Present and future tools for testing the Standard Model and beyond

Despite its incredible success in describing physics in a wide range of energies up to the electroweak (EW) scale, the Standard Model (SM) cannot explain many observed phenomena, such as the presence of dark matter, the matter-antimatter asymmetry or neutrino masses. Furthermore, theoretical issues like the Higgs hierarchy or the flavor problem suggest the existence of physic beyond the Standard Model (BSM). Therefore a huge effort has been dedicated to the formulation of BSM models capable of explaining such deviations, and at the same time to the analysis of their signatures at present and future experiments, to constrain the options and to find ways to potentially discover new physics. The first part of this thesis is mainly related to muon colliders (MuC), which represent one of the most promising option to explore the high-energy frontier. These machines, operating at the TeV scale, can test short-distance physics with the potential of discovering new particles, reaching at the same time high precision in the measurement of EW observables. We present one of the main novelties in the analysis of TeV-scale EW processes at lepton colliders, i.e. the partonic description of lepton collisions. This allows to systematically study processes involving collinear initial state radiation (ISR), whose cross sections dominate over those for lepton annihilation at high energies. We show the calculation of the parton distribution functions (PDFs) and discuss their features, with explicit applications to MuC processes. In particular, the impact of the muon neutrino PDF is studied and compared with the expected experimental precision of muon colliders. We also consider signatures relevant for $B-$meson decays, exploring the potential of MuC to discover new physics in some benchmark models. The latter analysis is extended to the complementary hadronic proposal, namely FCC-hh, and a comparison between the prospects at the two machines is presented. The second part of the thesis focuses instead on the use of present measurements of a large set of low-energy observables to constrain new physics in a model-independent way, within the framework of the Standard Model Effective Field Theory (SMEFT). Bounds on Wilson coefficients of top-quark operators are derived through a global analysis, and implications for explicit new physics models are discussed.