Direct CP Violation in Charmless Three-body Decays of $B$ Mesons

Abstract

Direct CP violation in charmless three-body hadronic decays of $B$ mesons is studied within the framework of a simple model based on the factorization approach. Three-body decays of heavy mesons receive both resonant and nonresonant contributions. Dominant nonresonant contributions to tree-dominated and penguin-dominated three-body decays arise from the $b\to u$ tree transition and $b\to s$ penguin transition, respectively. The former can be evaluated in the framework of heavy meson chiral perturbation theory with some modification, while the latter is governed by the matrix element of the scalar density $⟨M_1{M}_2|{\bar{q}}_1{q}_2|0⟩$. Strong phases in this work reside in effective Wilson coefficients, propagators of resonances and the matrix element of scalar density. In order to accommodate the branching fraction and CP asymmetries observed in $B^{-}\to K^{-}{\pi }^{+}{\pi }^{-}$, the matrix element $⟨K\pi |\bar{s}q|0⟩$ should have an additional strong phase, which might arise from some sort of power corrections such as final-state interactions. We calculate inclusive and regional CP asymmetries and find that nonresonant CP violation is usually much larger than the resonant one and that the interference effect is generally quite significant. If nonresonant contributions are turned off in the $K^{+}{K}^{-}{K}^{-}$ mode, the predicted CP asymmetries due to resonances will be wrong in sign when confronted with experiment. In our study of $B^{-}\to {\pi }^{-}{\pi }^{+}{\pi }^{-}$, we find that ${\mathcal{A}}_{CP}({\rho }^0{\pi }^{-})$ should be positive in order to account for CP asymmetries observed in this decay. However, all theories predict a large and negative CP violation in $B^{-}\to {\rho }^0{\pi }^{-}$. Measurements of CP-asymmetry Dalitz distributions put very stringent constraints on the theoretical models. We check the magnitude and the sign of violation in some (large) invariant mass regions to test our model.

arXiv comment32 pages, 3 figures

References in corpus (63)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• 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
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD
• Fat penguins and imaginary penguins in perturbative QCD
• Final State Interactions in Hadronic B Decays
• The Physics of the B Factories
• The 2004 UTfit Collaboration Report on the Status of the Unitarity Triangle in the Standard Model
• Charmless hadronic B decays involving scalar mesons: Implications to the nature of light scalar mesons
• Dalitz analysis of the three-body charmless decays B+=>K+Pi+Pi- and B+=>K+K+K-
• First observation of CP violation in the decays of Bs mesons
• Evidence for Large Direct CP Violation in B+-=>rho(770)0K+- from Analysis of the Three-Body Charmless B+-=>K+-pi+-pi-+ Decay
• 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
• Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+
• Charmless Three-body Decays of B Mesons
• Three-Body Non-Leptonic B Decays and QCD Factorization
• Revisiting Charmless Hadronic B_{u,d} Decays in QCD Factorization
• Branching Fractions and Direct CP Violation in Charmless Three-body Decays of B Mesons
• The Possibility of Large Direct CP Violation in B to K pi-Like Modes Due to Long Distance Rescattering Effects and Implications for the Angle gamma
• Three-body nonleptonic B decays in perturbative QCD
• Evidence for Direct CP Violation from Dalitz-plot analysis of B+/- -> K+/- pi+/- pi-/+
• Generalized Heavy-to-Light Form Factors in Light-Cone Sum Rules
• Dalitz Plot Analysis of B+- --> pi+-pi+-pi-+ Decays
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• Dalitz plot analysis of the decay B+- -> K+-K+-K-+
• CP asymmetries in three-body B+- decays to charged pions and kaons
• Direct CP asymmetries of three-body $B$ decays in perturbative QCD
• CP violation and CPT invariance in B+- decays with final state interactions
• Revisiting charmless hadronic B decays to scalar mesons
• Study of B meson decays to three-body charmless hadronic final states
• Time-dependent amplitude analysis of B0 --> K0S pi+ pi-
• Disentangling the Decay Observables in $B^{-}\to {\pi }^{+}{\pi }^{-}{\ell }^{-}{\bar{\nu }}_{\ell }$
• Dalitz Analysis of Three-body Charmless B0=>K0pi+pi- Decay
• Final state interaction phase in B decays
• U-spin analysis of CP violation in $B^{-}$ decays into three charged light pseudoscalar mesons
• Chiral Dynamics and S-wave Contributions in Semileptonic B decays
• Comprehensive Study of ${\overline{B}}^0\to K^0({\overline{K}}^0)K^{\mp }{\pi }^{\pm }$ Decays in the Factorization Approach
• CP violation: Dalitz interference, CPT and FSI
• Observation of the Decay B+ --> K+K-pi+
• Form factors in $B\to \pi \pi \ell {\bar{\nu }}_{\ell }$ from QCD light-cone sum rules
• Amplitude Analysis of B0-->K+ pi- pi0 and Evidence of Direct CP Violation in B--> K* pi decays
• Measurements of CP-Violating Asymmetries in the Decay B0-->K+K-K0
• Charmless B -> PPP Decays: the Fully-Symmetric Final State
• Localized direct CP violation in $B^{\pm }\to {\rho }^0(\omega ){\pi }^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$
• Large SU(3) breaking effects and CP violation in $B^{+}$ decays into three charged SU(3) octet pseudoscalar mesons
• Observation of the Decays B0->K+pi-pi0 and B0->rho-K+
• Amplitude analysis and measurement of the time-dependent CP asymmetry of $B^0\to K_0^S{K}_0^S{K}_0^S$ decays
• Rescattering effects in charmless B_{u,d,s} to P P decays
• Evidence for Factorization in Three-body B --> D(*) K- K0 Decays
• Observation of the rare decay B+->K+pi0pi0 and measurement of the quasi-two body contributions B+->K*(892)+pi0, B+->f0(980)K+ and B+->chic0K+
• Final state interaction on $B^{+}\to {\pi }^{-}{\pi }^{+}{\pi }^{+}$
• Dalitz-plot dependence of CP asymmetry in B+- --> K+- K+ K- decays
• 3- and 4-Body Final States in B, D and tau Decays about Features of New Dynamics with CPT Invariance or "Achaeans outside Troy"
• SU(3) and Isospin Breaking Effects on B to PPP Amplitudes
• CP violation induced by the interference of scalar and vector resonances in three-body decays of bottom mesons
• CP Asymmetries in Many-Body Final States in Beauty & Charm Transitions

Cited by in corpus (60)

• $B\to P$ and $B\to V$ Form Factors from $B$-Meson Light-Cone Sum Rules beyond Leading Twist
• Amplitude analysis of the $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay
• Observation of several sources of $CP$ violation in $B^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ decays
• Quasi-two-body decays $B_{(s)}\to P\rho \to P\pi \pi$ in perturbative QCD approach
• Resonant Contributions to Three-body $B\to KKK$ Decays in Perturbative QCD Approach
• Quasi-two-body decays $B_{(s)}\to K^{\ast }(892)h\to K\pi h$ in perturbative QCD approach
• Quasi-two-body decays $B_{(s)}\to P{\rho }^{\prime }(1450),P{\rho }^{\prime \prime }(1700)\to P\pi \pi$ in the perturbative QCD approach
• The $S$-wave resonance contributions to the three-body decays $B_{(s)}^0\to {\eta }_c{f}_0(X)\to {\eta }_c{\pi }^{+}{\pi }^{-}$ in perturbative QCD approach
• Finite-Width Effects in Three-Body B Decays
• $S$-wave $K\pi$ contributions to the hadronic charmonium $B$ decays in the perturbative QCD approach
• Quasi-two-body decays $B_{(s)}\to D(\rho (1450),\rho (1700))\to D\pi \pi$ in the perturbative QCD factorization approach
• 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
• Branching Fractions and CP Asymmetries of the Quasi-Two-Body Decays in $B_s\to K^0({\overline{K}}^0)K^{\pm }{\pi }^{\mp }$ within PQCD Approach
• Contributions of $K_0^{\ast }(1430)$ and $K_0^{\ast }(1950)$ in the three-body decays $B\to K\pi h$
• Branching Fractions and CP Violation in $B^{-}\to K^{+}{K}^{-}{\pi }^{-}$ and $B^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{-}$ Decays
• Quasi-two-body decays $B_{(s)}\to P{f}_2(1270)\to P\pi \pi$ in the perturbative QCD approach
• Four-body decays $B_{(s)}\to (K\pi {)}_{S/P}(K\pi {)}_{S/P}$ in the perturbative QCD approach
• $P$-wave contributions to $B\to \psi \pi \pi$ decays in perturbative QCD approach
• CP Violation in Three-body $B$ Decays: A Model Ansatz
• Quasi-two-body decays $B_{(s)}\to P{D}_0^{\ast }(2400)\to PD\pi$ in the perturbative QCD approach
• $S$-wave resonance contributions to the $B_{(s)}^0\to {\eta }_c(2S){\pi }^{+}{\pi }^{-}$ in the perturbative QCD factorization approach
• Quasi-two-body decays $B\to {\eta }_c(1S,2S)[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD approach
• Isovector scalar $a_0(980)$ and $a_0(1450)$ resonances in the $B\to \psi (K\bar{K},\pi \eta )$ decays
• Quasi-two-body decays $B\to D{K}^{\ast }(892)\to DK\pi$ in the perturbative QCD approach
• $S$, $P$ and $D$-wave resonance contributions to $B_{(s)}\to {\eta }_c(1S,2S)K\pi$ decays in the perturbative QCD approach
• Contributions for the kaon pair from $\rho (770)$, $\omega (782)$ and their excited states in the $B\to K\bar{K}h$ decays
• Study of $B_{(s)}\to (\pi \pi )(K\pi )$ decays in the perturbative QCD approach
• Resonance contributions $\varphi (1020,1680)\to K\bar{K}$ for the three-body decays $B\to K\bar{K}h$
• Direct CP violation in internal W-emission dominated baryonic B decays
• CP Violation of Baryon Decays with $N\pi$ Scatterings
• $P$-wave contributions to $B_{(s)}\to \psi K\pi$ decays in perturbative QCD approach
• Contributions of the kaon pair from $\rho (770)$ for the three-body decays $B\to DK\bar{K}$
• Quasi-two-body decays $B_c\to D_{(s)}[\rho (770),\rho (1450),\rho (1700)\to ]\pi \pi$ in the perturbative QCD factorization approach
• A novel observable for $CP$ violation in multi-body decays and its application potential to charm and beauty meson decays
• Study of the $B_s$ $\to$ $\varphi f_0(980)$ $\to$ $\varphi {\pi }^{+}{\pi }^{-}$ decay with perturbative QCD approach
• Direct $CP$ violation of three bodies decay process from the resonance effect
• Study of $B_{u,d,s}\to K_0^{\ast }(1430)P$ and $K_0^{\ast }(1430)V$ decays within QCD factorization
• Quasi-two-body $B_{(s)}\to V\pi \pi$ Decays with Resonance $f_0(980)$ in PQCD Approach
• Measurement of the relative branching fractions of $B^{+}\to h^{+}{h}^{\prime +}{h}^{\prime -}$ decays
• Resonant contributions to three-body $B_{(s)}\to [D^{(\ast )},{\bar{D}}^{(\ast )}]K^{+}{K}^{-}$ decays in the perturbative QCD approach
• Resonances $\rho (1450{)}^{+}$ and $\rho (1700{)}^{+}$ in $B\to DKK$ decays
• Dispersive $\pi \pi \to K\bar{K}$ amplitude and giant CP violation in B to three light-meson decays at LHCb
• Analysis of CKM-Favored Quasi-Two-Body $B\to D(R\to )K\pi$ Decays in PQCD Approach
• Quasi-two-body decays $B_c\to D^{\ast }h\to D\pi h$ in the perturbative QCD
• Role of $f_0(980)$ and $a_0(980)$ in the $B^{-}\to {\pi }^{-}{K}^{+}{K}^{-}$ and $B^{-}\to {\pi }^{-}{K}^0{\bar{K}}^0$ reactions
• Low-mass enhancement of kaon pairs in $B^{+}\to {\bar{D}}^{(\ast )0}{K}^{+}{\bar{K}}^0$ and $B^0\to D^{(\ast )-}{K}^{+}{\bar{K}}^0$ decays
• Study of $B^{-}\to \Lambda \bar{p}{\eta }^{{(}^{\prime })}$ and ${\bar{B}}_s^0\to \Lambda \bar{\Lambda }{\eta }^{{(}^{\prime })}$ decays
• CP Violation In Baryon Decays At LHCb
• The $\rho (770,1450)\to \omega \pi$ contributions for three-body decays $B\to {\bar{D}}^{(\ast )}\omega \pi$
• $D^{\ast }D\rho$ and $B^{\ast }B\rho$ strong couplings in light-cone sum rules
• Three body radiative decay $B_s\to \varphi {\bar{K}}^0\gamma$ in the PQCD approach
• Resonances $\varphi (1020)$ and $\varphi (1680)$ contributions for the three-body decays $B^{+}\to D_s^{+}K\bar{K}$
• Charmless Non-Leptonic Multi-Body B decays
• Quasi-two-body decays $B\to P{f}_0(500)\to P{\pi }^{+}{\pi }^{-}$ in the perturbative QCD approach
• Charmless Quasi-two-body $B$ Decays in Perturbative QCD Approach: Taking $B\to K(\mathcal{R}\to )K^{+}{K}^{-}$ As Examples
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods
• Study of quasi-two-body B^{0}\rightarrow T(ππ, K\bar{K},πη) decays in perturbative QCD approach
• CP Violation in $B$ Decays (and the Search for New Physics)
• Contributions of the subprocess $K_0^{\ast }(1430)\to K{\eta }^{\prime }$ in the charmless three-body $B$ meson decays
• The virtual contributions from $K^{\ast }$ in the $B\to K^{\ast }\pi h$ and $B\to K\rho h$ decays