Study of the CP nature of the top-Higgs coupling in $t\bar{t}H$ events at the LHC

In the Standard Model (SM), the Higgs boson is a scalar particle with no CP-violating interactions. After the observation of the Higgs boson production in association with a top quark pair ($t\bar{t}H$) by ATLAS and CMS in 2018, the measurement of an odd charge-parity (CP) component in one of the Higgs boson couplings would constitute an important discovery of physics beyond the SM (BSM). Recently, ATLAS and CMS searched for such a component in $t\bar{t}H$ events with the Higgs decaying into two photons. However, the coupling between the Higgs and the photons is loop-induced and could be modified by effects of new physics. This thesis describes the ongoing study of the CP nature of the Higgs Yukawa coupling to the top quarks by analyzing $t\bar{t}H$ events in the $H \rightarrow b\bar{b}$ decay channel, and provides projections of this search from the Large Hadron Collider (LHC) Run 2 to the High-Luminosity LHC (HL-LHC). The analysis uses the full Run 2 dataset of proton-proton collision collected with the ATLAS detector at a center-of-mass energy of $\sqrt{s}=13$ TeV and total integrated luminosity of $139$ fb$^{-1}$. Only events containing either one or two leptons in the final state from the decay of the top quark pair are used in the analysis. Then, the events are classified into regions according to the number of jets and the number of $b$-tagged jets. Two sets of multivariate classifiers are utilized to improve the analysis sensitivity. One classifier targets the classification of signal against backgrounds and the other targets the separation between different CP scenarios. Several CP sensitive variables, including lab-frame observables and angular variables calculated in specific frames, were used in the fit and in the training of the BDTs. A profile likelihood fit is performed over all analysis regions to constrain the background predictions and reduce the systematic uncertainties. The expected value for the CP mixing angle is presented. An extrapolation of the analysis is performed in order to provide projections on the measurement of the CP mixing angle for the HL-LHC. Different scenarios for the evolution of the systematic uncertainties with the expected increase in the luminosity were considered. The expected value for the CP mixing angle was obtained for several different values of luminosity up to $3000$ fb$^{-1}$. With the current systematic uncertainties, the pure CP-odd $t\bar{t}H$ production is expected to be excluded with $99.73\%$ confidence level (CL) only at the end of the HL-LHC project. The CP-odd exclusion significance is represented as a function of the luminosity for each of the scenarios considered, and the effects of the various types of uncertainties are evaluated.