theoretical predictions provide important tests of perturbative quantum choromodynamics (QCD). At present, the most precise predictions of σ tt are given by approximate next to next-to-leading order (NNLO) calculations [1][2][3], that set a goal for the experimental precision of the σ tt measurement of (6 -9)%. Furthermore, because σ tt depends on the top quark mass (m t ), it can * with visitors from a Augustana College, Sioux Falls, SD, USA, b The University of Liverpool, Liverpool, UK, c SLAC, Menlo Park, CA, USA, d University College London, London, UK, e Centro de Investigacion en Computacion -IPN, Mexico City, Mexico, f ECFM, Universidad Autonoma de Sinaloa, Culiacán, Mexico, and g Universität Bern, Bern, Switzerland. be used to measure m t [4,5]. Comparing the standard model (SM) prediction with the measured σ tt value allows testing for the presence of physics beyond the SM, for instance, scenarios in which the top quark would decay into a charged Higgs boson and a b quark [5].
In this Letter we present an updated measurement of σ tt in pp collisions at √ s = 1.96 TeV in the dilepton (ℓℓ ′ , ℓ = e, µ) channel. Within the SM, top quarks decay almost 100% of the time into a W boson and a b quark. We consider the leptonic decays of both W bosons from top quark decay into eν e , µν µ , or τ ν τ (throughout this letter, e, µ, τ refer to both charge conjugate states: e ± , µ ± or τ ± ), where only leptonic decays of the τ are considered.
This measurement complements the σ tt measurements in the lepton+jets (ℓj) channel, in which one of the W bosons decays hadronically into a qq ′ pair and the other W boson decays leptonically [6,7], as well as measurements in the all-hadronic channel, in which both W bosons decay hadronically [8].
The measurement is based on data collected with the D0 detector during Run II of the Fermilab Tevatron Collider that correspond to an integrated luminosity of 5.4 ± 0.3 fb −1 . This result supersedes our previous measurement [9], which used a dataset five times smaller than the one considered here. The CDF Collaboration has measured σ tt in the ℓℓ ′ channel using 2.8 fb −1 of integrated luminosity [10]. The ATLAS and CMS Collaborations recently published their first σ tt measurements in pp collisions at √ s = 7 TeV [11,12]. The D0 detector is described in detail in [13]. The region of the D0 detector closest to the interaction region contains a tracking system consisting of a silicon microstrip tracker and a central fiber tracker, both located inside a superconducting solenoid magnet which generates a magnetic field of 2 T. Hits in these two detectors are used to reconstruct tracks from charged particles in the pseudorapidity region |η| < 3 [30]. Surrounding the two tracking subdetectors are liquid-argon uranium calorimeters, segmented into electromagnetic and hadronic sections. The central section of the calorimeter (CC) covers pseudorapidities |η| < 1.1, and the two end calorimeters (EC) extend coverage to |η| ≈ 4.2 with all three housed in separate cryostats. The muon system surrounds the calorimeter and consists of three layers of tracking detectors and scintillator trigger counters covering |η| < 2. A toroidal iron magnet with a field of 1.8 T is located outside the innermost layer of the muon detector. The luminosity is calculated from the rate of inelastic pp collisions measured with plastic scintillator arrays located in front of the EC cryostats [14].
The D0 trigger is based on a three-level pipeline system. The first level is implemented in custom-designed hardware. The second level uses high-level processors to combine information from the different sub-detectors to construct simple physics objects. The software-based third level uses full event information obtained with a simplified reconstruction algorithm.

II. OBJECT IDENTIFICATION
The tt dilepton final state contains two leptons (electrons, muons or an electron and a muon), at least two jets, and significant missing transverse momentum (/ p T ) from escaping neutrinos.
Electrons are identified as energy clusters with radius R = (∆η) 2 + (∆φ) 2 < 0.2 in the calorimeter (φ is the azimuthal angle) which are consistent in their longitudinal and transverse profiles with those of an electromagnetic shower. More than 90% of the energy of the electron candidate must be deposited in the electromagnetic part of the calorimeter, and less than 20% of its energy may be deposited in an annulus of 0.2 < R < 0.4 around its direction. This cluster has to be matched to an inner detector track. We consider electrons in the CC with |η| < 1.1 and in the EC with 1.5 < |η| < 2.5. In addition, we make a requirement on the electron likelihood discriminant, based on tracking and calorimeter information, at a cut value chosen to have a high selection efficiency (near 85%) for electrons, and good rejection (near 90%) for jets misidentified as electrons. Electrons fulfilling all these criteria are called "tight electrons".
A muon is identified as a segment in at least one layer of the muon system in the full acceptance of the muon system that is matched to a track in the central tracking system. Reconstructed muons must satisfy two isolation criteria. First, the transverse energy deposited in an annulus around the muon 0.1 < R < 0.4 (E µ,iso T ) has to be less than 15% of the transverse momentum of the muon (p µ T ). Second, the sum of the transverse momenta of the tracks in a cone of radius R < 0.5 around the muon track in the central tracking system (p µ,iso T ) has to be less than 15% of p µ T . Muons that fulfill these isolation criteria are referred to as "tight isolated muons".
Monte Carlo (MC) generated events are processed through a geant3 [15] based simulation of the D0 detector and the same reconstruction programs used for the data. To simulate the effects from additional pp interactions, zero bias events with no trigger requirements selected randomly in collider data are overlayed on the fully simulated MC events. Residual differences between data and MC simulation in the electron and muon p T resolutions and identification efficiencies are corrected. These corrections are derived from a sample of Z/γ ⋆ → ℓℓ events in data and MC, applying tight requirements on one of the two leptons for selecting the events and using the other one to measure the efficiencies and resolutions.
Jets are identified with a cone algorithm with radius R < 0.5 [16] in the range |η| < 2.5. A jet energy scale correction (JES) is determined by calibrating the energy deposited in the jet cone using transverse momentum balance in γ+jet and dijet events. If a muon overlaps with the jet cone, the momentum of that muon is added to the jet p T , assuming that the muon originates from a semileptonic decay of a hadron belonging to the jet.
We require that the jets be matched to at least two tracks originating from the vertex of the primary pp interaction (PV). Jets in MC are corrected for the residual differences between data and MC in the energy resolution and JES. These correction factors are measured by comparing data and MC in (Z/γ ⋆ → ee)+jets events.
We use a neural-network (NN) tagging algorithm [17] to identify jets from b quarks. The algorithm combines information from the impact parameters of the tracks and variables that characterize the presence and properties of secondary vertices within the jet in a single discriminant.
In order to use this information for b tagging, the jet is required to be matched to a jet built from tracks. Jets fulfilling this requirement are called taggable jets. The NN discriminant has a value close to one for the b quark jets and close to zero for the light quark and gluon jets.
The / p T is reconstructed from the energy deposited in the calorimeter cells. Corrections for lepton and jet p T are propagated into the / p T . The missing transverse mo-mentum significance (σ / pT ) is defined in each event as a likelihood discriminant constructed using the ratio of / p T to its uncertainty.
More details about object identification can be found in [18].

III. EVENT SELECTION AND BACKGROUND ESTIMATION
The main sources of background in the ℓℓ ′ channel come from Drell-Yan and Z boson production (Z/γ ⋆ → ℓℓ), diboson production (WW, WZ, ZZ ), and instrumental background. The instrumental background mainly arises from multijet and (W → ℓν)+jets events in which one or two jets are misidentified as electrons and/or muons originating from the semileptonic decay of a heavy flavor hadron.
For this analysis we consider events that passed at least one of a set of single lepton triggers for the ee and µµ channels. For the eµ channel, we consider events selected by a mixture of single and multilepton triggers and lep-ton+jet triggers. Efficiencies for single lepton triggers have been measured with Z/γ ⋆ → ℓℓ data. These efficiencies are found to be around 99% for the ee channel and 80% for µµ. For the eµ channel the trigger efficiency is close to 100%.
In order to separate tt signal events from background, the following selection is applied: • We require at least one PV in the beam interaction region with |z| < 60 cm, where z is the coordinate along the beam axis, and z = 0 in the center of the detector. At least three tracks must be associated with this PV.
• We require at least two isolated leptons with p T > 15 GeV, originating from the same PV, i.e., the difference between the z coordinates of the two lepton tracks should be less than 2 cm, where the z coordinate is calculated at the point of the track's closest approach to the beam.
• We select the two highest p T leptons with opposite charges.
• In the eµ final state, we require the distance between the electron and the muon directions to be R(e, µ) > 0.3 to reduce the background from bremsstrahlung.
• In the eµ channel, we consider events with at least one jet with p T > 20 GeV. In the ee and µµ channels, we require at least two jets with p T > 20 GeV.
• To further improve the signal purity of the selected sample, we apply additional selection criteria based on global event properties. In the eµ channel with exactly one jet, we require H T > 105 GeV, where H T is the scalar sum of the transverse momenta of the leading lepton and the two leading jets. In the eµ final state with two jets, we require H T > 110 GeV. In the ee final state, we require σ / pT > 5, while in the µµ channel we require / p T > 40 GeV and σ / pT > 5.
In order to estimate the signal efficiency and the background contamination, we use the MC simulation for all contributions but for the instrumental background, the latter being derived from data. The tt and Z/γ ⋆ events are generated with the tree level matrix element generator alpgen [19] interfaced with the pythia [20] generator for parton showering and hadronization. Diboson events are generated with pythia. All simulated samples are generated using the CTEQ6L1 parton distribution functions (PDFs) [21]. The Z/γ ⋆ samples are normalized to the NNLO cross section computed with the fewz program [22]. We separately simulate Z/γ ⋆ with heavy flavor (HF) quarks, Z/γ ⋆ +bb (or Z/γ ⋆ +cc), using alpgen and enhance the corresponding leading order cross sections by a factor estimated with the mcfm program [23]. The diboson samples are normalized to the next-to-leading order cross section calculated with mcfm. Uncertainties in these normalization factors are taken into account as systematic uncertainties. In addition, we apply a correction to the Z/γ ⋆ +jets simulation based on data to address the imperfect modeling of the Z boson p T in the MC [24].
The instrumental background is estimated directly from data. In the ee and eµ channels we determine the contribution of events with jets misidentified as electrons using the signal data sample but without the electron likelihood discriminant requirement. We extract the number of events with jets misidentified as electrons, n f , and the number of events with real electrons, n e , by maximizing the function of the electron likelihood distribution where N is the number of selected events, x i is the electron likelihood discriminant value in the event i, and S(x i ) and B(x i ) are the signal and background probability density functions (pdfs). The signal pdf is measured in Z/γ ⋆ → ee data events. The background pdf is measured in eµ events with the same selection as the analysis sample but inverting the opposite sign lepton requirement (i.e., requiring leptons of the same sign) without any topological requirement but using muon with reversed isolation requirements: E µ,iso T /p µ T > 0.2 and p µ,iso T /p µ T > 0.2. The total number of events with a jet misidentified as an electron is given by n f scaled for the integral of B(x) over the region satisfying the likelihood requirement. The estimation is performed separately in the CC and EC. We find that the contribution of instrumental background to the ee channel is negligible. The limited size of the sample used to measure the background pdf is the main contribution to the systematic uncertainty on the instrumental background. Together with a possible p T dependence of the signal and background pdfs, these sources typically lead to systematic uncertainties of about 50%.
We also determine the number of events with an isolated muon arising from jets in the eµ and µµ channels. This number is estimated as n µ f = N loose f µ , where N loose is the number of events in the same sign sample with loose isolation criteria on the muon: E µ,iso T /p µ T < 0.5 and p µ,iso T /p µ T < 0.5, and f µ is the misidentification rate for isolated muons. In the µµ final state, we apply these loose isolation criteria only to one randomly chosen muon. In the eµ channel, the number of events with jets misidentified as electrons in the same sign sample is subtracted from N loose . The misidentification rate, f µ , is determined in a dimuon sample with at least one jet. In this sample we require one muon to be close to the jet (R(µ, jet) < 0.5) with reversed isolation criteria E µ,iso T /p µ T > 0.15 and p µ,iso T /p µ T > 0. 15. The other muon defined as the probe, should pass the loose isolation criteria E µ,iso T /p µ T < 0.5 and p µ,iso T /p µ T < 0.5. We compute f µ as the ratio of the number of events in which the probe muon passes the tight isolation criteria to the total number of events in this same sign sample. The systematic uncertainty on the f µ determination is about 10% and results mainly from the statistical uncertainty due to the limited size of the sample used for the muon misidentification rate calculation and the potential dependence of the misidentification rate on p T and / p T . The number of predicted background events as well as the expected number of signal events in the four channels are shown in Table I. The tt events have two b quark jets in the final state, but most of the background events have jets produced by light quarks or gluons. In order to achieve a better separation between signal and background when measuring the cross section, we use the distribution of the smallest of the two b-tagging NN discriminants of the two leading jets. If a jet does not satisfy the requirements to enter the NN computation (non-taggable jet), a value of -1 is assigned to it. These NN discriminant distributions for the different channels are shown in Fig. 1 We measure the tt cross section σ tt by simultaneously fitting the NN distributions in the four channels and maximizing the likelihood function where i runs over the channels and j over the bins of the NN distribution, and P [n, µ(σ tt )] is the Poisson probability function to observe n events when µ(σ tt ) events are expected.

IV. RESULTS AND UNCERTAINTIES
The main systematic uncertainties for the measurement of the tt cross section are described in the following. A 6.1% uncertainty [14] directly affects the cross section measurement because of the luminosity uncertainty but also the expected numbers of Z/γ ⋆ and diboson background events. Uncertainties in lepton identification efficiencies are determined by evaluating possible sources of bias in the data driven method used for the efficiency measurements and the possible impact of data/MC differences in Z/γ ⋆ → ℓℓ events. Uncertainties in the lepton energy resolution are determined by comparing the width of the Z boson invariant mass distributions in data and MC.
The uncertainty in the relative JES between data and MC for light quark jets has been evaluated by shifting the jets in MC by their corresponding JES uncertainty. The uncertainty on the difference between the light and b quark JES (1.8%) is estimated by propagating the difference in the single pion response between data and MC to the MC JES for b quark jets. Jet energy resolution uncertainties are estimated by comparing the resolutions measured in Z/γ ⋆ +jets events in data and in MC. The uncertainty on the jet identification efficiency is estimated by comparing the efficiencies measured in dijet events for data and MC. The b quark identification uncertainties include uncertainties in the probability of tagging a b quark jet, the probability of tagging a light quark jet or gluon, and the probability for a jet not to be taggable [17].
To estimate the uncertainty in the trigger efficiency, we use events selected with the same criteria as the tt signal but without jet requirements. In all four channels this selection is dominated by Z/γ ⋆ events. We compute the ratio of the expected and observed number of events for two cases: when both leptons are allowed to fire the trigger or when only one lepton is allowed to fire the trigger. The difference in these ratios is used to estimate the uncertainty on the trigger efficiency.
Several uncertainties on the signal modeling are considered. The effects of higher order corrections and the hadronization modeling are estimated as the difference in signal efficiencies using the default alpgen+ pythia simulation and using events generated with the mc@nlo [25] + herwig [26] simulation. The uncertainty coming from color reconnection is evaluated by comparing the tt efficiency using pythia v6.4 tune Apro and pythia v6.4 tune ACRpro [27]. The uncertainty on initial (ISR) and final (FSR) state radiation is evaluated by varying the ISR/FSR parameters in pythia up to 20% and evaluating the change in the signal efficiency. The uncertainty due to PDFs is estimated by reweighting the signal efficiency to the CTEQ6.1M PDFs [21] and looking at the efficiency variation for each eigenvector set that define the CTEQ6.1M uncertainty range. The uncertainty due to the simulation of b quark fragmentation is assigned to be the difference between tuning the parameters of the b quark fragmentation function to LEP or SLD data [28].
The uncertainty in the background normalization includes the theoretical uncertainties in the cross section and the uncertainty due to the correction for the Z boson b-tagging NN discriminant . The x axis represents the NN output non-uniformly mapped to 14 bins. The bin with central value 0 represents the lowest probability for a jet to be produced by a b quark. The bin with value 12 represents the highest probability. The bin with value −1 represents the jets which do not satisfy the requirements to enter the NN computation (non-taggable jets).
p T modeling. We also take into account an uncertainty due to the limited statistics of the signal and background templates of the NN discriminant. For the following systematic uncertainties, we take into account effects that change the shape of the differential distribution of the b-tagging NN output discriminant: jet energy scale, jet resolution, jet identification, and b quark identification uncertainties.
Maximizing the likelihood function in Eq. 2 and using the above systematic uncertainties, we measure the cross section assuming a top quark mass m t = 172.5 GeV and find σ tt = 8.05 +0.50 −0.48 (stat) +1.05 −0.97 (syst) pb.
In order to reduce the influence of systematic uncertainties on the cross section measurement, in the fol-lowing we use nuisance parameters [29] to constrain the overall uncertainty using the data NN output distribution itself. Using this technique, the likelihood (Eq. 2) is modified, where G(ν k ; 0, SD) denotes the Gaussian probability density with mean at zero and width corresponding to one standard deviation (SD) of the considered systematic uncertainty. Correlations of systematic uncertainties between channels and between the different samples are naturally taken into account by assigning the same nuisance parameter to the correlated systematic uncertainties. In Eq. 4, the free parameters of the fit are ν k and As can be seen from Eq. 3, the systematic uncertainties are the limiting uncertainties in the precision of the tt cross section measurement. Varying the systematic uncertainties and constraining them with data can therefore improve the measurement. Using nuisance parameters we find an overall improvement of the uncertainty of 20% and reach a relative precision of 11% in the tt cross section: The uncertainties on the tt cross section are summarized in Table II. For each category of systematic uncertainty listed in Table II, the corresponding nuisance parameters are set to their fitted value, and shifted by the uncertainty on the fit. In the columns "+σ" and "−σ," the positive and negative systematic uncertainties on the measured cross section for each category are listed.
We combine this measurement with the cross section measurement in the non-overlapping ℓj channel [6] using the same nuisance parameter approach and taking correlations between common systematics uncertainties into account. In the ℓj channel, the events are separated into events with three or at least four jets, of which zero, one, or at least two jets are b-tagged. In events that have three or four jets but no b-tagged jets or events with three jets and one b-tagged jet, we use a topological discriminant to improve the separation of signal and background. In [6], the separation into these channels and application of topological methods is referred to as the combined method. For this combination, we do not simultaneously fit the heavy flavor fraction for W +jet processes (W +HF) in the ℓj channel as was done in [6], making it unnecessary to use ℓj events with only two jets. With this change compared to [6], the measured ℓj tt cross section is σ tt = 7.90 +0.78 −0.69 (stat + syst) pb.
The combination of the measurements in the dilepton and lepton + jet final states is done by maximizing the product of the likelihood function for the ℓℓ ′ and ℓj channels, which yields σ tt = 7.56 +0.63 −0.56 (stat + syst) pb for m t = 172.5 GeV. This combination has a relative precision of 8% and represents an improvement of about 12% relative to the ℓj cross section measurement alone. The uncertainties for this combined measurement are summarized in Table II. Due to acceptance effects, the tt efficiency depends on the assumed m t in the MC. We extract the tt cross section using simulated tt events with different values of m t . The resulting cross sections can be fitted with the following functional form: with a = 6.5178 × 10 9 GeV 4 , b = 7.884 × 10 7 GeV 3 , c = 9.3069 × 10 5 GeV 2 , and d = −2.42 × 10 3 GeV and where σ tt and m t are in pb and GeV, respectively. The relative uncertainty on the cross section for different mass points is the same as the one obtained for m t = 172.5 GeV. Figure 2 shows this parameterization for the measurement as a function of top quark mass together with approximate NNLO computations [1][2][3].

V. CONCLUSION
In this Letter we presented an updated measurement of the tt production cross section in the dilepton final state using 5.4 fb −1 of integrated luminosity. This cross section measurement yields σ tt =7.36 +0.90 −0.79 (stat + syst) pb and has a relative precision of +12% −11% . It is currently the most precise measurement of the tt cross section in the dilepton channel. Combining this measurement with our result in the lepton + jets channel [6] yields 7.56 +0.63 −0.56 (stat + syst) pb which corresponds to a relative precision of 8%. This measurement is in good agreement with the SM prediction.