Dispersive $\pi \pi \to K\bar{K}$ amplitude and giant CP violation in B to three light-meson decays at LHCb

Abstract

The LHCb collaboration has recently reported the largest CP violation effect from a single amplitude, as well as other giant CP asymmetries in several $B$-meson decays into three charmless light mesons. It is also claimed that this is predominantly due to $\pi \pi \to K\bar{K}$ rescattering in the final state, particularly in the 1 to 1.5 GeV region. In these analyses the $\pi \pi \to K\bar{K}$ amplitude is by default estimated from the $\pi \pi$ elastic scattering amplitude and does not describe the existing $\pi \pi \to K\bar{K}$ scattering data. Here we show how the recent model-independent dispersive analysis of $\pi \pi \to K\bar{K}$ data can be easily implemented in the LHCb formalism. This leads to a more accurate description of the asymmetry, while being consistent with the measured scattering amplitude and confirming the prominent role of hadronic final state interactions, paving the way for more elaborated analyses.

arXiv comment9 pages, 6 figures. Minor corrections and discussions were added. Extended appendix with an additional improved model of the S-wave. Final version as published in Phys.Rev.Lett., where the appendix became supplemental material. Updated final values in the appendix

References in corpus (27)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• From controversy to precision on the sigma meson: a review on the status of the non-ordinary $f_0(500)$ resonance
• The pion-pion scattering amplitude
• Measurement of CP violation in the phase space of $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ and $B^{\pm }\to K^{\pm }{K}^{+}{K}^{-}$ decays
• Measurement of CP violation in the phase space of $B^{\pm }\to K^{+}{K}^{-}{\pi }^{\pm }$ and $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ decays
• Measurements of $CP$ violation in the three-body phase space of charmless $B^{\pm }$ decays
• Direct CP Violation in Charmless Three-body Decays of $B$ Mesons
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• CP violation and CPT invariance in B+- decays with final state interactions
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• Towards three-body unitarity in $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$
• Dispersion-theoretical analysis of the D^+ --> K^- pi^+ pi^+ Dalitz plot
• $\pi \pi \to K\bar{K}$ scattering up to 1.47 GeV with hyperbolic dispersion relations
• Final state interaction phase in B decays
• Amplitude analysis of $B^{\pm }\to {\pi }^{\pm }{K}^{+}{K}^{-}$ decays
• CP violation: Dalitz interference, CPT and FSI
• Global parameterization of $\pi \pi$ scattering up to 2 GeV
• Dispersive $\pi K\to \pi K$ and $\pi \pi \to K\bar{K}$ amplitudes from scattering data, threshold parameters and the lightest strange resonance $\kappa$ or $K_0^{\ast }(700)$
• Consistent Dalitz plot analysis of Cabibbo-favored $D^{+}\to \bar{K}\pi {\pi }^{+}$ decays
• Dalitz-plot decomposition for three-body decays
• Direct CP violation in beauty and charm hadron decays
• Coupled-channel analysis of $D^{+}\to K^{-}{\pi }^{+}{\pi }^{+}$ decay
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Charm Penguin in $B^{\pm }\to K^{\pm }{K}^{+}{K}^{-}$: partonic and hadronic loops
• Patterns of $C$- and $CP$-violation in hadronic $\eta$ and ${\eta }^{\prime }$ three-body decays
• CP asymmetry from hadronic charm rescattering in $B^{\pm }\to {\pi }^{-}{\pi }^{+}{\pi }^{\pm }$ decays at the high mass region

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