Searches for undiscovered processes using the multilepton final state in proton-proton collisions at CMS

The standard model (SM) of particle physics represents our most fundamental knowledge of nature. The model leaves several pressing questions unanswered, hinting at the existence of new physics. This dissertation is a small part of the large CMS Collaboration effort to answer these questions. Three distinct searches for undiscovered processes in 13 TeV proton-proton collision data collected with the CMS detector at the CERN LHC are presented. The searches target diverse physics, but are experimentally closely related. All of the searches use events with multiple charged leptons in the final state, with a particular focus on events with three leptons. The first search being presented is a search for sterile Majorana neutrinos in events with three charged light leptons, electrons or muons. It is the first sterile neutrino search in the multilepton final state at the LHC. This final state enables the study of sterile neutrinos in the mass range below 40 GeV, a first at a hadron collider. The sensitivity extends downwards to sterile neutrino masses of 1 GeV. In addition, the search marks the first time an analysis is able to probe sterile neutrino masses beyond 500 GeV, achieving sensitivity all the way up to 1.2 TeV. No excess over the SM hypothesis is found, and mass-dependent exclusion limits are placed on the square of the mixing parameter between sterile neutrinos and electron and muon neutrinos. The limits range from $1.2 \cdot 10^{-5}$ to 1 in the sterile neutrino mass range 1 GeV--1.2 TeV. Second is a search for single top quark production in association with a Z boson (tZq), an extremely rare SM process with an extraordinary sensitivity to new physics. Being about 50 times more rare than Higgs boson production in 13 TeV proton-proton collisions, tZq production remained undiscovered prior to the work presented here. The search analyzes events with three light leptons and at least one jet identified as originating from a b hadron decay. The use of a machine learning based lepton identification algorithm and a redesigned analysis strategy massively increase the sensitivity of the search compared to those that came before. This results in the first observation of tZq production with an observed (expected) significance of 8.2 (7.7) standard deviations over the background-only hypothesis. The tZq production cross section is measured with a relative uncertainty of 15\%, more than twice as precise as any earlier measurement. Lastly, a search for the direct electroweak production of charginos and neutralinos, superpartners of the electroweak gauge and Higgs bosons, is presented. The range of possible chargino and neutralino production and decay modes is vast. Events with three or more leptons, including up to two hadronically decaying $\tau$ leptons, as well as events with two light leptons of the same sign are analyzed. Events are divided into a large number of orthogonal categories by their lepton flavor and sign content. Each event category is sensitive to particular manifestations of supersymmetry. Events with three light leptons, at least two of which form an opposite-sign and same-flavor pair, provide the bulk of the search sensitivity to several important signal models. Unfortunately, the majority of SM background events also falls under this category. Several parametric neural networks are used to separate signal and background events in this region, vastly increasing the reach of the search over earlier results. This is the first time parametric neural networks are used in such a search. The signal extraction strategy in other event categories is also entirely redesigned compared to earlier work in CMS, resulting in a far greater sensitivity to all studied models of superpartner production. No excess of events over the SM expectation is observed, and chargino masses up to 1450 GeV are excluded under certain conditions. This is currently the overall highest excluded mass for an electroweak superpartner, under any production or decay hypothesis.