Top quark mass measurement using the template method in the $\mathrm{lepton}+\mathrm{jets}$ channel at CDF II

This article presents a measurement of the top quark mass using the CDF II detector at Fermilab. Colliding beams of protons and antiprotons at Fermilab’s Tevatron ($\sqrt{s}=1.96\mathrm{TeV}$) produce top/antitop pairs, which decay to $W^{+}{W}^{-}b\overline{b}$; events are selected where one $W$ decays to hadrons and the other $W$ decays to either $e$ or $\mu$ plus a neutrino. The data sample corresponds to an integrated luminosity of approximately $318{\mathrm{pb}}^{-1}$. A total of 165 $t\overline{t}$ events are separated into four subsamples based on jet transverse energy thresholds and the number of $b$ jets identified by reconstructing a displaced vertex. In each event, the reconstructed top quark invariant mass is determined by minimizing a ${\chi }^2$ for the overconstrained kinematic system. At the same time, the mass of the hadronically decaying $W$ boson is measured in the same event sample. The observed $W$ boson mass provides an in situ improvement in the determination of the hadronic jet energy scale. A simultaneous likelihood fit of the reconstructed top quark masses and the $W$ boson invariant masses in the data sample to distributions from simulated signal and background events gives a top quark mass of ${173.5}_{-3.8}^{+3.9}\mathrm{GeV}/c^2$.

Figure 1

An elevation view of the CDF II detector. From the collision region outwards, CDF consists of a silicon strip detector, a tracking drift chamber, an electromagnetic calorimeter, a hadronic calorimeter, and muon chambers.

Figure 2

The efficiency of the secondary vertex $b$-tagging algorithm is shown as a function of jet $E_T$ for $b$ jets in the central region of the detector ($|\eta |<1$), where the tracking efficiency is high. The shaded band gives the $\pm 1\sigma$ range for $b$-tagging efficiency. The curve is measured using a combination of data and Monte Carlo simulated samples.

Figure 3

The $t\overline{t}$-specific corrections are shown for $W$ jets (left) and $b$ jets (right) as a function of jet $p_T$ for several values of $|\eta |$. On the top is the correction factor, and on the bottom is the fractional resolution passed to the fitter. The histograms give the distributions of jet $p_T$ (arbitrarily normalized) from a signal Monte Carlo sample with generated top quark mass of $178\mathrm{GeV}/c^2$.

Figure 4

Results of the dijet balancing procedure are shown for data and simulated dijet events with $p_T^{\mathrm{jet}}>20\mathrm{GeV}/c$. Probe jets from throughout the detector are compared with a reference jet in the central region; the ratio of the $p_T$ of the jets is plotted as a function of the probe jet $\eta$. The simulation models well the detector response as a function of $\eta$.

Figure 5

The systematic uncertainties on jet energy are shown for jets in the central calorimeter ($0.2<|\eta |<0.6$). For noncentral jets, the total uncertainty has a different contribution from the eta-dependent uncertainty. In this plot the corrected jet transverse momentum $p_T^{\mathrm{corr}}$ is the process-independent estimate of the parton $p_T$. At low $p_T^{\mathrm{corr}}$, the main contribution to the systematic is from the uncertainty on the fraction of jet energy lost outside the cone, while at high $p_T^{\mathrm{corr}}$ it is from the linearity corrections to obtain an absolute jet energy scale.

Figure 6

For $\gamma$-jet events in both data and simulation, we find the fractional difference in $p_T$ between the jet and the photon after all jet corrections are applied. Plotted here, for different ranges of jet $\eta$, is the difference between this quantity in data and simulated events as a function of photon $p_T$. The solid lines show the $\pm 1\sigma$ range given by the jet energy systematics. The other lines follow the same definitions as in Fig. 5.

Figure 7

The light histograms show the reconstructed top quark mass distribution for the $178\mathrm{GeV}/c^2$ herwig $t\overline{t}$ sample at the nominal jet energy scale. Overlaid are darker histograms of the reconstructed mass distributions using the subset of events for which the leading four jets are matched (within $\Delta R=0.4$) to the four quarks from the $t\overline{t}$ decay and the correct jet-quark assignment has the lowest ${\chi }^2$. Distributions are shown for 2-tag (upper left), 1-tag(T) (upper right), 1-tag(L) (lower left), and 0-tag (lower right) events.

Figure 8

The reconstructed dijet mass distributions for the $178\mathrm{GeV}/c^2$ herwig $t\overline{t}$ sample at the nominal jet energy scale. Overlaid are darker histograms of the reconstructed mass distributions using the subset of events for which the leading four jets include two jets matched (within $\Delta R=0.4$) to the two quarks from the hadronic $W$ decay and plotting just the invariant mass of those two jets. Distributions are shown for 2-tag (upper left), 1-tag(T) (upper right), 1-tag(L) (lower left), and 0-tag (lower right) events.

Figure 9

The top histogram shows the reconstructed top quark mass $m_t^{\mathrm{reco}}$, and the bottom histogram shows the dijet reconstructed mass $m_{jj}$, with events from the four subsamples represented by separate stacked histograms. In the $m_{jj}$ plot, each event has a different number of jet pairs, depending on the number of $b$ tags in the event, but the entries are weighted so that the total contribution from each event is one unit. The highest $m_{jj}$ bin contains overflow entries.

Figure 10

The ${\chi }^2$ distribution is shown for data events and for signal and background simulated events in the expected ratio. Distributions are shown for 2-tag (upper left), 1-tag(T) (upper right), 1-tag(L) (lower left), and 0-tag (lower right) events.

Figure 11

Four $m_t^{\mathrm{reco}}$ signal templates for the 1-tag(T) sample are shown, with top quark masses ranging from $145\mathrm{GeV}/c^2$ to $205\mathrm{GeV}/c^2$ and with ${\Delta }_{\mathrm{JES}}$ set to 0. Overlaid are the fitted parameterizations at each generated mass, taken from the full parameterization given in Eq. (5.1).

Figure 12

Four $m_{jj}$ signal templates for the 2-tag sample are shown, with ${\Delta }_{\mathrm{JES}}$ values ranging from $-3{\sigma }_c$ to $3{\sigma }_c$ and with the top quark mass set to $180\mathrm{GeV}/c^2$. Overlaid are the fitted parameterizations at each value of the jet energy scale shift, taken from the full parameterization given in Eq. (5.1).

Figure 13

The templates for $Wc\overline{c}$ and $Wc$ background processes are compared to the high-statistics $Wb\overline{b}$ template for all tagged events. The agreement is good in both cases, so the $Wb\overline{b}$ template is used to represent all $W+\mathrm{h}.\mathrm{f}.$ processes.

Figure 14

Reconstructed top quark mass distributions of the combined backgrounds in each subsample. The contributions from different background templates are shown stacked; overlaid are the fitted curves [see Eq. (5.2) and (5.3)].

Figure 15

Reconstructed dijet mass distributions of the combined backgrounds in each subsample. The contributions from different background templates are shown stacked; overlaid are the fitted curves [see Eqs. (5.4) and (5.5)].

Figure 16

The mean (top) and width (bottom) of pull distributions from sets of 2500 pseudoexperiments are shown. On the left, the jet energy scale is fixed at its nominal value, and the generated top quark mass is varied from $150\mathrm{GeV}/c^2$ to $210\mathrm{GeV}/c^2$. On the right, the top quark mass is fixed at $180\mathrm{GeV}/c^2$, and the input jet energy scale shift is varied from $-3{\sigma }_c$ to $+3{\sigma }_c$. The error bars come mostly from the limited statistics of the Monte Carlo samples from which the pseudodata is taken.

Figure 17

The contours of the likelihood in the ${\mathrm{M}}_{\mathrm{top}}$-${\Delta }_{\mathrm{JES}}$ plane for the independent fit to each subsample in the data. At each point in the plane, the likelihood is maximized with respect to the other free parameters. A crosshair shows the maximum likelihood point from the combined fit, and contours are given at regular intervals in $\Delta \ln L$, the change in log-likelihood from its maximum. Upper left: 2-tag events; upper right: 1-tag(T) events; lower left: 1-tag(L) events; lower right: 0-tag events.

Figure 18

The contours of the likelihood in the ${\mathrm{M}}_{\mathrm{top}}$-${\Delta }_{\mathrm{JES}}$ plane for the combined fit to all four subsamples. At each point in the plane, the likelihood is maximized with respect to the other free parameters. The crosshair shows the best fit point, and contours are given at regular intervals in $\Delta \ln L$, the change in log-likelihood from its maximum.

Figure 19

The reconstructed top quark mass distribution for each subsample is shown overlaid with the expected distribution using the top quark mass, jet energy scale shift, signal normalization, and background normalization from the combined fit.

Figure 20

The reconstructed dijet mass distribution for each subsample is shown overlaid with the expected distribution using the top quark mass, jet energy scale, signal normalization, and background normalization from the combined fit.

Figure 21

The distributions of positive and negative uncertainties from the likelihood fit are shown, for pseudoexperiments generated with a top quark mass of $172.5\mathrm{GeV}/c^2$, the nominal jet energy scale, and the number of events in each subsample as observed in the data. Arrows indicate the positive and negative uncertainties from the likelihood fit to the data; 9.2% of the pseudoexperiments have smaller uncertainties.

Figure 22

The negative log-likelihood curves as a function of the top quark mass are shown for the ${\mathrm{M}}_{\mathrm{top}}$-only fit to each subsample in the data. Upper left: 2-tag events; upper right: 1-tag(T) events; lower left: 1-tag(L) events; lower right: 0-tag events.

Figure 23

The reconstructed top quark mass distribution for the 18 events with one secondary vertex tag and one JPB tag, overlaid with the expected distribution from the fit to this subsample. The inset shows the shape of $-\Delta \log \mathcal{L}$ for the fit to these events as a function of the top quark mass.

Figure 24

Top quark mass measurements using the ${\mathrm{M}}_{\mathrm{top}}$-only fit are compared for different assumptions [top-specific corrections (default) vs generic jet out-of-cone corrections, constrained backgrounds vs unconstrained] and different ways of subdividing the sample (two different run periods, electrons vs muons, positive-charge leptons vs negative-charge leptons). All results with only statistical errors are consistent.

Figure 25

Top quark mass measurements using the ${\mathrm{M}}_{\mathrm{top}}$-only fit are compared for various samples. From top to bottom: all four subsamples; 2-tag, 1-tag(T), and 1-tag(L) subsamples; 2-tag and 1-tag(T) subsamples only; 2-tag and 1-tag(T) subsamples only, additional jets $E_T<15\mathrm{GeV}$; 2-tag and 1-tag(T) subsamples only, additional jets $E_T<8\mathrm{GeV}$. All results with only statistical errors are found to be consistent.

Figure 26

The $p_T$ distribution of the reconstructed top quarks for 73 signal candidate events [2-tag and 1-tag(T) subsamples], compared to the prediction from herwig $t\overline{t}$ signal events (with generated top quark mass of $172.5\mathrm{GeV}/c^2$) and simulated background events.

Figure 27

The rapidity distribution of the reconstructed top quarks for 73 signal candidate events [2-tag and 1-tag(T) subsamples] compared to the prediction from herwig $t\overline{t}$ signal events (with generated top quark mass of $172.5\mathrm{GeV}/c^2$) and simulated background events.

Figure 28

The $p_T$ distribution of the reconstructed $b$ jets for 73 signal candidate events [2-tag and 1-tag(T) subsamples] compared to the prediction from herwig $t\overline{t}$ signal events (with generated top quark mass of $172.5\mathrm{GeV}/c^2$) and simulated background events.

Figure 29

The $p_T$ distribution of the reconstructed $W$ bosons for 73 signal candidate events [2-tag and 1-tag(T) subsamples] compared to the prediction from herwig $t\overline{t}$ signal events (with generated top quark mass of $172.5\mathrm{GeV}/c^2$) and simulated background events.

Figure 30

The $p_T$ distribution of the reconstructed $t\overline{t}$ system for 73 signal candidate events [2-tag and 1-tag(T) subsamples] compared to the prediction from herwig $t\overline{t}$ signal events (with generated top quark mass of $172.5\mathrm{GeV}/c^2$) and simulated background events.

Figure 31

The number of jets distribution for 73 signal candidate events [2-tag and 1-tag(T) subsamples] compared to the prediction from herwig $t\overline{t}$ signal events (with generated top quark mass of $172.5\mathrm{GeV}/c^2$) and simulated background events. Jets are required to have $E_T>8\mathrm{GeV}$ and $|\eta |<2.0$.

Figure 32

The average $p_T$ of the dilepton system, which corresponds to the level of ISR activity, shows a logarithmic dependence on the dilepton invariant mass $M_{ll}^2$. The data are compared with the predictions of pythia 6.2 and of the $+1{\sigma }_{\mathrm{ISR}}$ and $-1{\sigma }_{\mathrm{ISR}}$ samples.