Understanding large local CP violation in $B^\pm\to K^\pmπ^+π^-$ using dispersive methods

We utilize the universality of pion--pion ($ππ$) final-state interactions at small invariant masses to understand their enhanced local CP violation in $B^\pm\to K^\pmπ^+π^-$, 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 $ππ$ region, including the large local 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.