Search for a Higgs or a Z boson decaying to a J/\(\Psi \) or \( \Psi^{\prime} \) meson and a photon

The discovery of the Higgs boson at the CMS and ATLAS experiments in 2012 represents a milestone in the understanding of the electroweak sector of the Standard Model (SM) of elementary particles. The discovery started a new era of measurements at CMS aiming to determine to the highest possible accuracy the couplings of the Higgs boson to the other particles in the SM. A discrepancy between the experimental measurement and the theoretical expectation from the SM would imply a ``new physics'', hinting to new particles yet to be discovered. In particular, studying the couplings of the Higgs boson to the second generation quarks represents the real challenge of High-Luminosity LHC. A very rare but promising channel is the decay of the Higgs boson in an energetic photon (\( \gamma \)) and a \( \PJPsi \equiv \PPsiS \) or \( \PPsiPrime \equiv \PPsiSS \) meson, followed by the decay of the \( \PPsiNS \) to a pair of muons. The \( \PH \to \PPsiNS\gamma \) decay takes place also through charm quark loops, therefore an accurate measurement would allow to determine its couplings with the Higgs boson. The channel is experimentally very clean, thanks to the very low SM backgrounds and the excellent resolution on the invariant mass peak, but also very rare, thus requiring large amounts of data. The observation of the \( \PZ \to \PPsiNS\gamma \), whose rate is 100 times larger than the similar process with the Higgs boson and has never been observed before, is an intermediate objective that can be achieved with a reasonable amount of data. The thesis work holds on the previous premises and it presents a complete analysis for the search of these processes. The analysis is performed with data from proton-proton collisions corresponding to an integrated luminosity of 137 \( \si{fb^{-1}} \) at \( \sqrt{s} = 13 \ \si{TeV} \), collected with the CMS detector during the full LHC Run 2. Since the considered processes are still likely not observable, the aim of the work is to set an upper limit on the cross section at a certain confidence level, using signal Monte Carlo samples. This study would allow to have a perspective of how the analysis could evolve with a larger amount of data during the next phases of LHC, after which the experimental observation of rare decays of the Higgs and Z bosons might become a reality