A Dispersive Approach to the Giant Localized CP Violation in \(B^± → K^± π ^+π ^-\)

In this article, we review our recent dispersive analysis of the large localized CP-violating asymmetries observed by LHCb in \(B± → K±π ^+π ^-\) decays. Low-energy \(π π \) 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 \(mπ π\). 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. Abstract Published by the Jagiellonian University 2026 authors