Inclusive and Differential Cross-Section Measurements of $t$-channel single top-quark production at $\sqrt{s} = 7$ TeV with the ATLAS detector

This thesis presents measurements of the $t$-channel single top-quark ($t$) and top-antiquark ($\bar{t}$) total production cross sections $\sigma$ in proton--proton collisions at $\sqrt{s} = 7$ TeV at the LHC. Differential cross sections for the $tq$ and $\bar{t}q$ processes are measured as a function of the transverse momentum and the absolute value of the rapidity of $t$ and $\bar{t}$, respectively, for the first time. The analyzed data set was recorded with the ATLAS detector and corresponds to an integrated luminosity of 4.59~fb$^{-1}$. 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 $\sigma(tq)= 46\pm 6\; \mathrm{pb}$, $\sigma(\bar{t}q)= 23 \pm 4\; \mathrm{pb}$, and $\sigma(tq + \bar{t}q)= 68 \pm 8\; \mathrm{pb}$, and the uncertainty on each measured cross section is dominated by systematic uncertainties. In addition the ratio of top-quark to top-antiquark production $R_{t}= \sigma(tq)/\sigma(\bar{t}q)$ is measured to be $R_{t} = 2.04 \pm 0.18$. The uncertainty on $R_{t}$ is mainly statistical. Using the ratio of $\sigma(tq + \bar{t}q)$ to its theoretical prediction, and assuming that the top-quark-related CKM matrix elements obey the relation $|V_{tb}|\gg |V_{ts}|, |V_{td}|$, we determine $|V_{tb}|=1.02 \pm 0.07$. The differential cross sections are determined using an iterative unfolding method, that utilizes Bayes theorem. The uncertainties on the results are dominated by the limited data statistics. All results presented in this thesis are consistent with the Standard Model expectation.