5 purity is fitted using signal and background contributions as a function of p$_{T}$ , and applied as a smooth multiplica- tive factor to the data. The result is the background- corrected distribution shown as a solid line in Fig. 3. The reconstructed p$_{T}$ spectrum is subsequently cor- rected for effects of finite experimental resolution, based on a regularized unfolding method [24, 25] using a mi- gration matrix between the reconstructed and parton p$_{T}$ derived from simulation. The size of the p$_{T}$ bins was cho- sen based on the requirement that the purity (the fraction of parton-level events which are reconstructed in the cor- rect 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 com- pares the reconstructed and corrected results as a func- tion 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 arbi- trary 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 kine- matic restrictions of reconstructed quantities is applied to the unfolded distributions. into account the unreconstructed neutrino and finite ex- perimental 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 t ¯ t system are considered, and the solution of fitted leptonic and hadronic top-quark four- momenta with the smallest χ 2 (the goodness of the fit) is selected for further analysis. The b -jet assignment in- formation is not used in the selection of the best permu- tation 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 t ¯ t pair in 48% (17%) of events. 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), d σ/ d p$_{T}$ , is shown in Fig. 4 and tab- ulated in Table III together with the NLO pQCD pre- diction [26, 27]. The statistical uncertainties are esti- mated 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 affect- ing 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 res- olution ( ≈ 0 . 5%). The residual dependence of the un- The reconstructed top-quark mass ( m$_{t}$ ) from the best fit in data, simulated t ¯ t 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 ob- tain a background-subtracted data spectrum, the signal p T (GeV /c ) 0–45 45–90 90–140 140–200 200–300 300–400 0–45 0.530 0.162 0.062 0.020 0.003 0.000 45–90 0.344 0.578 0.227 0.072 0.021 0.000 90–140 0.103 0.228 0.560 0.223 0.055 0.031 140–200 0.019 0.029 0.145 0.581 0.232 0.071 200–300 0.002 0.002 0.006 0.103 0.650 0.363 300–400 0.000 0.000 0.000 0.001 0.038 0.535 TABLE II: The migration matrix between the reconstructed (rows) and parton (columns) top-quark p T derived from alpgen t ¯ t events passed through full detector simulation. The matrix indicates the fraction of events migrated from a given parton bin to the reconstructed bins. The binning used for correlating reconstructed and parton levels of p T are given at the left and top, respectively. Results in bold print are for diagonal terms. FIG. 1: The reconstructed top-quark mass compared with expectation. Hashed areas represent statistical and jet energy calibration uncertainties on the prediction. ] 2 t m [GeV/c 100 150 200 250 300 350 400 -1 ] 2 t dN / dm [GeV/c 1 2 3 4 5  -1 DØ data, 1 fb  tt - Background