Comprehensive measurements of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>t</mml:mi></mml:math>-channel single top-quark production cross sections at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:mn>7</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:mrow></mml:math>with the ATLAS detector

This article presents measurements of the $t$-channel single top-quark ($t$) and top-antiquark ($\overline{t}$) total production cross sections $\ensuremath{\sigma}(tq)$ and $\ensuremath{\sigma}(\overline{t}q)$, their ratio ${R}_{t}=\ensuremath{\sigma}(tq)/\ensuremath{\sigma}(\overline{t}q)$, and a measurement of the inclusive production cross section $\ensuremath{\sigma}(tq+\overline{t}q)$ in proton-proton collisions at $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ at the LHC. Differential cross sections for the $tq$ and $\overline{t}q$ processes are measured as a function of the transverse momentum and the absolute value of the rapidity of $t$ and $\overline{t}$, respectively. The analyzed data set was recorded with the ATLAS detector and corresponds to an integrated luminosity of $4.59\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. Selected events contain one charged lepton, large missing transverse momentum, and two or three jets. The cross sections are measured by performing a binned maximum-likelihood fit to the output distributions of neural networks. The resulting measurements are $\ensuremath{\sigma}(tq)=46\ifmmode\pm\else\textpm\fi{}1(\text{stat})\ifmmode\pm\else\textpm\fi{}6(\text{syst})\text{ }\text{ }\mathrm{pb}$, $\ensuremath{\sigma}(\overline{t}q)=23\ifmmode\pm\else\textpm\fi{}1(\text{stat})\ifmmode\pm\else\textpm\fi{}3(\text{syst})\text{ }\text{ }\mathrm{pb}$, ${R}_{t}=2.04\ifmmode\pm\else\textpm\fi{}0.13(\text{stat})\ifmmode\pm\else\textpm\fi{}0.12(\text{syst})$, and $\ensuremath{\sigma}(tq+\overline{t}q)=68\ifmmode\pm\else\textpm\fi{}2(\text{stat})\ifmmode\pm\else\textpm\fi{}8(\text{syst})\text{ }\text{ }\mathrm{pb}$, consistent with the Standard Model expectation. The uncertainty on the measured cross sections is dominated by systematic uncertainties, while the uncertainty on ${R}_{t}$ is mainly statistical. Using the ratio of $\ensuremath{\sigma}(tq+\overline{t}q)$ to its theoretical prediction, and assuming that the top-quark-related CKM matrix elements obey the relation $|{V}_{tb}|\ensuremath{\gg}|{V}_{ts}|,|{V}_{td}|$, we determine $|{V}_{tb}|=1.02\ifmmode\pm\else\textpm\fi{}0.07$.

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