Study of the production processes of top quarks and missing energy predicted by the Standard Model and its extensions, in leptonic final states with the CMS detector at the LHC using machine learning techniques.

In this thesis, measurements of Standard Model (SM) processes and searches for processes beyond the SM related to the top quark in final states with leptons are presented using data from proton-proton collisions produced at the LHC and collected by the CMS experiment at CERN. The first measurement of the cross section of the top-antitop quark pair production process has been performed with the initial data of the Run 3 of the LHC at the new centre-of-mass energy of 13.6 TeV, yielding a cross-section of σ = 888 ± 34 (syst. + stat.) ± 20 (lumi) pb. This result is consistent with SM predictions and achieves a precision comparable to theoretical expectations. Additionally, a methodology has been developed for measuring the cross section of this process at a centre-of-mass energy of 5.02 TeV in semilepton final states, aiming to enhance the precision of this measurement and combine it with the result obtained in dilepton final states. The goal is to reduce the total uncertainty compared to the previous result by half. The 5.02 TeV dataset has also been used to measure, for the first time at this energy, the cross section of processes associated with two massive vector bosons (WW, WZ, and ZZ). The obtained results are in agreement with SM predictions. Two searches for processes beyond the SM related to the top quark are presented, both using the data collected during the Run 2 of the LHC at 13 TeV. The first is the search for the supersymmetric top quark (stop) assuming it decays into a top quark and a neutralino, in a phase space where the mass difference between the stop and the neutralino is very similar to the top quark mass. This makes it challenging to distinguish the signal process from top quark pair production, needing a dedicated search as other searches do not have sensitivity in this region. Using a parametric neural network, the entire search region is excluded for first time at a 95% confidence level. Another search has been performed under the framework of the effective field theory for processes associated with top quark production in final states with leptons. The effect of a total of 26 operators is studied simultaneously in six different signal processes. In all cases, the results are consistent with SM predictions, and the confidence intervals are improved compared to previous results. Finally, a technique for muon identification has been developed using a machine learning model that improves the strategy used to date, providing more robust results against the number of vertices produced in collisions, which has increased in Run 3.