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.

arXiv comment16 pages, 12 figures. Changes in the pages format to match published version

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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