Rare Semileptonic Decays from Kaons to B Mesons

Abstract: Rare semileptonic decays provide some of the most sensitive probes of the Standard Model across both light- and heavy-quark sectors. I will begin with a brief pedagogical introduction to how flavor-changing processes connect kaon and B-meson physics, and why rare decays are especially powerful tools for testing the flavor structure of the Standard Model. I will then discuss how effective field theory methods can be used to separate short-distance weak dynamics from long-distance strong-interaction effects, with an emphasis on higher-order electroweak corrections that probe hadronic structure. The main focus will be on $K to pi nu bar{nu}$ and $B to X_s nu bar{nu}$ decays, highlighting both the common theoretical ideas and the important differences between the light- and heavy-quark regimes.