Measurement of the differential dileptonic t$\bar{\text{t}}$ cross section in a BSM phase space with the CMS detector using the full LHC Run 2 data set

The top quark is the heaviest of all known elementary particles described by the standard model of particle physics (SM). In proton-proton (pp) collisions it is mainly produced in quark-antiquark pairs (t$\bar{\text{t}}$). Measurements of the corresponding t$\bar{\text{t}}$ production cross section yield important precision tests of the SM, while also probing theories describing physics beyond the SM (BSM). In this thesis, differential cross section measurements of the SM dileptonic t$\bar{\text{t}}$ process in a phase space, where additional contributions from BSM physics could be found, are presented. The measurements are performed for pp collisions at a center-of-mass energy of $13\,\text{TeV}$, recorded by the CMS experiment between 2016 and 2018 during Run 2 of the LHC, corresponding to an integrated luminosity of $138\,\text{fb}^{-1}$. The results are derived by combining the $ee$, $\mu\mu$ and $e\mu$ decay channels. The BSM scenarios considered in this thesis include supersymmetric and dark matter models, which predict final states similar to the dileptonic t$\bar{\text{t}}$ process, characterized by two charged leptons, two b jets and significant missing transverse momentum produced by undetected particles. Measurements of such complex signatures require a proper reconstruction of the final state particles, which, among others, relies on a good alignment of the silicon sensors in the CMS tracking system. Within the scope of the thesis performance studies of the online tracker alignment and an improvement of the alignment method are presented. Unlike previous cross section measurements, where differential results were mainly derived as a function of kinematic variables of the leptons or top quarks, the present analysis focuses on two observables, which separate potential BSM contributions from the SM dileptonic t$\bar{\text{t}}$ process. On detector level, these observables are given by the missing transverse momentum and the minimal azimuthal distance between the missing transverse momentum and a lepton. In order to increase the sensitivity of the analysis, additional corrections of the missing transverse momentum based on machine learning techniques are developed within this thesis, which significantly improve the corresponding response and resolution in the final state of interest. In the first step of the measurements, the observed pp-collision data and SM predictions based on Monte Carlo (MC) simulations are compared on detector level based on the one-dimensional distributions as well as the two-dimensional combination of both detector-level observables. For all three distributions, good agreement between the recorded data and the SM predictions with no significant indications for potential BSM contributions is observed. In the second step, absolute and normalized differential cross sections on particle level are derived by unfolding the three detector-level distributions. The cross sections are obtained as a function of the transverse momentum of the dineutrino system and the minimal azimuthal distance between the dineutrino system and a lepton, which match the detector-level observables for the dileptonic t$\bar{\text{t}}$ process. So far, differential t$\bar{\text{t}}$ cross sections as a function of these two observables have not been measured at the LHC. To study the impact of different descriptions for the background contribution from single top production in association with a W boson (tW) in simulation, two sets of results based on the diagram removal (DR) and the diagram subtraction (DS) scheme are provided. The results are compared to two MC-based theory predictions using NLO matrix element accuracy as well as two fixed-order calculations, which correspond to NLO and NNLO accuracy in QCD. All four theory predictions provide reasonable descriptions of the measured absolute and normalized cross section spectra, while the measurements of the dineutrino momenta seem to prefer the tW description based on the DS scheme.