Detailed measurements of $t$-channel single top-quark production are presented. They use 20.2 fb$^{-1}$ 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 $\sigma_{\mathrm{tot}}(tq) = 56.7^{+4.3}_{-3.8}\;$pb for top-quark production and $\sigma_{\mathrm{tot}}(\bar{t}q) = 32.9^{+3.0}_{-2.7}\;$pb 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 $R_t=1.72 \pm 0.09$, with an improved relative precision of 4.9 % since several systematic uncertainties cancel in the ratio. 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.
Predicted and observed event yields for the signal region (SR). The multijet background prediction is obtained from a binned maximum-likelihood fit to the $E_{\mathrm{T}}^{\mathrm{miss}}$ distribution. All the other predictions are derived using theoretical cross-sections, given for the backgrounds in Sect. 6 and for the signal in Sect. 1. The quoted uncertainties are in the predicted cross-sections or in the number of multijet events, in case of the multijet process.
Predicted and observed event yields for the signal region (SR). The multijet background prediction is obtained from a binned maximum-likelihood fit to the $E_{\mathrm{T}}^{\mathrm{miss}}$ distribution. All the other predictions are derived using theoretical cross-sections, given for the backgrounds in Sect. 6 and for the signal in Sect. 1. The quoted uncertainties are in the predicted cross-sections or in the number of multijet events, in case of the multijet process.
Definition of the fiducial phase space.
A measurement of the $t$-channel single-top-quark and single-top-antiquark production cross-sections in the lepton+je ts channel is presented, using 3.2 fb$^{-1}$ of proton--proton collision data at a centre-of-mass energy of 13 TeV, recorded with the ATLAS detector at the LHC in 2015. Events are selected by requiring one charged lepton (electron or muon), missing transverse momentum, and two jets with high transverse momentum, exactly one of which is required to be $b$-tagged. Using a binned maximum-likelihood fit to the discriminant distribution of a neural network, the cross-sections are determined to be $\sigma(tq) = 156 \pm 5 \, (\mathrm{stat.}) \pm 27 \, (\mathrm{syst.}) \pm 3\,(\mathrm{lumi.})$ pb for single top-quark production and $\sigma(\bar{t}q) = 91 \pm 4 \, (\mathrm{stat.}) \pm 18 \, (\mathrm{syst.}) \pm 2\,(\mathrm{lumi.})$ pb for single top-antiquark production, assuming a top-quark mass of 172.5 GeV. The cross-section ratio is measured to be $R_t = \sigma(tq)/\sigma(\bar{t}q) = 1.72 \pm 0.09 \, (\mathrm{stat.}) \pm 0.18 \, (\mathrm{syst.})$.
Predicted and observed event yields for the signal region. The quoted uncertainties include uncertainties in the theoretical cross-sections, in the number of multijet events, and the statistical uncertainties. The event yield of the $W^+ + $jets process in the $\ell^-$ channel is reported to be $<1$ in the paper. To provide a numerical value for this table in HEPdata, the yield is approximated with $1\pm 1$. The same is done for the event yield of the $W^- + $jets process in the $\ell^+$ channel.
Estimated scale factors, $\hat{\beta}$, and number of events, $\hat{\nu}=\hat{\beta}\cdot\nu$, for the $\ell^+$ and $\ell^-$ channel from the minimisation of the likelihood function. The quoted uncertainties in $\hat{\beta}$ and $\hat{\nu}$ include the statistical uncertainty and the uncertainties from the constraints on the background normalisation as used in the likelihood function.
Measured total cross sections of single top-quark and single top-antiquark production and their ratio $R_t$. In addition, the sum of top-quark and top-antiquark production is provided as well. Based on the total cross section the value of $f_\mathrm{LV}\cdot |V_{tb}|$ is determined.
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