Naturalness confronts nature: searches for supersymmetry with the CMS detector in pp collisions at $\sqrt{s}=8$ and $13$ TeV

In this thesis, we present two inclusive searches for supersymmetric particles at $\sqrt{s}=8$ and $13$ TeV using the razor variables and guided by the principle of naturalness. We build a framework to explore the natural supersymmetry parameter space of gluino and top squark masses and branching ratios, which is a unique attempt to cover this parameter space in a more complete way than ever before using LHC data. With this approach, the production of top squarks and gluinos are excluded below $\sim700$ GeV and $\sim1.6$ TeV, respectively, independent of the branching ratios, constituting one of the tightest constraints on natural supersymmetry from the LHC. Motivated by the need to mitigate the effects of multiple interactions per bunch crossing (pileup), an essential feature of present and future hadron colliders, in this thesis we also study the precision timing capabilities of a LYSO-based sampling calorimeter, and achieve a time resolution of $\sim30$ ps in electron test beam measurements. The achieved resolution corresponds to the precision needed to significantly reduce the inclusion of pileup particles in the reconstruction of the event of interest. This study is foundational in building an R\&D program on precision timing for the high-luminosity LHC and other future hadron colliders. We also propose alternative simplified models to study Higgs-plus-jets events at the LHC, and reinterpret an excess observed at $8$ TeV in the context of these models. Finally, we discuss a search for narrow resonances in the dijet mass spectrum at $13$ TeV using the data-scouting technique at CMS, which records a smaller event format to increase the maximum recordable rate. For the benchmark models with a vector or axial-vector mediator that couples to quarks and dark matter particles, the dijet search excludes mediator masses from $0.5$ TeV up to $\sim2.7$ TeV largely independent of the dark matter particle mass, which constitutes a larger exclusion than traditional mono-X searches at the LHC. In the plane of the dark matter-nucleon interaction cross section versus dark matter mass, the dijet search is also more sensitive than direct detection experiments for spin-dependent cross sections.