Top quark mass measurement from dilepton events at CDF II with the matrix-element method

We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from $p\overline{p}$ collisions with $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron. The likelihood in top quark mass is calculated for each event by convoluting the leading order matrix element describing $q\overline{q}\to t\overline{t}\to b\ell {\nu }_{\ell }\overline{b}{\ell }^{\prime }{\nu }_{{\ell }^{\prime }}$ with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of $340{\mathrm{pb}}^{-1}$, we observe 33 candidate events and measure $M_{\mathrm{top}}=165.2\pm 6.1(\mathrm{stat}.)\pm 3.4(\mathrm{syst}.)\mathrm{GeV}/c^2.$ This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.

Figure 1

Top, difference of $E_p-E_j$ between parton and jet energy for reconstructed jets matched in angle to $b$ quarks (see text). Center, distribution of $E_j$ of jet energy. Bottom, input distribution of parton energy $E_p$. Histograms are simulated events for $M_t=178\mathrm{GeV}/c^2$; curves in the upper two histograms show the distributions calculated using $W(E_p,E_j)$.

Figure 2

Comparison of simulated $E_j$ with calculations from $W(E_p,E_j)$ from six ranges of $E_p$. Histograms are simulated events; curves show the calculated distributions using $W(E_p,E_j)$.

Figure 3

Comparison of simulated $E_j$ with calculations from $W(E_p,E_j)$ from distributions $E_p$ in simulated samples with $M_t=150$, 160, 170, 180, 190, and $200\mathrm{GeV}/c^2$. Histograms are simulated events for $M_t=178\mathrm{GeV}/c^2$; lines show the calculated distributions using $W(E_p,E_j)$ derived using partons from $M_t=178\mathrm{GeV}/c^2$.

Figure 4

Top, mean of measured $M_t$ in Monte Carlo experiments with only $t\overline{t}$ events. Bottom, fitted widths of pull distributions from the same Monte Carlo experiments.

Figure 5

Correlation between the mean $p_T$ of the $t\overline{t}$ system and the number of reconstructed jets in pythia simulated $t\overline{t}$ events.

Figure 6

Angular distance, $R$, between a reconstructed jet and the closest $b$ quark in $t\overline{t}$ events simulated with herwig. The width of the distribution demonstrates the angular resolution. 20% of jet-parton pairs have $R\ge 0.7$ (not shown), coming from jets with no corresponding $b$ quark.

Figure 7

Top, mean of measured $M_t$ in Monte Carlo experiments with $t\overline{t}$ events as well as background events. Bottom, fitted widths of pull distributions from the same Monte Carlo experiments.

Figure 8

Left, distribution of measured $M_t$ in Monte Carlo experiments with $t\overline{t}$ events at $M_t=165\mathrm{GeV}/c^2$ and background events. Measured statistical error, center, and pull distribution, right, are also shown. All mass and error corrections have been applied.

Figure 9

Left, distribution of measured $M_t$ in Monte Carlo experiments with $t\overline{t}$ events at $M_t=178\mathrm{GeV}/c^2$ and background events. Measured statistical error, center, and pull distribution, right, are also shown. All mass and error corrections have been applied.

Figure 10

Systematic uncertainties for several sources in the jet energy scale, as a function of the corrected $p_T$ of jets ($p_T^{\mathrm{corr}}$) in the central ($0.2<|\eta |<0.6$) calorimeter.

Figure 11

Comparison of the missing transverse energy in dilepton events in data, pythia simulated $Z/{\gamma }^{*}\to ll$ events, and simulated events weighted as described in the text to enhance or suppress events with large missing transverse energy. Top shows $\mu \mu$ data and bottom shows $ee$ data.

Figure 12

Likelihood in top quark mass for the 33 candidate events in $340{\mathrm{pb}}^{-1}$ of run II CDF data. Horizontal axis is top quark mass over the range of $M_t=130$ to $220\mathrm{GeV}/c^2$. Vertical axis is shown on a linear scale between 0 and 1.

Figure 13

Joint probability density for the 33 event data sample in $340{\mathrm{pb}}^{-1}$ of run II CDF data as a function of the top quark mass. The bias and error corrections have been applied.

Figure 14

Distribution of expected uncertainties for $M_t=165\mathrm{GeV}/c^2$ in Monte Carlo experiments. The measured uncertainty is shown as the line; 17% of Monte Carlo experiments yield a smaller uncertainty.