Precision measurement of the top-quark mass in $\mathbf{\text{lepton}}\mathbf{+}\mathbf{\text{jets}}$ final states

We measure the mass of the top quark in $\text{lepton}+\text{jets}$ final states using the full sample of $p\overline{p}$ collision data collected by the D0 experiment in Run II of the Fermilab Tevatron Collider at $\sqrt{s}=1.96\mathrm{TeV}$, corresponding to $9.7{\mathrm{fb}}^{-1}$ of integrated luminosity. We use a matrix element technique that calculates the probabilities for each event to result from $t\overline{t}$ production or background. The overall jet energy scale is constrained in situ by the mass of the $W$ boson. We measure $m_t=174.98\pm 0.76\mathrm{GeV}$. This constitutes the most precise single measurement of the top-quark mass.

Figure 1

The total partonic cross section for $t\overline{t}$ production in $p\overline{p}$ collisions through quark-antiquark annihilation at LO, as defined in Eq. (10).

Figure 2

Mean acceptance $⟨A(m_t,k_{\mathrm{JES}}\equiv 1){⟩}_{\overrightarrow{x}}$ with respect to the total partonic cross section for $p\overline{p}\to t\overline{t}$ production, as a function of $m_t$ for different $k_{\mathrm{JES}}$ values in the $e+\text{jets}$ final state, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3. The acceptance tends to decrease for later epochs due to a decreased reconstruction efficiency, which is mainly caused by the higher instantaneous luminosity in the second half of Run II and detector aging.

Figure 3

Same as Fig. 2, but for the $\mu +\text{jets}$ final state for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 4

The TF $W_{\text{jet}}(E_x,E_y;k_{\mathrm{JES}})$ for light-quark jets at $k_{\mathrm{JES}}\equiv 1$ in Run IIb2, as a function of the measured jet energy $E_x$, for different parton energies $E_y$, as indicated in the legend. The TF are shown in four pseudorapidity regions: (a) $|\eta |\le 0.4$, (b) $0.4<|\eta |\le 0.8$, (c) $0.8<|\eta |\le 1.6$, and (d) $1.6<|\eta |\le 2.5$. Energies $E_x>150\mathrm{GeV}$ are also considered, but not shown.

Figure 5

Same as Fig. 4, but for $b$-quark jets with at least one muon inside the jet cone. The TF are shown in four pseudorapidity regions: (a) $|\eta |\le 0.4$, (b) $0.4<|\eta |\le 0.8$, (c) $0.8<|\eta |\le 1.6$, and (d) $1.6<|\eta |\le 2.5$.

Figure 6

Same as Fig. 4, but for $b$-quark jets without muons inside the jet cone. The TF are shown in four pseudorapidity regions: (a) $|\eta |\le 0.4$, (b) $0.4<|\eta |\le 0.8$, (c) $0.8<|\eta |\le 1.6$, and (d) $1.6<|\eta |\le 2.5$.

Figure 7

Invariant mass of the dijet system matched to the $W\to q{\overline{q}}^{\prime }$ decay for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3. Fully simulated jet-parton matched MC events passing all selection requirements are compared to partons with energies smeared using the jet TF, and then applying the same standard event selection criteria.

Figure 8

Same as Fig. 7, but for the invariant mass of the trijet system matched to the hadronic decay of the top quark for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 9

The response of the ME technique in $f$, derived from the average of $f^{\text{fit}}$ over 1000 PEs at each $f^{\text{gen}}$ point, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3 in the $e+\text{jets}$ final state. The response is fitted with a linear function shown as a solid black line, whose slope and offset values are given at the bottom of the plots. The broken red line represents an ideal response.

Figure 10

Same as Fig. 9, but in the $\mu +\text{jets}$ final state, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 11

The response of the ME technique in $m_t$, obtained using simulations from the average of $m_t^{\text{fit}}$ in 1000 PEs at each $m_t^{\text{gen}}$ point, as a function of $m_t^{\text{gen}}$, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3 in the $e+\text{jets}$ final state. The response is fitted with a linear function shown as a solid black line, whose slope and offset values are summarized at the bottom of the plots. The red broken line represents an ideal response.

Figure 12

Same as Fig. 11, but in the $\mu +\text{jets}$ final state, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 13

The response of the ME technique in $k_{\mathrm{JES}}$, obtained using simulations from the average of $k_{\mathrm{JES}}^{\text{fit}}$ in 1000 PEs at each $k_{\mathrm{JES}}^{\text{gen}}$ point, as a function of $k_{\mathrm{JES}}^{\text{gen}}$, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3 in the $e+\text{jets}$ final state. The response is fitted with a linear function shown as a solid black line, whose slope and offset values are summarized at the bottom of the plots. The red broken line represents an ideal response. The poor compatibility of data with the linear fit displayed in panel (a) likely to occur if many fits, in our case, 16, are performed.

Figure 14

Same as Fig. 13, but in the $\mu +\text{jets}$ final state, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 15

The width of the distribution of the pull in $m_t$, obtained using simulations at each $m_t^{\text{gen}}$ point, as a function of $m_t^{\text{gen}}$, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3 in the $e+\text{jets}$ final state. The error bars are given by the uncertainty on the width of the distribution in ${\pi }_{m_t}$, which is not corrected for the effect that the same event can appear in many PEs, and therefore somewhat underestimated. The pull is fitted with a constant shown as a solid black line, whose value is given at the bottom of the plots. The red broken line represents an ideal pull width of unity.

Figure 16

Same as Fig. 15, but in the $\mu +\text{jets}$ final state, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 17

The width of the distribution of the pull in $k_{\mathrm{JES}}$, derived using simulations at each $k_{\mathrm{JES}}^{\text{gen}}$ point, as a function of $k_{\mathrm{JES}}^{\text{gen}}$, for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3 in the $e+\text{jets}$ final state. The error bars are given by the uncertainty on the width of the distribution in ${\pi }_{k_{\mathrm{JES}}}$, which is not corrected for the effect that the same event can appear in many PEs, and therefore somewhat underestimated. The pull is fitted with a constant shown as a solid black line, whose value is given at the bottom of the plots. The broken line represents the case of ideal pull width of unity.

Figure 18

Same as Fig. 15, but in the $\mu +\text{jets}$ final state, as derived for (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 19

Summary of the measured $m_t$ values with their statistical uncertainties for each data-taking epoch and split according to final state. The red-shaded band indicates the statistical uncertainty on the combined $m_t$ value in Run II data corresponding to $9.7{\mathrm{fb}}^{-1}$ of integrated luminosity.

Figure 20

Distribution of expected statistical uncertainties ${\sigma }_{m_t}$ in $e+\text{jets}$ final states in (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3, obtained in 1000 PEs at $m_t^{\text{gen}}=172.5\mathrm{GeV}$ and $k_{\mathrm{JES}}=1$, after calibrating for nonunit width of the distribution in ${\pi }_{m_t}$. The observed statistical uncertainties in data are indicated by arrows.

Figure 21

Same as Fig. 20, in $\mu +\text{jets}$ final states in (a) Run IIa, (b) Run IIb1, (c) Run IIb2, and (d) Run IIb3.

Figure 22

Same as Fig. 19, but for the $k_{\mathrm{JES}}$ parameter.

Figure 23

Two-dimensional likelihood $\mathcal{L}({\mathbb{X}}_N;m_t,k_{\mathrm{JES}})/{\mathcal{L}}_{\max }$ for data. Fitted contours of equal probability are overlaid as solid lines. The maximum is marked with a cross. Note that the bin boundaries do not necessarily correspond to the grid points on which $\mathcal{L}$ is calculated.

Figure 24

(a) Distribution of the expected uncertainty on $m_t$, as obtained using PEs where the $t\overline{t}$ contribution is taken at $m_t^{\text{gen}}=172.5\mathrm{GeV}$ and $k_{\mathrm{JES}}=1$, after calibration. The observed statistical uncertainty is indicated by an arrow. (b) Same for uncertainty on $k_{\mathrm{JES}}$.

Figure 25

(a) Two-dimensional likelihood $\mathcal{L}({\mathbb{X}}_N;m_t,k_{\mathrm{JES}})/{\mathcal{L}}_{\max }$ for data in the $e+\text{jets}$ final state. Fitted contours of equal probability are overlaid as solid lines. The maximum is marked with a cross. (b) Distribution in expected uncertainty on $m_t$ in $e+\text{jets}$ final states, obtained using PEs where the $t\overline{t}$ contribution is taken at $m_t^{\text{gen}}=172.5\mathrm{GeV}$ and $k_{\mathrm{JES}}=1$, after calibration. The observed statistical uncertainty in data is indicated by the arrow. (c) Same as (a), but for the $\mu +\text{jets}$ channel. (d) Same as (b), but for the $\mu +\text{jets}$ channel.

Figure 26

The invariant mass of the $t\overline{t}$ system in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ final states, assuming $m_t^{\text{gen}}=172.5\mathrm{GeV}$, $k_{\mathrm{JES}}=1$, and ${\sigma }_{t\overline{t}}=7.24{\mathrm{pb}}^{-1}$ [40]. The same observable in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ final states for $m_t^{\text{gen}}=175\mathrm{GeV}$, with energies of jets scaled up by $k_{\mathrm{JES}}=1.025$, corresponding to their measured values. The fractions of signal events, $f$, are set to their measured values of 63% in the $e+\text{jets}$ and 70% in the $\mu +\text{jets}$ final states in (c) and (d) (cf. Sec. 6b). The category “Other bgs” encompasses $Z+\text{jets}$, $WW$, $WZ$, $ZZ$, and single top quark production, as well as dileptonic $t\overline{t}$ decays. The production of a $W$ boson in association with at least one $b$ or $c$ quark is denoted as “$W+\mathrm{hf}$”, while “$W+\mathrm{lf}$” stands for all other flavor configurations. The last bin includes overflow events. The ratio shows the number of observed events divided by the number of expected events in a given bin. The band of systematic uncertainty is indicated by the shaded area in the ratio plots, and includes contributions from dominant sources: JES, jet energy resolution, jet identification, flavor dependence of the detector response, $b$ tagging, lepton identification, lepton momentum scale, trigger, as well as hadronization and higher-order effects for $t\overline{t}$ events.

Figure 27

Same as Fig. 26, but for the invariant mass of the dijet system matched to the $W$ boson, assuming $m_t^{\text{gen}}=172.5\mathrm{GeV}$, $k_{\mathrm{JES}}=1$, and ${\sigma }_{t\overline{t}}=7.24{\mathrm{pb}}^{-1}$ [40] in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ final states, and for $m_t^{\text{gen}}=175\mathrm{GeV}$, $k_{\mathrm{JES}}=1.025$, and $f$ corresponding to their measured values in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ final states.

Figure 28

The scalar sum of $E_T$ of the four jets $H_T$ in (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ final states, for the transverse momentum of the $t\overline{t}$ system in (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ final states, as well as for the transverse momentum of the top quarks in (a) $e+\text{jets}$ or (b) $\mu +\text{jets}$ final states. All panels are for $m_t^{\text{gen}}=175\mathrm{GeV}$, with energies of jets scaled up by $k_{\mathrm{JES}}=1.025$, corresponding to their measured values. The fractions of signal events, $f$, are set to their measured values of 63% in the $e+\text{jets}$ and 70% in the $\mu +\text{jets}$ final states in (c) and (d) (cf. Sec. 6b). The list of included background contributions and sources of systematic uncertainties considered are identical to those from Fig. 26. Panels (e) and (f) have two entries per event, one for each of the $t$ and $\overline{t}$ quarks.

Figure 29

Same as Fig. 28, but for the transverse momentum of the (a) electron or (b) muon, for the missing transverse momentum in (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ final states, as well as for the transverse mass of the $W\to \ell {\nu }_{\ell }$ decay in (e) $e+\text{jets}$ and (f) $\mu +\text{jets}$ final states.

Figure 30

Same as Fig. 28, but for the invariant mass of the trijet system matched to the hadronic decay of the top quark in $\ell +\text{jets}$ final states.

Figure 31

(a) The ratio of predicted differential cross sections from $\mathrm{ALPGEN}+\mathrm{HERWIG}$ to those from $\mathrm{ALPGEN}+\mathrm{PYTHIA}$ as a function of $p_T^{t\overline{t}}$ at particle level. Also shown is the fit with a second-order polynomial used for reweighting $\mathrm{ALPGEN}+\mathrm{PYTHIA}$ events in $p_T^{t\overline{t}}$ for $35\mathrm{GeV}<p_T^{t\overline{t}}<200\mathrm{GeV}$. Below that range the reweighting is performed according to the histogram, and above with a constant factor of 1.67. Uncertainties are only statistical. (b) Same ratio in the range $p_T^{t\overline{t}}<35\mathrm{GeV}$.

Figure 32

The ratio $Q_{\text{corr}}^b=F_{\text{corr},\mathrm{ALPGEN}+\mathrm{HERWIG}}^b/F_{\text{corr},\mathrm{ALPGEN}+\mathrm{PYTHIA}}^b$ for $b$-quark jets in simulated $t\overline{t}$ events and $\ell +\text{jets}$ final state as a function of the $p_T$ of the jet. The ideal $Q_{\text{corr}}^b$ of unity is indicated as the broken line. The uncertainties on the points reflect the finite size of the MC sample. The total uncertainty on the standard flavor-dependent correction for $\mathrm{ALPGEN}+\mathrm{PYTHIA}$ is indicated as the band around unity.

Figure 33

The ratio $R_{bq}=(p_T^{b_1}+p_T^{b_2})/(p_T^{j_1}+p_T^{j_2})$ for events with $\ge 2$ $b$-tagged jets, and $R_{bq}=2p_T^b/(p_T^{j_1}+p_T^{j_2})$ for events with one $b$-tagged jet, after all selections. The category “Other bgs” encompasses $Z+\text{jets}$, $WW$, $WZ$, $ZZ$, and single top quark production, as well as dileptonic $t\overline{t}$ decays. The production of a $W$ boson in association with at least one $b$ or $c$ quark is denoted as “$W+\mathrm{hf}$”, while “$W+\text{lf}$” stands for all other flavor configurations. The last bin includes overflow events. The ratio shows the number of observed events divided by the number of expected events in a given bin. The band of systematic uncertainty is indicated as a shaded area in the ratio plots, and includes dominant sources: JES, jet energy resolution, jet identification, flavor dependence of the detector response, and $b$ tagging.

Figure 34

Summary of the measurements performed in Run II of the Tevatron which are used as inputs to the Tevatron combination [8]. The inner error bars indicate the statistical uncertainties, while the outer bars represent the total uncertainties. The Tevatron average value of $m_t$ obtained using input measurements from Run I and Run II is given at the bottom and its uncertainty is shown by the band. The Figure is adapted from Ref. [8].

Figure 35

(a) Ratio of the unfolded differential cross section $\mathrm{d}{\sigma }_{Z/{\gamma }^{*}\to e^{+}{e}^{-}}/\mathrm{d}{\varphi }^{*}$ and the nominal predictions from alpgen$+$pythia for $0<|y|<1$, where the error bars represent the total uncertainties in the data. The ratios of predictions determined with alpgen$+$pythia where the amount of radiation is changed up and down relative the nominal predictions from alpgen$+$pythia are shown, respectively, as red broken and blue dash-dotted lines. The statistical uncertainties from the finite number of simulated MC events are negligible compared to the uncertainties in the data. (b) Same as (a), but for $1<|y|<2$. (c) Same as (a), but for $|y|>2$.

Figure 36

(a) Ratio of the unfolded differential cross section $\mathrm{d}{\sigma }_{Z/{\gamma }^{*}\to {\mu }^{+}{\mu }^{-}}/\mathrm{d}{\varphi }^{*}$ and the nominal predictions from alpgen$+$pythia for $0<|y|<1$, where the error bars represent the total uncertainties in the data. The ratios of predictions obtained with alpgen$+$pythia where the amount of radiation is changed up and down relative the nominal predictions from alpgen$+$pythia are shown, respectively, as red broken and blue dash-dotted lines. The statistical uncertainties from the finite number of simulated MC events are negligible compared to the uncertainties in the data. (b) Same as (a), but for $1<|y|<2$.