Dependence of the $t\bar{t}$ production cross section on the transverse momentum of the top quark

We present a measurement of the differential cross section for $t\bar{t}$ events produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV as a function of the transverse momentum ($p_T$) of the top quark. The selected events contain a high-$p_T$ lepton ($\ell$), four or more jets, and a large imbalance in $p_T$, and correspond to 1 fb${}^{-1}$ of integrated luminosity recorded with the D0 detector. Each event must have at least one candidate for a $b$ jet. Objects in the event are associated through a constrained kinematic fit to the $t\bar{t}\to WbW\bar{b} \to \ell\nu b q\bar{q}'\bar{b}$ process. Results from next-to-leading-order perturbative QCD calculations agree with the measured differential cross section. Comparisons are also provided to predictions from Monte Carlo event generators using QCD calculations at different levels of precision.

The transverse momentum (p T ) of top quarks in tt events provides a unique window on heavy-quark production at large momentum scales. In the standard model (SM), the lifetime of the top quark is far shorter than the characteristic hadron-formation time of quantum chromodynamics (QCD), which provides access to the properties and kinematics of a "bare" quark, such as mass, charge, spin, and p T , that are almost unaffected by bound-state formation or final-state interactions [8]. The top quark is unique in that it has a mass close to the scale of electroweak symmetry breaking. Detailed studies of the properties of this bare quark beyond the measure-ment of its total production rate, such as the measurement of its quantum numbers and of its couplings to other SM particles, may indicate whether the top quark plays a privileged role in the symmetry breaking. Focusing on details of the tt production, measurements of differential cross sections in the tt system test perturbative QCD (pQCD) for heavy-quark production and can constrain potential new physics beyond the SM [9], e.g., by measuring the transverse momentum of the top quark [10].
In this Letter, we present a new measurement of the inclusive differential cross section for pp → tt + X production at √ s = 1.96 TeV as a function of the p T of the top quark. The measurement is corrected for detector efficiency, acceptance and resolution effects, making it possible to perform direct comparisons with different theoretical predictions. The data were acquired with the D0 detector at the Fermilab Tevatron Collider and correspond to an integrated luminosity of ≈ 1 fb −1 . This measurement was performed in the ℓ+jets decay channel of tt → W bWb → ℓν + bb + ≥ 2 jets, where ℓ represents an e or µ from the decay of the W boson or from W → τ → ℓ. The dependence of the cross section on the p T of the top quark was examined previously using ≈ 100 pb −1 of Tevatron Run I data at √ s = 1.8 TeV [11], where no deviations from the SM were reported.
The D0 detector [12] is equipped with a 2 T solenoidal magnet surrounding silicon-microstrip and scintillatingfiber trackers. These are followed by electromagnetic (EM) and hadronic uranium/liquid argon calorimeters, and a muon spectrometer consisting of 1.8 T iron toroidal magnets and wire chambers and scintillation counters. Electrons are identified as track-matched energy clusters in the EM calorimeter. Muons are identified by matching tracks in the inner tracking detector with those in the muon spectrometer. Jets are reconstructed from calorimeter energies using the Run II iterative seed-based midpoint cone algorithm with a radius of 0.5 [13]. Jets are identified as originating from a b quark using an artificial neural network (b NN) which combines several tracking variables [14]. Large missing transverse energy, E T (the negative of the vector sum of transverse energies of calorimeter cells, corrected for reconstructed muons) signifies the presence of an energetic neutrino. Events are selected using a three-level trigger system, which has access to tracking, calorimeter, and muon information, and assures that only events with the desired topology or with objects above certain energy thresholds are kept for further analysis.
The analysis uses similar data samples, event selection, and corrections as used in the inclusive tt → ℓ+jets cross-section measurements detailed in Ref. [15]. Events accepted by lepton+jets triggers are subject to additional selection criteria including exactly one isolated lepton with p T > 20 GeV/c and ≥ 4 jets with p T > 20 GeV/c and |η| < 2.5 [16]; at least one jet must have p T > 40 GeV/c. At least one jet is also required to be tagged by the b NN algorithm. Additionally, we require E T > 20 GeV (25 GeV) for the e+jets (µ+jets) channel and electrons (muons) with |η| < 1.1 (2.0).
Our measurement uses the alpgen [17] event generator, with pythia [18] for parton showering, hadronization, and modeling of the underlying event, to simulate the inclusive tt signal. A pythia sample serves as a cross check. The CTEQ6L1 set of parton distribution functions (PDFs) [19] was used with a common factorization and renormalization scale set to µ = m t + p jets T for m t = 170 GeV/c 2 . Backgrounds are modeled with alpgen+pythia for W +jets and Z+jets production, pythia for diboson (W W , W Z, and ZZ) production, and comphep [20] for single top-quark production. The detector response is simulated using geant [21]. The simulated tt signal is normalized to the cross section measured by a dedicated likelihood fit in the same final state using the same event selections (including the b-tagging requirement) and data as Ref. [15], namely to 8.46 +1.09 −0.97 pb at a top-quark mass m t = 170 GeV/c 2 (in good agreement with the value extracted in this study by integrating the differential cross section). The diboson and single top-quark backgrounds are normalized to their SM predictions, Z+jets to the prediction from nextto-leading-order (NLO) pQCD, and W +jets such that the predicted number of events matches the data before applying b tagging.
The small multijet background, in which a jet is misidentified as an isolated lepton, is non-negligible only in the e+jets channel. Its rate is estimated from data using the large difference in the probability of electromagnetic showers of real electrons or misidentified jets to satisfy the electron selection criteria. The details of the sample composition and the observed yields before and after requiring the jets to be tagged as b-jet are presented in Table I.
The selection yields 145 and 141 events in the e+jets and µ+jets decay channels, respectively. The measured tt signal fraction is 0.79, indicating that this sample is suitable for detailed studies of tt production. A constrained kinematic fit to the tt final state, which takes  into account the unreconstructed neutrino and finite experimental resolution, is used to associate leptons and jets with individual top quarks [22,23]. The fit assumes equal masses for the two reconstructed top quarks and the two reconstructed W boson masses are constrained to 80.4 GeV/c 2 . All possible permutations of objects needed to produce the tt system are considered, and the solution of fitted leptonic and hadronic top-quark fourmomenta with the smallest χ 2 (the goodness of the fit) is selected for further analysis. The b-jet assignment information is not used in the selection of the best permutation to avoid the associated efficiency loss. The effects of possibly selecting a wrong permutation when choosing the one with the best χ 2 are taken into account in the corrections of the measurement to the parton level. The solution with the best (second best) χ 2 corresponds to the correct assignment of the quarks from the decay of the tt pair in 48% (17%) of events.
The reconstructed top-quark mass (m t ) from the best fit in data, simulated tt signal, and background is shown in Fig. 1. There is good agreement between the data and the sum of signal and background expectations in terms of the shape, resolution, and mean of the distribution in m t (χ 2 /NDF = 1.28). The p T spectrum of the top quark (for leptonic and hadronic entries) in data, together with predicted signal and background, is shown in Fig. 2 for the best solution but now refitted with a top-quark mass fixed to 170 GeV/c 2 (the value used in the inclusive cross section measurement [15]) to improve resolution. To obtain a background-subtracted data spectrum, the signal purity is fitted using signal and background contributions as a function of p T , and applied as a smooth multiplicative factor to the data. The result is the backgroundcorrected distribution shown as a solid line in Fig. 3.
The reconstructed p T spectrum is subsequently corrected for effects of finite experimental resolution, based on a regularized unfolding method [24,25] using a migration matrix between the reconstructed and parton p T derived from simulation. The size of the p T bins was chosen based on the requirement that the purity (the fraction of parton-level events which are reconstructed in the correct p T range) is > 50%, as shown in Table II. This also results in p T bins which are larger than the experimental resolution for the top quark p T . The correlation between reconstructed and correct p T is > 80%. Figure 3 compares the reconstructed and corrected results as a function of the p T of the top quark. The dependence of the unfolding on the parton spectrum shape in the migration matrix is tested by reweighting the distribution with arbitrary functions. Shape variations of ≈ 20% induce 2−6% changes in the differential cross section. A correction for acceptance from the dependence of the spectrum on kinematic restrictions of reconstructed quantities is applied to the unfolded distributions.
The measured differential cross section as a function of the p T of the top quark (using for each event the two measurements obtained from the leptonic and hadronic top quark decays), dσ/dp T , is shown in Fig. 4 and tabulated in Table III together with the NLO pQCD prediction [26,27]. The statistical uncertainties are estimated by performing 1000 pseudo-experiments where, in each experiment, the background-corrected spectrum is allowed to vary according to Poisson statistics and is then unfolded using the regularized migration matrix (Table II). The largest experimental uncertainties affecting the shape of the p T distribution include jet energy calibration in data and in simulation (1.5 − 5.0%), jet reconstruction efficiency (0.7 − 3.5%), and jet energy resolution (≈ 0.5%). The residual dependence of the un-   folded result on the top-quark mass is 2 − 6% for m t in the 170-175 GeV/c 2 range. This additional uncertainty does not need to be considered for comparisons with models in which m t is set to 170 GeV/c 2 . For the main background sources, W/Z+jets, we have also considered the variations of the background shape caused by uncertainties in the k-factors and in additional scale factors for heavy-flavour jets. Other systematic uncertainties [15] account for uncertainties in the modeling of the signal, estimated from the difference between alpgen and pythia, for uncertainties in the PDFs and in the bquark fragmentation. The uncertainty on the integrated luminosity is 6.1%. The systematic uncertainties quoted in the following combine the uncertainty on the normalization (independent of p T ) with the shape-dependent systematics. The total correlated systematic uncertainty is 9.6% (including the uncertainty on luminosity) and the total systematic uncertainty on the cross section, integrating over p T , is 10.7%. Results from NLO pQCD [26,27] calculations obtained using CTEQ61 [28] PDFs (using the scale µ = m t = 170 GeV/c 2 ) are overlaid on the measured differential cross section in Fig. 4. Also shown are results from an approximate next-to-NLO (NNLO) pQCD calculation [29] computed using MSTW2008 NLO PDFs [30] and same scales choices as the NLO result, and from the mc@nlo [31] (using CTEQ61 PDFs), alpgen, and pythia event generators. The QCD scale uncertainty was evaluated for the NLO pQCD calculation [26,27]  by varying µ = m t = 170 GeV/c 2 by factors of 2 and 1/2, and the PDF uncertainty by the approximate NNLO code [29]. The total uncertainty is < 4% with only a small (< 1%) shape variation. A comparison of the ratio of dσ/dp T relative to a NLO pQCD calculation is shown in Fig. 5. The NLO pQCD calculations agree with the measured cross section, however, results from alpgen (pythia) have a normalization shift of about 45% (30%) with respect to data. A shape comparison of the ratio of (1/σ) dσ/dp T relative to NLO pQCD is shown in Fig. 6. All of the calculations reproduce the observed shape. The χ 2 and corresponding χ 2 probabilities [32] for the comparisons in Figs. 5 and 6 of predictions to data are given in Table IV.
In conclusion, we have presented a 1 fb −1 measurement of the differential cross section of the top-quark p T for tt production in the ℓ+jets channel using pp collisions at √ s = 1.96 TeV. Results from NLO and NNLO pQCD calculations and from the mc@nlo event generator agree with the normalization and shape of the measured cross section. Results from alpgen+pythia and pythia describe the shape of the data distribution, but not its normalization. We thank the staffs at    The gray band encompasses uncertainties on the scale of pQCD and parton distribution functions. Also shown are ratios relative to NLO pQCD for an approximate NNLO pQCD calculation and of predictions for several event generators. Inner and outer error bars represent statistical and total (statistical and systematic added in quadrature) uncertainties, respectively.