Search for HH→bbμμ events with the CMS experiment and future Higgs boson factories

This thesis presents a search for Higgs boson pair production (HH) using datasets corresponding to proton-proton collision data produced at a center-of-mass energy of $\sqrt{s} = 13$ TeV and collected by the \ac{CMS} experiment at the \ac{CERN} \ac{LHC}. The analysis specifically looks at events where one Higgs decays into two b-quarks and the other decays into two muons ($HH \to b\overline{b} \mu^{+}\mu^{-}$), focusing on the HH nonresonant gluon-gluon fusion production mechanism. HH production gives access to the Higgs boson trilinear self-coupling and is sensitive to the presence of \ac{BSM} physics. The search is particularly challenging due to the small branching ratio of the channel under study, leading to a low signal yield compared to the background. To address this, a considerable effort has been devoted to the development of an extension of the current seeding algorithm, for the online and offline reconstruction of charged particle tracks, which is going to be integrated into the data taking to face the particle detection failures expected due to the aging of tracking detectors as the \ac{LHC} transitions to Run 3 and \ac{HL-LHC} operations. The algorithm implementation included dedicated fake and duplicate rejection criteria to incorporate data from strip tracker detectors and enhance track momentum resolution and tracking efficiency of 10-20\%. Its structure, optimization and implementation, its commissioning for the \ac{LHC} data-taking at $\sqrt{s} = 13.6$ TeV, and the measurement of its performance are presented. The algorithm is an essential element in the search for HH production. Additionally, a new strategy has been implemented for evaluating muon tracking performance at the offline track reconstruction level using the tag-and-probe technique. To investigate the $HH\to bb\mu^{+}\mu^{-}$ process, a dedicated event selection and categorization are developed and optimized to enhance the sensitivity, and multivariate techniques are applied for the first time to this final state to separate the signal from the background. Results are derived using an integrated luminosity of 137 fb$^{-1}$. Upper limits are set on the nonresonant HH production cross section and constrain the parameter space of the anomalous Higgs boson couplings. The expected upper limits are about 170 times the \ac{SM} prediction. Looking forward, this thesis also explores prospects for future measurements of HH production at the \ac{FCC-ee} and FCC-hh. A new particle identification technique based on cluster counting is proposed to enhance of a factor 2 the particle discrimination power in high-luminosity environments. Finally, prospects for future measurements of HH production at the \ac{LHC} are presented by extrapolating the current results to an integrated luminosity of 3000 fb$^{-1}$ under different detector and analysis performance scenarios.