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.

32 pages, 3 figures

References in corpus (7)

• Measurements of $CP$ violation in the three-body phase space of charmless $B^{\pm }$ decays
• Charmless Three-body Decays of B Mesons
• CP violation in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ in the region with low invariant mass of one ${\pi }^{+}{\pi }^{-}$ pair
• Amplitude Analysis of B0-->K+ pi- pi0 and Evidence of Direct CP Violation in B--> K* pi decays
• Charmless B -> PPP Decays: the Fully-Symmetric Final State
• Rescattering effects in charmless B_{u,d,s} to P P decays
• SU(3) and Isospin Breaking Effects on B to PPP Amplitudes

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