Abstract

Rare semileptonic decays mediated by the quark-level transition b → s l+ l- remain a central testing ground for the Standard Model. A key hadronic uncertainty in channels such as B → K٭ l+ l- arises from the resonant nature of the K٭, which appears through the strongly interacting Kπ final state rather than as an asymptotic state. While most phenomenological treatments and existing lattice calculations rely on the narrow-width or stable-particle approximation, this simplification becomes increasingly inadequate at the level of precision targeted by current and future experiments. In this talk, I discuss recent lattice QCD work towards B → Kπ l+ l- form factors, based on a fully dynamical description of the Kπ system. Focusing on the P-wave channel, I describe our calculation of the finite-volume spectrum associated with the K٭ resonance. These results provide essential input for formulating and ultimately computing the physical B → Kπ transition amplitudes in a framework that treats resonances consistently, without assuming a stable K٭. I will discuss implications for precision flavor observables and future lattice studies.