Fiducial, total and differential cross-section measurements of t-channel single top-quark production in pp collisions at 8 TeV using data collected by the ATLAS detector

Abstract

Detailed measurements of t-channel single top-quark production are presented. They use 20.2 fb[Formula: see text] of data collected by the ATLAS experiment in proton-proton collisions at a centre-of-mass energy of 8 TeV at the LHC. Total, fiducial and differential cross-sections are measured for both top-quark and top-antiquark production. The fiducial cross-section is measured with a precision of 5.8% (top quark) and 7.8% (top antiquark), respectively. The total cross-sections are measured to be [Formula: see text] for top-quark production and [Formula: see text] for top-antiquark production, in agreement with the Standard Model prediction. In addition, the ratio of top-quark to top-antiquark production cross-sections is determined to be [Formula: see text]. The differential cross-sections as a function of the transverse momentum and rapidity of both the top quark and the top antiquark are measured at both the parton and particle levels. The transverse momentum and rapidity differential cross-sections of the accompanying jet from the t-channel scattering are measured at particle level. All measurements are compared to various Monte Carlo predictions as well as to fixed-order QCD calculations where available.

Fig. 1

Representative leading-order Feynman diagrams for a single top-quark production and b single top-antiquark production via the t-channel exchange of a virtual $W^{\ast }$ boson, including the decay of the top quark and top antiquark, respectively

Fig. 2

Observed distributions of the missing transverse momentum, $E_{\text{T}}^{\text{miss}}$, in the signal region (SR), including events with $E_{\text{T}}^{\text{miss}}<30\mathrm{GeV}$, for a events in the $e^{+}$ channel with an electron in the barrel region and for b events in the ${\mathit{\mu }}^{+}$ channel, compared to the model obtained from simulated events. The normalisation is obtained from the binned maximum-likelihood fit to the full $E_{\text{T}}^{\text{miss}}$ distributions, and applied to the SR. The hatched uncertainty band represents the MC statistical uncertainty and the normalisation of the multijet background. The ratio of observed (Data) to predicted (Pred.) number of events in each bin is shown in the lower panel. Events beyond the x-axis range are included in the last bin

Fig. 3

Probability densities of the two most discriminating input variables to the NN: a the invariant mass m(jb) of the untagged jet and the b-tagged jet, and b the absolute value of the pseudorapidity of the untagged jet $|\mathit{\eta }(j)|$. The distributions are shown for the tq signal process, the $W^{+}$ + jets background and the top-quark background in the ${\ell }^{+}$ SR. Events beyond the x-axis range are included in the last bin

Fig. 4

Probability densities of the NN discriminants in the signal region (SR) for the tq and $\overline{t}q$ signal processes, the $W$ + jets background and the top-quark background: a in the ${\ell }^{+}$ SR and b in the ${\ell }^{-}$ SR

Fig. 5

Observed $O_{\text{NN}}$ distributions (a, b) in the $W$ + jets VR and (c, d) in the $t\overline{t}$ VR compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fits of the $E_{\text{T}}^{\text{miss}}$ distributions as described in Sect. 6. The hatched uncertainty band represents the uncertainty in the pre-fit process cross-sections and the bin-by-bin MC statistical uncertainty, added in quadrature. The lower panels show the ratio of the observed to the expected number of events in each bin

Fig. 6

Observed $O_{\text{NN}}$ distributions in a the ${\ell }^{+}$ SR and in b the ${\ell }^{-}$ SR compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fit to the discriminants. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature. The lower panels show the ratio of the observed to the expected number of events in each bin to illustrate the goodness-of-fit.

Fig. 7

Observed distributions of the three most important input variables to the NN in the SR compared to the model obtained with simulated events. The definitions of the variables can be found in Table 2. The simulated distributions are normalised to the event rates obtained by the maximum-likelihood fit to the NN discriminants. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature. The lower panels show the ratio of the observed to the expected number of events in each bin to illustrate the goodness-of-fit. Events beyond the x-axis range in (a), (b), (e) and (f)

Fig. 8

Observed distributions of $cos{\mathit{\theta }}^{\ast }(\ell ,j)$ in a the ${\ell }^{+}$ SR and in b the ${\ell }^{-}$ SR compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fit to the $O_{\text{NN}}$ distributions. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature. The lower panels show the ratio of the observed to the expected number of events in each bin to illustrate the goodness-of-fit.

Fig. 9

Measured t-channel a single-top-quark and b single-top-antiquark fiducial cross-sections compared to predictions by the NLO MC generators Powheg-Box and MadGraph5_aMC@NLO in the four-flavour scheme (4FS) and five-flavour scheme (5FS) combined with different parton-shower models. The uncertainties in the predictions include the uncertainty due to the scale choice using the method of independent restricted scale variations and the intra-PDF uncertainty in the CT10 PDF set

Fig. 10

Extrapolated t-channel a single-top-quark and b single-top-antiquark production cross-sections for different MC-generator setups compared to fixed-order NLO calculations. For the three calculations, the uncertainty from the renormalisation and factorisation scales are indicated in darker shading, and the total uncertainties, including the renormalisation and factorisation scale as well as the PDF + ${\mathit{\alpha }}_{\text{S}}$ uncertainties, are indicated in lighter shading. For the NNLO prediction, only the renormalisation and factorisation scale uncertainty is provided in Ref. [22]. For comparison, the PDF + ${\mathit{\alpha }}_{\text{S}}$ uncertainties from the NLO prediction [14] are added to the NNLO renormalisation and factorisation scale uncertainty reflected in the lighter shaded uncertainty band. For this comparison, the uncertainty in the extrapolation does not include the contribution from the NLO-matching method and from the choice of parton-shower model

Fig. 11

Predicted values of $R_t={\mathit{\sigma }}_{\text{tot}}(tq)/{\mathit{\sigma }}_{\text{tot}}(\overline{t}q)$ calculated with HatHor  [14] at NLO accuracy in QCD [15] in the 5FS using different NLO PDF sets [–85] compared to the measured value. The error bars on the predictions include the uncertainty in the renormalisation and factorisation scales and the combined internal PDF and ${\mathit{\alpha }}_{\text{S}}$ uncertainty. The dashed black line indicates the central value of the measured $R_t$ value. The combined statistical and systematic uncertainty of the measurement is shown in green, while the statistical uncertainty is represented by the yellow error band. The uncertainty in the measured $R_t$ value does not include the PDF components for this comparison

Fig. 12

Observed distributions of the first three input variables to the default neural network in the signal region (SR), after a cut of $O_{\text{NN}}>0.8$ on the network output. The distributions are compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fit to the discriminants. The definitions of the variables can be found in Table 2. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature. Events beyond the x-axis range in a and b are included in the last bin. The lower panels show the ratio of the observed to the expected number of events in each bin to illustrate the goodness-of-fit

Fig. 13

Neural network output distribution ($O_{\text{NN2}}$) of the neural network without $|\mathit{\eta }(j)|$ normalised to the fit results of the default network for a the ${\ell }^{+}$ and b the ${\ell }^{-}$ signal region (SR). The distributions are compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fit to the discriminants. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature.

Fig. 14

Measured distributions of (a, b) $p_{\text{T}}(\ell \mathit{\nu }b)$ and (c, d) $|y(\ell \mathit{\nu }b)|$ for (a, c) ${\ell }^{+}$ and (b, d) ${\ell }^{-}$ events in the signal region (SR) after a cut of $O_{\text{NN}}>0.8$. The distributions are compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fit to the discriminants. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature. The lower panels show the ratio of the observed to the expected number of events in each bin to illustrate the goodness-of-fit

Fig. 15

Measured distributions of (a, b) $p_{\text{T}}(j)$ and (c, d) $|y(j)|$ at reconstruction level for (a, c) ${\ell }^{+}$ and (b, d) ${\ell }^{-}$ events in the signal region (SR) after a cut of $O_{\text{NN}}(O_{\text{NN2}})>0.8$ The distributions are compared to the model obtained from simulated events. The simulated distributions are normalised to the event rates obtained by the fit to the discriminants. The hatched uncertainty band represents the total uncertainty in the rates of all processes after the fit and the bin-by-bin MC statistical uncertainty, added in quadrature. The lower panels show the ratio of the observed to the expected number of events in each bin to illustrate the goodness-of-fit

Fig. 16

Migration matrices for a $p_{\text{T}}(\widehat{t})$, b $p_{\text{T}}(t)$, c $|y(\widehat{t})|$ and d $|y(t)|$. a, c Particle level, while b and d are for parton level. The pseudo top quark or parton-level quark is shown on the y-axis and the reconstructed variable is shown on the x-axis

Fig. 17

Absolute unfolded differential cross-sections as a function of $p_{\text{T}}(\widehat{t})$ for a top quarks and b top antiquarks. The unfolded distributions are compared to various MC predictions. The vertical error bars on the data points denote the total uncertainty. The inner (yellow) band in the bottom part of each figure represents the statistical uncertainty of the measurement, and the outer (green) band the total uncertainty.

Fig. 18

Absolute unfolded differential cross-sections as a function of $|y(\widehat{t})|$ for a top quarks and b top antiquarks. The unfolded distributions are compared to various MC predictions. The vertical error bars on the data points denote the total uncertainty. The inner (yellow) band in the bottom part of each figure represents the statistical uncertainty of the measurement, and the outer (green) band the total uncertainty.

Fig. 19

Absolute unfolded differential cross-sections as a function of $p_{\text{T}}(\widehat{j})$ for a top quarks b top antiquarks. The unfolded distributions are compared to various MC predictions. The vertical error bars on the data points denote the total uncertainty. The inner (yellow) band in the bottom part of each figure represents the statistical uncertainty of the measurement, and the outer (green) band the total uncertainty.

Fig. 20

Absolute unfolded differential cross-sections as a function of $|y(\widehat{j})|$ for a top quarks and b top antiquarks. The unfolded distributions are compared to various MC predictions. The vertical error bars on the data points denote the total uncertainty. The inner (yellow) band in the bottom part of each figure represents the statistical uncertainty of the measurement, and the outer (green) band the total uncertainty.

Fig. 21

Absolute unfolded differential cross-sections as a function of $p_{\text{T}}(t)$ for a top quarks and b top antiquarks. The unfolded distributions are compared to QCD NLO and NLO + NNLL calculations as well as various MC predictions. The vertical error bars on the data points denote the total uncertainty. The dashed (red) line in the central distribution shows the NLO prediction calculated using MCFM. The dash-dot (blue) line is the NLO + NNLL prediction [25]. The bottom distribution compares the data with the MC predictions from Powheg-Box (orange dashed line) and MadGraph5_aMC@NLO (purple dash-dotted line). The inner (yellow) band in the bottom part of each figure represents the statistical uncertainty of the measurement, and the outer (green) band the total uncertainty.

Fig. 22

Absolute unfolded differential cross-sections as a function of $|y(t)|$ for a top quarks and b top antiquarks. The unfolded distributions are compared to a QCD NLO calculation and various MC predictions The vertical error bars on the data points denote the total uncertainty. The dashed (red) line in the central distribution shows the NLO prediction calculated using MCFM. The bottom distribution compares the data with the MC predictions from Powheg-Box (orange dashed line) and MadGraph5_aMC@NLO (purple dash-dotted line). The inner (yellow) band in the bottom part of each figure represents the statistical uncertainty of the measurement, and the outer (green) band the total uncertainty