A Dispersive Approach to the Giant Localized CP Violation in \(B^\pm \to K^\pm \pi ^+\pi ^-\)

In this article, we review our recent dispersive analysis of the large localized CP-violating asymmetries observed by LHCb in \(B^{\pm } \to K^{\pm }\pi ^+\pi ^-\) decays. Low-energy \(\pi \pi \) final-state interactions are treated in a model-independent way, and the weak decay is described as a short-distance source. By fitting angular-projected data, we reproduce the Dalitz-plot CP-asymmetry pattern at low \(m_{\pi \pi }\). Our framework highlights the essential role of the non-resonant isospin-\(2\) \(S\) wave, ensures unitarity, and can be extended to other three-body decays. Published by the Jagiellonian University 2026 authors