Flavor physics at high-energy colliders

Flavor physics is a key aspect of the Standard Model (SM) of particle physics, allowing us to study fundamental interactions and search for deviations from the SM. In three parts, this thesis explores flavor dynamics at high-energy colliders and the complementarity with low-energy flavor observables, aiming both to build on the successes of the SM and to identify areas where it falls short.
The first part of the thesis revisits the landscape of short-distance new physics by analysing rare decays of $b$ hadrons and high-energy Drell-Yan processes. One of the main contributions of this work is the implementation of the SM Effective Field Theory (SMEFT) predictions and experimental data of the high-mass Drell-Yan tails within the {\tt flavio} framework. This implementation is then used together with recent experimental data from $b \to q \ell^+ \ell^-$ transitions, to explore the potential for new physics beyond the SM in these rare decays. Our analysis explores the parameter space of the SMEFT as well as several explicit models, such as $Z'$ and leptoquark scenarios, to assess their compatibility with the experimental data.
In the second part, we explore exclusive charged current semileptonic decays of $b$ hadrons with underlying $b \to u \ell \nu$ transitions as a window into new physics. By leveraging the SMEFT framework again, we show that the new physics contributions to these decays are closely correlated with effects in rare neutral current $b$ decays, neutral $B$ meson mixing and high-mass Drell-Yan tails. Considering all the available experimental data, we find that the parameter space relevant for $b \to u \ell \nu$ decays is already highly constrained, leaving little room for new physics. We also identify tree-level mediators that could contribute to the $b \to u \ell \nu$ transitions, show how they are mostly constrained by the complementary observables, and construct an explicit model where $b \to u \ell \nu$ decays put relevant bounds on the parameter space.
Finally, the last part takes motivation from the hints of new physics in rare flavor-changing neutral current transitions $b \to s \mu^+ \mu^-$, and explores the discovery prospects of possible new physics at future high-energy colliders, in particular the FCC-hh and a multi-TeV muon collider. A model-independent analysis concerning semileptonic SMEFT operators as well as construction of explicit models featuring $Z^\prime$ bosons and leptoquarks is carried out to assess the potential for discovery at these colliders. For the scenarios at hand, we find similar prospects for FCC-hh and 3 TeV muon collider to be effective in probing the parameter space of SMEFT and $Z'$ models while a 10 TeV (or higher) muon collider is required to fully probe the parameter space of leptoquark models.