Measurement of the top-quark pair production cross-section in $pp$ collisions at $\sqrt{s} = 7$ TeV using final states with an electron or a muon and a hadronically decaying $\tau$-lepton

The $t$-quark is the heaviest elementary particle observed so far (172.9$\pm$1.5 GeV). Owing to its largest mass, the $t$-quark is believed to have a strong connection with physics beyond the Standard Model (SM). It is thus essential to understand the production and the decay process of the $t$-quark in the context of the SM through a measurement of the $t$-quark pair ($t\bar{t}$) production cross-section ($\sigma_{t\bar{t}}$) at the collider experiment. By using a large number of proton-proton ($pp$) collision data at $\sqrt{s} = 7$ TeV produced by the Large Hadron Collider (LHC), ATLAS experiment has been measured $\sigma_{t\bar{t}}$ in the single-lepton ($t\bar{t}\rightarrow \ell^{+}\nu_{\ell} qq^{'}b\bar{b}$), di-lepton ($t\bar{t}\rightarrow \ell^{+} \nu_{\ell} \ell^{-} \bar{\nu_{\ell}} b\bar{b}$) and all-hadronic ($t\bar{t}\rightarrow qq^{'}q^{''}q^{'''}b\bar{b}$) channel ($\ell=e,\mu$). The combined result (177$\pm11$ pb) is in good agreement with the SM prediction (164${}^{+11}_{-16}$ pb). This thesis reports on the first ATLAS measurement of the $\sigma_{t\bar{t}}$ using final states characterized by a lepton (a muon or an electron) and a hadronically decaying $\tau$-lepton ($t\bar{t}\rightarrow\tau^{+} \nu_{\tau} \ell^{-} \bar{\nu_{\ell}} b\bar{b}$). This measurement is of importance toward the search for charged Higgs boson ($H^{\pm}$) that in some scenarios predominantly decays into $\tau\nu_\tau$ and contribute to this decay process. Candidate events are extracted from the 2.05 fb$^{-1}$ $pp$ collision data by requiring a lepton, a hadronically decaying $\tau$ candidate, more than two jets where at least one of them is identified as originating from a $b$-quark and a large missing transverse momentum. The $\tau$-lepton either decays into leptonic (35%, $\tau\rightarrow\ell\nu_\ell\nu_\tau$) or hadronic (65%, $\tau\rightarrow h+n\pi^{0}$, where $h=\pi^{\pm}, K^{\pm}$), where the former case is not used for the identification as it is not distinguishable to that of primary leptons. The hadronically decaying $\tau$-lepton is reconstructed as a narrow and collimated jet compared to the quark, gluon originated jet. However, as there is no distinct variable that can separate between them, a majority of the candidate events come from $t\bar{t}$ single-lepton events by one of the jets misidentified as a hadronically decaying $\tau$-lepton. In order to isolate signal events among candidate events, the analysis exploits a multivariate analysis based on more than 8 parameters related to the observed $\tau$ candidate to calculate the similarity to the real $\tau$-lepton, which leads to the discrimination of the signal events from background processes. This is then followed by the background estimation in a data-driven way to minimize the systematic uncertainty. As the result, $\sigma_{t\bar{t}}$ is measured to be: \begin{equation} \sigma_{t\bar{t}} = 186 \pm 13 \text{ (stat.)} \pm 20 \text{ (syst.)} \pm 7 \text{ (lumi.)}~\text{pb,} \nonumber \end{equation} where each uncertainty represents the statistical uncertainty, the systematic uncertainty, and the uncertainty related to the luminosity determination, respectively. The observed cross-section is the first $\sigma_{t\bar{t}}$ measurement with $\tau$-lepton final state at $\sqrt{s} = 7$ TeV, with unprecedented accuracy of d$\sigma/\sigma = $13%. The observed cross-section is consistent with the theoretical calculation based on the Standard Model. Using the measurement obtained in this thesis, the upper limit on the branching ratio that the $t$-quark decays into $t\rightarrow H^{\pm}b$ has been calculated to be 4 - 8% with 95% confidence level, depending on the assumed charged Higgs boson mass. The ratio of the observed cross-section with that of measured in di-lepton channel gives $1.00\pm0.09$. With above results, this thesis demonstrated the validity of the SM, especially about the $t$-quark decay into a hadronically decaying $\tau$-lepton ($t\rightarrow \tau^{+}\nu b$).