Measurement of the differential cross sections for top quark pair production as a function of kinematic event variables in $pp$ collisions at $\sqrt{s}=7$ and 8 TeV

Measurements are reported of the normalized differential cross sections for top quark pair production with respect to four kinematic event variables: the missing transverse energy; the scalar sum of the jet transverse momentum ($p_{\mathrm{T}}$); the scalar sum of the $p_{\mathrm{T}}$ of all objects in the event; and the $p_{\mathrm{T}}$ of leptonically decaying $W$ bosons from top quark decays. The data sample, collected using the CMS detector at the LHC, consists of $5.0{\mathrm{fb}}^{-1}$ of proton-proton collisions at $\sqrt{s}=7\mathrm{TeV}$ and $19.7{\mathrm{fb}}^{-1}$ at $\sqrt{s}=8\mathrm{TeV}$. Top quark pair events containing one electron or muon are selected. The results are presented after correcting for detector effects to allow direct comparison with theoretical predictions. No significant deviations from the predictions of several standard model event simulation generators are observed.

Figure 1

The observed distributions of $E_{\mathrm{T}}^{\text{miss}}$ (top) and $H_{\mathrm{T}}$ (bottom) in the $\sqrt{s}=8\mathrm{TeV}$ $\text{electron}+\text{jets}$ (left) and $\text{muon}+\text{jets}$ (right) data samples, compared to predictions from simulation. The points are the data histograms, with the vertical bars showing the statistical uncertainty, and the predictions from the simulation are the solid histograms. The shaded region shows the uncertainty in the values from simulation. These include contributions from the statistical uncertainty and the uncertainty in the $t\overline{t}$ cross section. The lower plots show the ratio of the number of events from data and the prediction from the MC simulation.

Figure 2

The observed distributions of $S_{\mathrm{T}}$ (top) and $p_{\mathrm{T}}^W$ (bottom) in the $\sqrt{s}=8\mathrm{TeV}$ $\text{electron}+\text{jets}$ (left) and $\text{muon}+\text{jets}$ (right) data samples, compared to predictions from simulation. The points are the data histograms, with the vertical bars showing the statistical uncertainty, and the predictions from the simulation are the solid histograms. The shaded region shows the uncertainty in the values from simulation. These include contributions from the statistical uncertainty and the uncertainty in the $t\overline{t}$ cross section. The lower plots show the ratio of the number of events from data and the prediction from the MC simulation.

Figure 3

Normalized $E_{\mathrm{T}}^{\text{miss}}$ (top) and $H_{\mathrm{T}}$ (bottom) differential $t\overline{t}$ cross sections from the combined electron and muon data at $\sqrt{s}=7\mathrm{TeV}$. The vertical bars on the data points represent the statistical and systematic uncertainties added in quadrature. The inner section of the vertical bars, denoted by the tick marks, show the statistical uncertainty. Left: comparison with different simulation event generators: MadGraph$+$pythia (both the default and after reweighting the top quark $p_{\mathrm{T}}$ spectrum), powheg v2$+$herwig, and powheg v2$+$pythia. Right: comparison with predictions from the MadGraph$+$pythia event generator found by varying the matching threshold and renormalization scales (${\mu }_{\mathrm{R}}$, ${\mu }_{\mathrm{F}}$) up and down by a factor of 2. The lower plots show the ratio of the predictions to the data, with the statistical and total uncertainties in the ratios indicated by the two shaded bands.

Figure 4

Normalized $S_{\mathrm{T}}$ (top) and $p_{\mathrm{T}}^W$ (bottom) differential $t\overline{t}$ cross sections from combined electron and muon data at $\sqrt{s}=7\mathrm{TeV}$. The vertical bars on the data points represent the statistical and systematic uncertainties added in quadrature. The inner section of the vertical bars, denoted by the tick marks, show the statistical uncertainty. Left: comparison with different simulation event generators: MadGraph$+$pythia (both the default and after reweighting the top quark $p_{\mathrm{T}}$ spectrum), powheg v2$+$herwig, and powheg v2$+$pythia. Right: comparison with predictions from the MadGraph$+$pythia event generator found by varying the matching threshold and renormalization scales (${\mu }_{\mathrm{R}}$, ${\mu }_{\mathrm{F}}$) up and down by a factor of 2. The lower plots show the ratio of the predictions to the data, with the statistical and total uncertainties in the ratios indicated by the two shaded bands.

Figure 5

Normalized $E_{\mathrm{T}}^{\text{miss}}$ (top) and $H_{\mathrm{T}}$ (bottom) differential $t\overline{t}$ cross sections from combined electron and muon data at $\sqrt{s}=8\mathrm{TeV}$. The vertical bars on the data points represent the statistical and systematic uncertainties added in quadrature. The inner section of the vertical bars, denoted by the tick marks, show the statistical uncertainty. Left: comparison with different simulation event generators: MadGraph$+$pythia (both the default and after reweighting the top quark $p_{\mathrm{T}}$ spectrum), mc@nlo$+$herwig, powheg v1$+$herwig, powheg v1$+$pythia, powheg v2$+$herwig, and powheg v2$+$pythia. Right: comparison with predictions from the pythia event generator found by varying the matching threshold and renormalization scales (${\mu }_{\mathrm{R}}$, ${\mu }_{\mathrm{F}}$) up and down by a factor of 2. The lower plots show the ratio of the predictions to the data, with the statistical and total uncertainties in the ratios indicated by the two shaded bands.

Figure 6

Normalized $S_{\mathrm{T}}$ (top) and $p_{\mathrm{T}}^W$ (bottom) differential $t\overline{t}$ cross sections from combined electron and muon data at $\sqrt{s}=8\mathrm{TeV}$. The vertical bars on the data points represent the statistical and systematic uncertainties added in quadrature. The inner section of the vertical bars, denoted by the tick marks, show the statistical uncertainty. Left: comparison with different simulation event generators: MadGraph$+$pythia (both the default and after reweighting the top quark $p_{\mathrm{T}}$ spectrum), mc@nlo$+$herwig, powheg v1$+$herwig, powheg v1$+$pythia, powheg v2$+$herwig, and powheg v2$+$pythia. Right: comparison with predictions from the MadGraph$+$pythia event generator found by varying the matching threshold and renormalization scales (${\mu }_{\mathrm{R}}$, ${\mu }_{\mathrm{F}}$) up and down by a factor of 2. The lower plots show the ratio of the predictions to the data, with the statistical and total uncertainties in the ratios indicated by the two shaded bands.