Rare flavour-changing processes provide some of the most sensitive probes of physics beyond the Standard Model, often accessing energy scales far above the direct reach of current colliders. Fully exploiting this sensitivity requires precise theoretical control over both short-distance dynamics and long-distance hadronic effects. This talk discusses recent progress in rare B- and K-meson decays aimed at strengthening the theoretical foundations needed to turn precision measurements into robust tests of the Standard Model.
In rare \tos transitions, persistent tensions with Standard Model predictions motivate model-independent global analyses of current data. These studies systematically assess theoretical uncertainties, with particular emphasis on nonlocal hadronic contributions that can mimic signals of new physics. Data-driven approaches based on analyticity and unitarity, together with first-principles calculations using light-cone sum rules and dispersive methods, provide complementary strategies to disentangle hadronic effects from genuine short-distance contributions, enabling consistent effective-field-theory interpretations and translating precision measurements into quantitative constraints on high-scale new physics.
Rare kaon decays offer an independent and complementary laboratory, where long-distance dynamics play a more prominent role but can be brought under control. New constraints on vector, axial-vector, scalar, and pseudoscalar interactions from charged- and neutral-lepton modes are also highlighted, alongside improved non-perturbative inputs from global analyses of $K \to 3\pi$ data, with implications for ongoing and future high-intensity kaon experiments.
