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.

We present a method for exploring the presence of noise, which may mimic systematic errors in experimental datasets, particularly when such errors introduce inconsistencies. The method is based on Padé approximants designed for Stieltjes functions, with extensions to holomorphic functions in the region covered by the data. It uses the known analytic properties of these functions to identify noise and systematically adjust data points that deviate from expected behavior, preserving the full information content of the dataset while maintaining physical and mathematical coherence. Its effectiveness and robustness are illustrated through simple examples, highlighting its advantages as a practical tool  compared to conventional data-removal procedures. 

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