Giant CP violation in charmless three-body $B$ meson decays at LHCb: all order formalism for meson-meson final state interactions

LHCb has observed giant CP violation in localized regions of the Dalitz plots of B to three charmless light mesons. This has been interpreted as an enhancement due to strong two-body final state interactions. In this talk, we show how such interactions, described with dispersive analyses of data, can be implemented beyond the leading order expansion in the two-body re-scattering amplitude.