Precision measurements of differential $\mathrm{t\overline{t}}$ production cross sections as a function of kinematic event variables at 13 TeV at CMS.

This thesis sets out to test the current understanding of the pair production of the top quark standard model. To do so, it first introduces the theoretical knowledge behind the standard model and the production of the top quark, before discussing how the top quark is modelled in simulation. Next, the large and complex machinery required to produce and detect high-energy collisions is described and the algorithm used to reconstruct particles from the deposits. These particles are used to perform measurements of the differential $\mathrm{t}\overline{\mathrm{t}}}$ production cross sections. These are presented in the single-lepton ($e$ or $\mu$) decay channel, as a function of several kinematic event variables. These kinematic event variables do not require the reconstruction of the $\mathrm{t}\overline{\mathrm{t}}}$ system and are $N_{\mathrm{jets}}$, $H_{\mathrm{T}}$, $S_{\mathrm{T}}$, $p_{\mathrm{T}}^{\mathrm{miss}}$, $p_{\mathrm{T}}^{\mathrm{W}}$, $p_{\mathrm{T}}^{\ell}$ and $\lvert \eta^{\ell}} \rvert$. The measurements are performed with proton-proton collision data collected by the CMS experiment at the LHC during 2016, with an integrated luminosity of 35.9~$\mathrm{fb}^{-1}$. The $\mathrm{t}\overline{\mathrm{t}}}$ yield in each decay channel is calculated by subtracting the single top quark, vector boson in association with jets and multijet QCD production backgrounds from the total data yield. The $\mathrm{t}\overline{\mathrm{t}}}$ yields are then extrapolated, using a $\mathrm{t}\overline{\mathrm{t}}}$ model, with respect to the stable particles that form depositions detectable by CMS to a common phase space in order to be able to consistently combine the two channels. The data are also naturally smeared by the resolution of the detector and contain effects due to the detector efficiency and acceptance. The method to undo the thumbprint of the detector and to perform the extrapolation is discussed in detail. From the combined, unsmeared $\mathrm{t}\overline{\mathrm{t}}}$ yields, both the normalised and absolute differential cross sections are calculated together with the statistical and systematic uncertainties. The cross section measurements are compared to state-of-the-art leading order and next-to-leading order $\mathrm{t}\overline{\mathrm{t}}}$ simulations by means of a goodness-of-fit test, incorporating the total covariance matrix describing the correlations of the uncertainties between bins of the measurement. Finally, brief studies into the possible future of these differential cross sections measurements is discussed.