Searches for New Physics at the Compact Muon Solenoid Experiment and Precision Timing Calorimetry

In this thesis, we present several searches for beyond the standard model physics in proton-proton collisions recorded by the Compact Muon Solenoid Experiment at center-of-mass energy of 8 and 13\TeV. We search for particle dark matter in events with two or more jets and missing transverse momentum at $\sqrt{s} = 8$ TeV, in this search we use the razor variables to discriminate signal from background events and thus improve the overall sensitivity of the analysis. We observe agreement between the observation and the background estimation. The interpretation of the results is carried out in the context of an effective field theory that couples the standard model quarks to the dark matter candidate. A search for anomalous production of Higgs bosons using 15.3 $\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV is also presented; this search selects events with a Higgs boson in association with jets, where the Higgs candidate decays into two photons. We also employ the razor variables ($\mathrm{M_{R}}, \mathrm{R}^{2}$) to discriminate signal from background. We observe an excess of events in one of the search bins with relatively high values of $\mathrm{M_{R}}$ and $\mathrm{R}^{2}$. The interpretation of this analysis is pair production of bottom squarks in the context of supersymmetry, this model is also presented in one of the appendices of this thesis. In the other appendix of this thesis, we present a search for new phenomena in high-mass diphoton events using 12.9 $\mathrm{fb}^{-1}$ of proton-proton collisions at $\sqrt{s} = 13$ TeV. This search observed a significant excess (3.4 standard deviations, local) with 2015 data at a diphoton invariant mass of 750 GeV, equivalent to $\approx$ 20% of the current dataset. By repeating the search with the larger dataset collected in 2016, we found that the aforementioned excess has been greatly disfavored. Additionally, in order to confirm the robustness and correctness of the data analysis techniques used in this search, we have carried out a second -- completely independent -- analysis, which confirms the absence of an excess at a diphoton invariant mass of 750 GeV. We also present detector research and developments studies of electromagnetic calorimeters equipped with precision timing capabilities. We present several calorimeter prototypes that were tested at the Fermilab Test Beam Facility. These prototypes include LYSO-based calorimeters, tungsten-LYSO "shashlik" sampling calorimeters, micro-channel-plate sampling calorimeters, and silicon-based sampling calorimeters. The results of these studies indicate that time resolutions of the order of $\sim$ 30 ps are readily available when measuring electromagnetic showers. A discussion about the applications of precision timing in high energy physics experiments is also presented, with a particular interest in pileup rejection in the context of the high-luminosity upgrade of the Large Hadron Collider foreseen to start in 2025.