Measurement of the top quark mass in the lepton+jets channel using the ideogram method

A measurement of the top quark mass using events with one charged lepton, missing transverse energy, and jets in the final state, collected by the D0 detector from $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron collider, is presented. A constrained fit is used to fully reconstruct the kinematics of the events. For every event a top quark mass likelihood is calculated taking into account all possible jet assignments and the probability that an event is signal or background. Lifetime-based identification of $b$ jets is employed to enhance the separation between $t\overline{t}$ signal and background from other physics processes and to improve the assignment of the observed jets to the quarks in the $t\overline{t}$ hypothesis. We extract a multiplicative jet energy scale (JES) factor in situ, greatly reducing the systematic effect related to the jet energy measurement. In a data sample with an integrated luminosity of $425{\mathrm{pb}}^{-1}$, we observe 230 candidate events, with an estimated background of 123 events, and measure $m_t=173.7\pm 4.4(\mathrm{stat}+\mathrm{JES}{)}_{-2.0}^{+2.1}(\mathrm{syst})\mathrm{GeV}$. This result represents the first application of the ideogram technique to the measurement of the top quark mass in lepton+jets events.

Figure 1

Combined likelihood discriminant $D$ in data and MC simulation in the electron+jets channel (left) and muon+jets channel (right). The $t\overline{t}$, $W$+jets, and multijet contributions are normalized according to the fitted fractions.

Figure 2

Histograms showing the background shape from a weighted sum (see text) of all 24 masses from each event from the $W$+jets background sample (points with error bars), for the electron+jets channel (left) and muon+jets (right). The histograms show the shapes that are used in the likelihood. To reduce statistical fluctuations, the shapes are calculated as the average value in a sliding window of $\pm 5\mathrm{GeV}$ around each fitted mass.

Figure 3

Prediction of the shapes of the fitted mass distribution for the wrong and the correct permutations (hatched) and the sum of the two (black line) using the fitted parameters shown in Table 3. The sum of the two is compared to the simulated data containing a weighted sum of all solutions (correct and wrong), for the default jet energy scale and a generated top quark mass of 175 GeV for events with 0 (top), 1 (middle), or more than 1 (bottom) $b$ tags.

Figure 4

Same as Fig. 3, for different values of the generated top quark mass, combining all events irrespective of the number of $b$ tags.

Figure 5

The mean fitted JES and pull width as a function of the generated top quark mass $M_{\mathrm{gen}}$ for a true JES of 0.97 (left), 1.00 (middle), and 1.03 (right), for the lepton+jets channel ($e+\mu$ combined). The fitted JES is stable as a function of generated top quark mass.

Figure 6

The difference between the mean fitted mass $M_{\mathrm{fit}}$ and the generated top quark mass $M_{\mathrm{gen}}$ as a function of the generated top quark mass for a true JES of 0.97 (left), 1.00 (middle), and 1.03 (right), for the lepton+jets channel ($e+\mu$ combined). At a generated mass of 175 GeV, the mass bias changes by 1 GeV when the true JES is varied by $\pm 3\%$.

Figure 7

The expected statistical uncertainty from ensemble tests is shown as a function of the generated top quark mass for three scenarios: with the JES parameter fixed to 1 (left), allowing the JES parameter to float freely in the fit, but only calibrating the mass fit for a true $\mathrm{JES}=1$ (middle), allowing the JES parameter to float freely in the fit and applying the full calibration as a function of true top quark mass and true JES (right). In each plot the width of the band indicates the estimated uncertainty.

Figure 8

Overall likelihood curves for the events observed in data, in the electron+jets channel (left), muon+jets (middle), and both channels combined (right). The top plots show the full 2-dimensional likelihood as a function of the jet energy scale parameter (JES) and top quark mass. Each contour, $n$, corresponds to a difference in likelihood of $\Delta \ln (\mathcal{L})=-n^2/2$ with respect to the maximum likelihood. The fitted value of the JES parameter as a function of the top quark mass is plotted as the gray line superimposed on the 2D likelihoods. The bottom plots show the likelihood as a function of the top quark mass along the gray line from the upper plots. The fitted values from these distributions have to be corrected for the calibration from MC simulation to obtain the final results.

Figure 9

Distribution of the estimated statistical uncertainty on the top quark mass measurement (left) and JES measurement (right) for the fully calibrated analysis, in the combined lepton+jets channel. The values observed in data are indicated by the arrows.