Measurement of top quark pair production in association with charm quarks at $\sqrt{s}=13\,$TeV with the ATLAS detector

The Large Hadron Collider at CERN has produced a uniquely large set of proton-proton collision data at never-before-seen energies since the beginning of its operation in 2010. Using data collected by the ATLAS detector at a centre-of-mass energy of $13\ \text{TeV}$ between 2015 and 2018, corresponding to an integrated luminosity of $140\ \text{fb}^{-1}$, this thesis presents the results of the first dedicated ATLAS measurement of the production cross-section of top quark pairs in association with charm quarks. This measurement tests and provides information for future improvements of the modelling in quantum chromodynamics of systems which act at multiple distinct energy scales. This process is also an important background to measurements of other, much rarer, top quark processes such as $t\bar{t}H$ ($H\rightarrow b\bar{b}$) and $t\bar{t}t\bar{t}$. A key challenge of this measurement is the simultaneous identification of $b$- and $c$-jets, for which a custom heavy-flavour tagging algorithm is employed. A profile likelihood fit is used to extract the cross-sections for top quark pairs in association with two or more $c$-jets ($t\bar{t}+\geq2c$) and with one $c$-jet ($t\bar{t}+1c$). This measurement is performed both in a fiducial phase space designed to mimic the acceptance of the ATLAS detector, and in a more inclusive phase space. In the fiducial phase space this measures cross-sections of $1.28^{+0.27}_{-0.24}\ \text{pb}$ and $6.4^{+1.0}_{-0.9}\ \text{pb}$ for $t\bar{t}+\geq2c$ and $t\bar{t}+1c$ production, respectively. An additional fit extracts the ratios of $t\bar{t}+\geq2c$ and $t\bar{t}+1c$ cross-sections to that of total $t\bar{t}+\text{jets}$ production. The measured values tend to exceed predictions from simulation, but nonetheless are consistent with them within 0.5 to 2 standard deviations. Sensitivity is ultimately limited by uncertainties in the modelling of the $t\bar{t}$ system, as well as in the calibration of the heavy-flavour tagging algorithm and by limited data statistics. A focus is placed in this thesis on the work done to validate and understand the fit model.