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 $B^{\pm }\to {\rho }^0{\pi }^{\pm }$

Abstract

The decay amplitude analyses of $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ decays in the Dalitz plot performed by LHCb indicate that CP asymmetry for the dominant quasi-two-body decay $B^{\pm }\to \rho (770{)}^0{\pi }^{\pm }$ was found to be consistent with zero in all three approaches for the $S$-wave component and that CP-violation effects related to the interference between the $\rho (770{)}^0$ resonance and the $S$-wave were clearly observed. We show that the nearly vanishing CP violation in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$ is understandable within the framework of QCD factorization. There are two $1/m_b$ power corrections, one from penguin annihilation and the other from hard spectator interactions. They contribute destructively to $A_{CP}(B^{\pm }\to {\rho }^0{\pi }^{\pm })$ to render it compatible with zero, in contrast to the sizable negative CP asymmetry predicted in most of the existing models. We next show that the measured interference pattern between the $\rho$ and $S$-wave contributions in the low $m_{{\pi }^{+}{\pi }^{-}}$ region separated by the sign of value of $\cos \theta$ with $\theta$ being the angle between the two same charged pions measured in the rest frame of the $\rho$ resonance can be explained in terms of the smallness of $A_{CP}(B^{+}\to {\rho }^0{\pi }^{+})$ and the interference between $\rho (770)$ and $\sigma /f_0(500)$. If CP asymmetry in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$ is not negligible as predicted in many existing models, the observed interference pattern will be destroyed. We conclude that the experimental observation of the interference pattern between $P$- and $S$-waves in the low-$m_{{\pi }^{+}{\pi }^{-}}$ region between 0.5 and 1.0 GeV is consistent with a nearly vanishing CP violation in $B^{\pm }\to {\rho }^0{\pi }^{\pm }$.

arXiv comment18 pages, 5 figures, accepted for publication in PRD. arXiv admin note: text overlap with arXiv:2005.06080, arXiv:2007.02558

References in corpus (30)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• CP Violation and the CKM Matrix: Assessing the Impact of the Asymmetric B Factories
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• QCD factorization for B->PP and B->PV decays
• Final State Interactions in Hadronic B Decays
• Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons
• Direct CP Violating Asymmetry in B0 -> K+pi- Decays
• QCD Factorization for Charmless Hadronic B_s Decays Revisited
• Revisiting Charmless Hadronic B_{u,d} Decays in QCD Factorization
• Updating B --> PP, VP decays in the framework of flavor symmetry
• Dalitz Plot Analysis of B+- --> pi+-pi+-pi-+ Decays
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• Revisiting charmless hadronic B decays to scalar mesons
• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Charmless Two-body $B(B_s)\to VP$ decays In Soft-Collinear-Effective-Theory
• Analysis of Charmless Two-body B decays in Factorization Assisted Topological Amplitude Approach
• CP violation: Dalitz interference, CPT and FSI
• Evidence for the charmless annihilation decay mode $B_s^0\to {\pi }^{+}{\pi }^{-}$
• Direct CP violation in beauty and charm hadron decays
• Finite-Width Effects in Three-Body B Decays
• Observation of the annihilation decay mode $B^0\to K^{+}{K}^{-}$
• Flavor dependence of annihilation parameters in QCD factorization
• Resolving B-CP Puzzles in QCD Factorization
• Implications of the recent measurement of pure annihilation $B_s\to {\pi }^{+}{\pi }^{-}$ decays in QCD factorization
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• Width effects in resonant three-body decays: $B$ decay as an example
• Constraints on hard spectator scattering and annihilation corrections in $B_{u,d}$ $\to$ $PV$ decays within QCD factorization
• Amplitude analysis of the decay ${\overline{B}}^0\to K_S^0{\pi }^{+}{\pi }^{-}$ and first observation of the CP asymmetry in ${\overline{B}}^0\to K^{\ast }(892{)}^{-}{\pi }^{+}$
• Suppressed $B\to PV$ CP asymmetry: CPT constraint

Cited by in corpus (1)

• Phenomenological analysis of charmless $B\to PV$ decays in the modified perturbative QCD approach