Seeing a single top quark: Search for $pp\to tq\gamma$ production and The combination of ATLAS searches for flavor changing neutral currents in $t\to Hq$ decays

The top quark is the heaviest known elementary particle. With a coupling to the Higgs boson close to unity, the top quark plays a special role in electroweak symmetry breaking as well as in physics beyond the Standard Model. An accurate measurement of its properties can provide key information for understanding the physics at the TeV scale. In this dissertation, two measurements of the top quark properties are presented. The first part of this dissertation presents the first-ever ATLAS search for the associated production of a single top quark and a photon. This analysis is performed with 139 fb$^{-1}$ of $pp$ collision data collected by the ATLAS detector at the LHC at $\sqrt{s}$ = 13 TeV. Only final states with exactly one lepton and at least one photon are considered in this analysis. Major backgrounds for the signal are $t\bar{t}\gamma$, $W\gamma$ and $t\bar{t}$. A deep learning, neural network approach is used for separating signal and background events. A binned profile likelihood fit is performed with neural network output as the discriminant. The expected best-fit value of the ratio of the observed $tq\gamma$ cross-section to that of the SM prediction is $1.0^{+0.14}_{-0.14}$ = $1.0\ ^{+0.05}_{-0.05}$ (stat.) $^{+0.13}_{-0.13}$ (syst.). This corresponds to an expected p-value of 6.5 $\sigma$ for the no-signal hypothesis. In the second part, results from the combination of ATLAS searches for flavor changing neutral currents (FCNC) in $t\to Hq$ decays are presented. Four FCNC analyses, probing different Higgs decay modes, performed with 36.1 fb$^{-1}$ of proton-proton collision data collected by the ATLAS detector in 2015-2016 are considered in the combination. They search for top-quark pair events in which one top quark decays into $Wb$ and the other top quark decay into $Hq$. The targeted Higgs decay modes are$\colon$ $\gamma \gamma, WW^*, \tau \tau, ZZ^*, b\bar{b}$. The combination of these searches yields observed (expected) 95\% CL upper limits on the $t\to Hc$ and $t\to Hu$ branching ratios of $1.1\times 10^{-3}$ ($8.3\times 10^{-4}$) and $1.2\times 10^{-3}$ ($8.3\times 10^{-4}$), assuming $\mathscr{B}(t\to Hu)$ =0 and $\mathscr{B}(t\to Hc)$ =0 respectively. The corresponding combined observed (expected) upper limits on the $|\lambda_{tcH}|$ and $|\lambda_{tuH}|$ are 0.064 (0.055) and 0.066 (0.055) respectively. These results are the most restrictive direct bounds on $tqH$ interactions measured to date.