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.

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

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• Three-Body Non-Leptonic B Decays and QCD Factorization
• Final state interaction in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ with $K\pi$ I=1/2 and 3/2 channels
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Cited by in corpus (35)

• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• Quasi-two-body decays $B\to K\rho \to K\pi \pi$ in perturbative QCD approach
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• $\pi \pi \to K\bar{K}$ scattering up to 1.47 GeV with hyperbolic dispersion relations
• Amplitude analysis of $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays
• The S-wave resonance contributions in the $B_s^0$ decays into $\psi (2S,3S)$ plus pion pair
• CP violation in the B system
• Direct CP violation in beauty and charm hadron decays
• Finite-Width Effects in Three-Body B Decays
• The quasi-two-body decays $B_{(s)}\to (D_{(s)},{\bar{D}}_{(s)})\rho \to (D_{(s)},{\bar{D}}_{(s)})\pi \pi$ in the perturbative QCD factorization approach
• Quasi-two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))\to D\pi \pi$ in the perturbative QCD factorization approach
• $f_0(980)$ production in $D_s^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ and $D_s^{+}\to {\pi }^{+}{K}^{+}{K}^{-}$ decays
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• Enhanced charm CP asymmetries from final state interactions
• CP Violation in Three-body $B$ Decays: A Model Ansatz
• $S$-wave resonance contributions to the $B_{(s)}^0\to {\eta }_c(2S){\pi }^{+}{\pi }^{-}$ in the perturbative QCD factorization approach
• Hadronic Footprint of GeV-Mass Dark Matter
• Suppressed $B\to PV$ CP asymmetry: CPT constraint
• Charm Penguin in $B^{\pm }\to K^{\pm }{K}^{+}{K}^{-}$: partonic and hadronic loops
• CP Violation of Baryon Decays with $N\pi$ Scatterings
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• CP asymmetry from hadronic charm rescattering in $B^{\pm }\to {\pi }^{-}{\pi }^{+}{\pi }^{\pm }$ decays at the high mass region
• Dispersive $\pi \pi \to K\bar{K}$ amplitude and giant CP violation in B to three light-meson decays at LHCb
• Final-state rescattering mechanism in bottom-baryon decays
• CP violation in the interference between $\rho (770{)}^0$ and $S$-wave in $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ decays and its implication for CP asymmetry in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$
• Forward-backward asymmetry induced $CP$ asymmetry of $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$
• Analysis of $CP$ violation in $D^0\to K^{+}{K}^{-}{\pi }^0$
• Global CP asymmetries in charmless three-body $B$ decays with final state interactions
• Multibody decay analyses -- a new phenomenological model for meson-meson subamplitudes
• Inelastic Meson-Meson Scattering in Hadronic Matter
• $B^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$: three-body final state interactions and $K\pi$ isospin states
• Charm rescattering contribution in rare $B_c^{+}\to K^{+}{K}^{-}{\pi }^{+}$ decay
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays