CP violation: Dalitz interference, CPT and FSI

Resonances and final state interactions (FSI) play a role in the formation of CP violation (CPV) constrained by CPT invariance. We provide a general formulation of CPV including resonances and FSI starting from the CPT constraint. Our discussion is elaborated within a simple \(B\) decay model with the \(\rho\) and \(f_0(980)\) resonances plus a non resonant background including the \(\pi\pi \to KK\) coupled amplitude. We consider few illustrative examples to show the interference patterns appearing in the CP asymmetry, namely, that from the \(\rho\) resonance plus a non-resonant amplitude, and that from the interference of the \(\rho\) and \(f_0(980)\) resonances. We perform the fit of the CP asymmetry for the charmless three-body \(B^\pm\) decay channel \(B^{\pm}\to \pi^{\pm} \pi^+\pi^-\) and obtain as outcome the \(B^{\pm}\to \pi^{\pm} K^+K^-\) for \(\pi\pi\) channel asymmetry in the mass region below \(1.6\) GeV in fair agreement with the new data LHCb data. Analogously, we also describe the CP asymmetry of the \(B^\pm\to K^\pm\pi^+\pi^-\) decay, with that from the \(B^\pm\to K^\pm K^+K^-\) channel obtained as output. As in the previous case, we also found agreement with LHCb experimental data.