Measurements of normalized differential cross sections for $t\overline{t}$ production in $pp$ collisions at $\sqrt{(s)}=7\mathrm{TeV}$ using the ATLAS detector

Measurements of normalized differential cross sections for top-quark pair production are presented as a function of the top-quark transverse momentum, and of the mass, transverse momentum, and rapidity of the $t\overline{t}$ system, in proton–proton collisions at a center-of-mass energy of $\sqrt{s}=7\mathrm{TeV}$. The data set corresponds to an integrated luminosity of $4.6{\mathrm{fb}}^{-1}$, recorded in 2011 with the ATLAS detector at the CERN Large Hadron Collider. Events are selected in the $\mathrm{lepton}+\text{jets}$ channel, requiring exactly one lepton and at least four jets with at least one of the jets tagged as originating from a $b$-quark. The measured spectra are corrected for detector efficiency and resolution effects and are compared to several Monte Carlo simulations and theory calculations. The results are in fair agreement with the predictions in a wide kinematic range. Nevertheless, data distributions are softer than predicted for higher values of the mass of the $t\overline{t}$ system and of the top-quark transverse momentum. The measurements can also discriminate among different sets of parton distribution functions.

Figure 1

Distribution of the logarithm of the likelihood [$\log (ℒ)$] obtained from the kinematic fit in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ channels. Data distributions are compared to predictions, using Alpgen+Herwig as the $t\overline{t}$ signal model. The hashed area indicates the combined statistical and systematic uncertainties in the prediction, excluding systematic uncertainties related to the modeling of the $t\overline{t}$ system. Signal and background processes are shown in different colors, with “Other" including the small backgrounds from diboson and $Z+\text{jets}$ production. The lower parts of the figures show the ratios of data to the predictions.

Figure 2

Observables at the reconstruction level: $W$ transverse mass ($m_{\mathrm{T}}^W$) in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ channels, missing transverse momentum ($E_{\mathrm{T}}^{\text{miss}}$) in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ channels, and leading $b$-tagged jet $p_{\mathrm{T}}$ in the (e) $e+\text{jets}$ and (f) $\mu +\text{jets}$ channels. Data distributions are compared to predictions, using Alpgen+Herwig as the $t\overline{t}$ signal model. The hashed area indicates the combined statistical and systematic uncertainties in the total prediction, excluding systematic uncertainties related to the modeling of the $t\overline{t}$ system. Signal and background processes are shown in different colors, with “Other” including the small backgrounds from diboson and $Z+\text{jets}$ production. Events beyond the range of the horizontal axis are included in the last bin. The lower parts of the figures show the ratios of data to the predictions.

Figure 3

Reconstructed distributions for the transverse momentum of the hadronically decaying top quark ($p_{\mathrm{T}}^t$) in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ channels and for the mass of the $t\overline{t}$ system ($m_{t\overline{t}}$) in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ channels. Data distributions are compared to predictions, using Alpgen+Herwig as the $t\overline{t}$ signal model. The hashed area indicates the combined statistical and systematic uncertainties in the total prediction, excluding systematic uncertainties related to the modeling of the $t\overline{t}$ system. Signal and background processes are shown in different colors, with “Other” including the small backgrounds from diboson and $Z+\text{jets}$ production. Events beyond the axis range are included in the last bin. The lower parts of the figures show the ratios of data to the predictions.

Figure 4

Reconstructed distributions for the transverse momentum of the $t\overline{t}$ system ($p_{\mathrm{T}}^{t\overline{t}}$) in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ channels and for the rapidity of the $t\overline{t}$ system ($y_{t\overline{t}}$) in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ channels. Data distributions are compared to predictions, using Alpgen+Herwig as the $t\overline{t}$ signal model. The hashed area indicates the combined statistical and systematic uncertainties in the total prediction, excluding systematic uncertainties related to the modeling of the $t\overline{t}$ system. Signal and background processes are shown in different colors, with “Other” including the small backgrounds from diboson and $Z+\text{jets}$ production. Events beyond the axis range are included in the last bin, or in the case of the $y_{t\overline{t}}$ spectrum the first and last bin. The lower parts of the figures show the ratios of data to the predictions.

Figure 5

The selection efficiencies binned in the (a) transverse momentum of the top-quark ($p_{\mathrm{T}}^t$), and the (b) mass ($m_{t\overline{t}}$), (c) transverse momentum ($p_{\mathrm{T}}^{t\overline{t}}$) and the (d) absolute value of the rapidity ($|y_{t\overline{t}}|$) of the $t\overline{t}$ system obtained from the Alpgen+Herwig simulation of the $t\overline{t}$ signal. The horizontal axes refers to parton-level variables.

Figure 6

The migration matrices obtained from the Alpgen+Herwig simulation, relating the parton and reconstructed levels for the transverse momentum of the hadronically decaying top quark ($p_{\mathrm{T}}^t$) in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ channels, and the mass of the $t\overline{t}$ system ($m_{t\overline{t}}$) in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ channels. The linear correlation coefficient is given below each plot and all columns are normalized to unity (before rounding off).

Figure 7

The migration matrices obtained from the Alpgen+Herwig simulation, relating the parton and reconstructed levels for the transverse momentum of the $t\overline{t}$ system ($p_{\mathrm{T}}^{t\overline{t}}$) in the (a) $e+\text{jets}$ and (b) $\mu +\text{jets}$ channels, and the absolute value of the rapidity of the $t\overline{t}$ system ($|y_{t\overline{t}}|$) in the (c) $e+\text{jets}$ and (d) $\mu +\text{jets}$ channels. The linear correlation coefficient is given below each plot and all columns are normalized to unity (before rounding off).

Figure 8

Normalized differential cross sections for the (a) transverse momentum of the hadronically decaying top quark ($p_{\mathrm{T}}^t$), and the (b) mass ($m_{t\overline{t}}$), (c) transverse momentum ($p_{\mathrm{T}}^{t\overline{t}}$) and the (d) absolute value of the rapidity ($|y_{t\overline{t}}|$) of the $t\overline{t}$ system. Generator predictions are shown as markers for Alpgen+Herwig (circles), MC@NLO+Herwig (squares), Powheg+Herwig (triangles), and Powheg+Pythia (inverted triangles). The markers are offset within each bin to allow for better visibility. The gray bands indicate the total uncertainty on the data in each bin. The lower part of each figure shows the ratio of the generator predictions to data. For $p_{\mathrm{T}}^{t\overline{t}}$ the Powheg+Pythia marker cannot be seen in the last bin of the ratio plot because it falls beyond the axis range. The cross section in each bin is given as the integral of the differential cross section over the bin width, divided by the bin width. The calculation of the cross sections in the last bins includes events falling outside of the bin edges, and the normalization is done within the quoted bin width. The bin ranges along the horizontal axis (and not the position of the markers) can be associated with the normalized differential cross-section values along the vertical axis.

Figure 9

Normalized differential cross sections for the (a) transverse momentum of the hadronically decaying top-quark ($p_{\mathrm{T}}^t$), and the (b) mass ($m_{t\overline{t}}$), (c) transverse momentum ($p_{\mathrm{T}}^{t\overline{t}}$) and the (d) absolute value of the rapidity ($|y_{t\overline{t}}|$) of the $t\overline{t}$ system. The distributions are compared to NLO QCD predictions (based on MCFM [70] with the CT10 PDF). The bin ranges along the horizontal axis (and not the position of the markers) can be associated with the normalized differential cross-section values along the vertical axis. The error bars correspond to the PDF and fixed scale uncertainties in the theoretical prediction. The gray bands indicate the total uncertainty on the data in each bin. The lower part of each figure shows the ratio of the NLO QCD predictions to data. The cross section in each bin is given as the integral of the differential cross section over the bin width, divided by the bin width. The calculation of the cross sections in the last bins includes events falling outside of the bin edges, and the normalization is done within the quoted bin width.

Figure 10

Normalized differential cross sections for the (a) transverse momentum of the hadronically decaying top-quark ($p_{\mathrm{T}}^t$), the (b) mass of the $t\overline{t}$ system ($m_{t\overline{t}}$), and the (c) transverse momentum of the $t\overline{t}$ system ($p_{\mathrm{T}}^{t\overline{t}}$). The distributions are compared to the predictions from $\mathrm{NLO}+\mathrm{NNLL}$ calculations for $p_{\mathrm{T}}^t$ [12], $m_{t\overline{t}}$ [13], and $p_{\mathrm{T}}^{t\overline{t}}$ [14, 15], all using the MSTW2008NNLO PDF. The bin ranges along the horizontal axis (and not the position of the markers) can be associated with the normalized differential cross-section values along the vertical axis. The error bars correspond to the fixed (and dynamic in the case of $p_{\mathrm{T}}^t$) scale uncertainties in the theoretical prediction. The gray bands indicate the total uncertainty on the data in each bin. The lower part of each figure shows the ratio of the $\mathrm{NLO}+\mathrm{NNLL}$ calculations to data. The cross section in each bin is given as the integral of the differential cross section over the bin width, divided by the bin width. The calculation of the cross sections in the last bins includes events falling outside of the bin edges, and the normalization is done within the quoted bin width.

Figure 11

Ratios of the NLO QCD predictions [70] to the measured normalized differential cross sections for different PDF sets (CT10 [25], MSTW2008NLO [67], NNPDF2.3 [68], and HERAPDF1.5 [75]) (markers) for the (a) transverse momentum of the hadronically decaying top-quark ($p_{\mathrm{T}}^t$), and the (b) mass ($m_{t\overline{t}}$), the (c) transverse momentum ($p_{\mathrm{T}}^{t\overline{t}}$), and the (d) absolute value of the rapidity ($|y_{t\overline{t}}|$) of the $t\overline{t}$ system. The markers are offset in each bin and the bins are of equal size to allow for better visibility. The gray bands indicate the total uncertainty on the data in each bin, while the error bars denote the uncertainties in the predictions, which include the internal PDF set variations and also fixed scale uncertainties.

Figure 12

Graphical representation of the statistical correlation matrix between the normalized differential cross sections. All variables are included to show the correlations between different bins of different variables. From left to right and bottom to top the rows and columns are labeled by bin number for each variable and the variables are ordered: $p_{\mathrm{T}}^t$, $m_{t\overline{t}}$, $p_{\mathrm{T}}^{t\overline{t}}$, and $|y_{t\overline{t}}|$.