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We propose a theoretical framework to understand the observable charge-parity(CP) violation in charmless three-body $B^\pm$ decays. The decay amplitudes puttogether the $\pi\pi \to KK $ re-scattering and the U-spin symmetry, treatedwithin a CPT invariant framework. This approach applied to a two-channel modelprovides the magnitudes and signs of the ratios of the global CP asymmetriesfor $B^\pm \to K^\pm \pi^+ \pi^- \,$, $B^\pm \to K^\pm K^+ K^- \,$, $B^\pm \to\pi^\pm K^+ K^- \,$ and $B^\pm \to \pi^\pm \pi^+\pi^- \,$ decays, compatiblewith those obtained from the available experimental data. In addition, byconsidering the neutral channels we predict the ratios for the global CPasymmetries for these decays.

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