CP violation: Dalitz interference, CPT and FSI

Abstract

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.

Comments: 16 pages, 12 figures. Changes in the pages format to match published version