First simultaneous measurement of the top quark mass in the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ and dilepton channels at CDF

We present a measurement of the mass of the top quark using data corresponding to an integrated luminosity of $1.9{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions collected at $\sqrt{s}=1.96\mathrm{TeV}$ with the CDF II detector at Fermilab’s Tevatron. This is the first measurement of the top quark mass using top-antitop pair candidate events in the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ and dilepton decay channels simultaneously. We reconstruct two observables in each channel and use a nonparametric kernel density estimation technique to derive two-dimensional probability density functions from simulated signal and background samples. The observables are the top quark mass and the invariant mass of two jets from the $W$ decay in the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ channel, and the top quark mass and the scalar sum of transverse energy of the event in the dilepton channel. We perform a simultaneous fit for the top quark mass and the jet energy scale, which is constrained in situ by the hadronic $W$ boson mass. Using 332 $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ candidate events and 144 dilepton candidate events, we measure the top quark mass to be $M_{\mathrm{top}}=171.9\pm 1.7(\mathrm{stat}+\mathrm{JES})\pm 1.1(\mathrm{\text{other}}\mathrm{syst})\mathrm{GeV}/c^2=171.9\pm 2.0\mathrm{GeV}/c^2$.

Figure 1

Fractional uncertainty on corrected jet $p_T$ as a function of corrected jet $p_T$.

Figure 2

Template distributions for MC events passing the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ selection. Shown are the 1-tag $m_t^{\mathrm{reco}}$ (a) and $m_{jj}$ (b) distributions, and the 2-tag $m_t^{\mathrm{reco}}$ (c) and $m_{jj}$ (d) distributions. The $m_t^{\mathrm{reco}}$ distributions are plotted using events with three values of $M_{\mathrm{top}}$ and with the nominal ${\Delta }_{\mathrm{JES}}=0.0{\sigma }_c$. The $m_{jj}$ distributions are plotted using events with three values of ${\Delta }_{\mathrm{JES}}$ and with $M_{\mathrm{top}}=170\mathrm{GeV}/c^2$.

Figure 3

Template distributions for MC events passing the dilepton selection. Shown are the 0-tag $m_t^{\mathrm{NWA}}$ (a) and $H_T$ (b) distributions, and the tagged $m_t^{\mathrm{NWA}}$ (c) and $H_T$ (d) distributions. The distributions are plotted using events with three values of $M_{\mathrm{top}}$ and with the nominal ${\Delta }_{\mathrm{JES}}=0.0{\sigma }_c$.

Figure 4

Kernel density estimates at $M_{\mathrm{top}}=170\mathrm{GeV}/c^2$ and ${\Delta }_{\mathrm{JES}}=0.0$ for $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ 1-tag (a) and 2-tag (b) events, and for dilepton untagged (c) and tagged (d) events.

Figure 5

Kernel density estimates at ${\Delta }_{\mathrm{JES}}=0.0$ for $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ 1-tag (a) and 2-tag (b) background events, and for dilepton untagged (c) and tagged (d) events.

Figure 6

Checks for bias in the fitted top quark mass for (a) $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ only fit, (b) dilepton-only fit and (c) combined fit.

Figure 7

Width of the pull distribution for the fitted $M_{\mathrm{top}}$ for the (a) $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ only fit, (b) dilepton-only fit and (c) combined fit.

Figure 8

Negative log-likelihood contours for the combined fit. The minimum is indicated by the “x” and corresponds to the most probable top quark mass and ${\Delta }_{\mathrm{JES}}$, given the data. The contours are drawn at values of 0.5, 2.0 and 4.5 of the increase of the log-likelihood from the minimum value. These curves correspond to the 1, 2 and $3\sigma$ uncertainty on the measurement of the top quark mass.

Figure 9

One-dimensional log-likelihood for the dilepton-only fit.

Figure 10

Negative log-likelihood contours for the $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$-only fit. The minimum is indicated by the “x” and corresponds to the most probable top quark mass and ${\Delta }_{\mathrm{JES}}$, given the data. The contours are drawn at values of 0.5, 2.0 and 4.5 of the increase of the log-likelihood from the minimum value. These curves correspond to the 1, 2 and $3\sigma$ uncertainty on the measurement of the top quark mass.

Figure 11

One-dimensional $\mathrm{\text{lepton}}+\mathrm{\text{jets}}$ data with density estimates overlaid using $M_{\mathrm{top}}=172.0\mathrm{GeV}/c^2$, ${\Delta }_{\mathrm{JES}}=0.0$, and a full background model. The expected numbers of events are set to the values from the constrained fit. Shown are the 1-tag $m_t^{\mathrm{reco}}$ (a) and $m_{jj}$ (b) distributions, and the 2-tag $m_t^{\mathrm{reco}}$ (c) and $m_{jj}$(d) distributions.

Figure 12

One-dimensional dilepton data with density estimates overlaid using $M_{\mathrm{top}}=172.0\mathrm{GeV}/c^2$, ${\Delta }_{\mathrm{JES}}=0.0$, and full background model. The expected numbers of events are set to the values from the constrained fit. Shown are the 0-tag $m_t^{\mathrm{NWA}}$ (a) and $H_T$ (b) distributions, and the tagged $m_t^{\mathrm{NWA}}$ (c) and $H_T$ (d) distributions.