Hidden sectors search at the CMS experiment and predictions for future colliders

The last sixty years have been a constant stream of achievements for particle physics. The experimental discovery of the Higgs boson, which was for decades just a prediction, decreed the completion of the Standard Model (SM). This gauge theory is the current framework to describe elementary particles and their interactions. Its predictions have been verified with great precision, but many questions remain unsolved. Why is electroweak symmetry broken and what sets the scale? Is it broken by the SM Higgs or by a richer Higgs sector? Is the Higgs an elementary or a composite particle? What is dark matter made of? What is the origin of the asymmetry between baryons and anti-baryons in the Universe? These are only a few hints that the SM is not the end of the story and there is physics beyond to explore. In order to try to answer these questions, new theories have been proposed such as supersymmetry (SUSY). This is a generalization of the space-time symmetry of a quantum field theory that associates a fermion to each SM boson and the other way around. It also foresees the existence of a particle, the lightest neutralino, which is one of the most promising candidates for dark matter (DM). DM is the most fascinating evidence of physics beyond SM. The existence of DM is in fact confirmed by astrophysical observations but its nature is still a mystery. Collections of new particles, called hidden sectors, have been proposed to solve this issue. They are not directly charged under SM strong, weak and electromagnetic forces, and interact with ordinary matter through a mediator. According to the mediator's spin and parity, different portals between SM and DM can be distinguished. The dark-SUSY is a vector-portal hidden sector that adds to the minimal SUSY model the gauge symmetry group U(1)D that spontaneously breaks giving rise to a light dark photon. A possible strategy to search for DM exploits the potential of colliders. The latest achievements confirm that these machines are at the forefront of scientific discoveries in high-energy physics. The Compact Muon Solenoid (CMS) is one of the experiments hosted along the ring of the Large Hadron Collider (LHC). Together with ATLAS, it announced the discovery of the Higgs boson in 2012 and is still working incessantly to collect data and shed light both on the SM and new physics. In addition to existing apparatus, new colliders are proposed to deepen our understanding of the SM open questions and to tackle novel challenges that might emerge from future discoveries at the LHC. Among these, the Muon Collider would combine the high precision of electron-positron colliders and the high center-of-mass energy and luminosities of hadron machines leading to an unprecedented discovery potential. In this context, we examine an extension of the dark-SUSY model with a dark Higgs boson, originating from a neutralino, decaying into two dark photons that then decay into pairs of muons. In total, starting from neutralino pair production, eight muons are present in the final state. The thesis deals with the search for this hidden sector in the CMS experiment (Part I) and also furnishes preliminary predictions for a future Muon Collider (Part II). The work is organised as follows. After a brief introduction about the SM, Chapter 1 presents an overview of the physics beyond the SM, focusing in particular on supersymmetry, dark matter and hidden sectors. Chapter 2 shows the work done from a theoretical point of view to implement the extension of the model to be used in event generators. Concerning the CMS experiment, Chapter 3 describes the LHC machine with design and operational parameters and the CMS detector with information about physics object reconstruction. Chapter 4 reports the search including signal sample generation, background estimation, analysis strategy for event selection, discussion of systematic uncertainties and statistical interpretation of the limits found on the cross section. For the Muon Collider, on the other hand, Chapter 5 introduces the physics case and the machine and detector design. The last section is dedicated to studies performed on the muon system. The contribution of the beam-induced background (BIB), i.e. the collection of particles originating from the interaction of electrons and positrons from muon decay with the machine, in this region is examined and different technologies to be implemented are discussed. Finally, Chapter 6 presents the preliminary predictions obtained on the signal yield and the algorithms tested and developed for muon reconstruction with and without the BIB.