Clustering and Spike Killing Algorithms for CMS Electromagnetic Calorimeter Phase II Upgrade and Search for Non-Resonant New Physics in High Mass Dilepton Events in Association with b-tagged Jets

This thesis details work completed in the search for physics beyond the Standard Model. The first half of the thesis focuses on the upcoming Phase~II upgrade for the crystal electromagnetic calorimeter of the Compact Muon Solenoid. Test beam data was analysed using available Phase~II prototype electronics and this study found that, in the absence of a magnetic field, a cluster of a 3$\times$3 crystal matrix provides better energy resolution than a single crystal or a 3$\times$5 crystal matrix. An energy correction method to recover energy when an electron impacts on the side of a crystal was also tested and found to return the resolution to close to that for electrons impacting on the centre of the crystal. Algorithms that will cluster energy and reject anomalous signals for the Phase~II upgrade were also tested in software and on hardware using an existing board that was designed for the L1 trigger. The clustering algorithm was tested on 1000 events in hardware with no discrepancies, and both anomalous signal rejection algorithms were found to have the required 99.9 % efficiency from 2 or 10~GeV, depending on the algorithm. The second half of this thesis focuses on the ongoing search for a non-resonant Z' boson decaying to a dilepton pair in association with b-tagged jets, using 137~fb$^{-1}$ of data collected by the Compact Muon Solenoid experiment, as well as a test of lepton flavour universality. Two models are considered for this search, both based on contact interactions. One considers the interaction between two b quarks and two leptons, where the b quarks can be in the initial and/or final state, and the second model considers the transition $b\rightarrow s \ell \ell$. The dilepton mass distribution of both of these models depends on the energy scale of the new physics. The dielectron part of this search requires the use of a dedicated high-energy electron/positron identification criteria which was studied in detail to ensure that its behaviour was fully understood. For 2018, the efficiency of this dedicated criteria was found to be $86.94 \pm 0.05 \% $ in data, compared to an efficiency of $89.32 \pm 0.07\%$ in the CMS detector simulation. The scale factor of 0.973~$\pm$~0.001~(stat)~$\pm$~0.004~(sys) gives the ratio between the data and simulation and is used as a correction in the $Z'$ boson search. The flavour ratio is measured which compares the differential cross sections as a function of dilepton mass for a quark-antiquark pair decaying to a dimuon or a dielectron pair. For a data sample with no b-tagged jets, the flavour ratio is in agreement with unity, which is consistent with lepton flavour universality as expected. The predicted lepton flavour ratio for a sample with 1 b-tagged jet shows that for some energy scales of new physics, there will be a deviation from unity at high mass. Once finished by the $Z'$ group, this analysis is expected to probe higher energy scale ranges than previous analyses. The results are expected to either provide hints of physics beyond the Standard Model or allow more stringent limits on new physics to be set.