Understanding large localized CP violation in $B^\pm\to K^\pm\pi^+\pi^-$ using dispersive methods

We utilize the universality of pion-pion ($\pi\pi$) final-state interactions at small invariant masses to understand the enhanced localized CP violation in $B^\pm\to K^\pm\pi^+\pi^-$, using a dispersive approach. From a fit to the integrated CP-asymmetry data, we successfully predict the Dalitz-plot kinematic distribution of the asymmetry in the low-energy $\pi\pi$ region, including the large localized CP violation recently observed by LHCb. An essential role is played by the contributions of isospin 2. This formalism, whose parameters have a physical meaning, can be adapted straightforwardly to other systems with CP violation enhanced by final-state interactions.