Differential ratio measurements of $\mathrm{t\bar{t}\gamma}$/$\mathrm{t\bar{t}}$ and a search for exclusive $\mathrm{t\bar{t}}$ with the CMS experiment

In this thesis, measurements performed using proton-proton collision data at $\sqrt{s} = 13~$TeV collected by the CMS experiment at the CERN LHC, in the years 2016, 2017, and 2018, are presented. The data correspond to an integrated luminosity of 138 fb$^{-1}$. New results on top quark pair production in association with a photon ($\mathrm{t\bar{t}\gamma}$) are presented. Differential cross sections are presented, measuring five different observables that are sensitive to modelling aspects and possible effects of new physics. In particular, top quark observables are measured for the first time, using a top quark pair ($\mathrm{t\bar{t}}$) reconstruction algorithm. Experiment independent distributions are obtained at the parton level. The ratio between the cross sections for $\mathrm{t\bar{t}\gamma}$ and $\mathrm{t\bar{t}}$ is measured for the first time at the LHC, inclusively and differentially. Additionally, the top quark charge asymmetry is measured in $\mathrm{t\bar{t}\gamma}$ events. The results are obtained using maximum likelihood fits which directly account for and constrain backgrounds and systematic uncertainties. The results are compared to theory predictions. No significant deviations from standard model predictions are observed. Using a fraction of the same data, collected in 2017, a search for central exclusive production of $\mathrm{t\bar{t}}$ where the protons remain intact and are measured in the Precision Proton Spectrometer, is also presented. An upper limit for the cross section of this process is obtained.