Global CP asymmetries in charmless three-body $B$ decays with final state interactions

We propose a theoretical framework to understand the observable charge-parity (CP) violation in charmless three-body $B^{\pm }$ decays. The decay amplitudes put together the $\pi \pi \to KK$ re-scattering and the U-spin symmetry, treated within a CPT invariant framework. This approach applied to a two-channel model provides the magnitudes and signs of the ratios of the global CP asymmetries for $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$, $B^{\pm }\to K^{\pm }{K}^{+}{K}^{-}$, $B^\pm \to \pi^\pm K^+ K^- ,$and$B^\pm \to \pi^\pm \pi^+\pi^- ,$ decays, compatible with those obtained from the available experimental data. In addition, by considering the neutral channels we predict the ratios for the global CP asymmetries for these decays.