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Register a new userExtraction of the weak angle gamma from B to charm decays
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We give a summary of the discussions in Working Group V of the CKM2010 workshop dealing with determinations of the angle gamma of the unitarity triangle of the Cabibbo-Kobayashi-Maskawa matrix from B-meson decays into charmed final states.
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Proceedings of the CKM 2005 Workshop (WG5), UC San Diego, 15-18 March 2005.
Some years ago, a method was proposed for measuring the CP-violating phase gamma using pairs of two-body decays that are related by U-spin reflection (d <-> s). In this paper we adapt this method to charmless B -> PPP decays. Time-dependent Dalitz-plot analyses of these three-body decays are required for the measurement of the mixing-induced CP asymmetries. However, isobar analyses of the decay amplitudes are not necessary. A potential advantage of using three-body decays is that the effects of U-spin breaking may be reduced by averaging over the Dalitz plot. This can be tested independently using the measurements of direct CP asymmetries and branching ratios in three-body charged B decays.
To date, the weak-phase $gamma$ has been measured using two-body $B$-meson decays such as $Bto D K$ and $Bto Dpi$, whose amplitudes contain only tree-level diagrams. But $gamma$ can also be extracted from three-body charmless hadronic $B$ decays. Since the amplitudes for such decays contain both tree- and loop-level diagrams, $gamma$ obtained in this way is sensitive to new physics that can enter into these loops. The comparison of the values of $gamma$ extracted using tree-level and loop-level methods is therefore an excellent test for new physics. In this talk, we will show how U-spin and flavor-SU(3) symmetries can be used to develop methods for extracting $gamma$ from $Bto Kpipi$ and $Bto KK{bar K}$ decays. We describe a successful implementation of the flavor-SU(3) symmetry method applied to BaBar data.
A new and simple procedure to measure the angle $gamma$ from $B^{pm} to pi^{pm}pi^+pi^-$ and $B^{pm} to K^{pm}pi^+pi^-$ decays using SU(3) symmetry is presented. It is based on a full Dalitz plot analysis of these decays. All diagrams, including strong and electroweak penguins, are considered in the procedure. The method is also free from final state interaction problems. The theoretical error in the extraction of $gamma$ within the method should be of the order of $10^{rm o}$ or even less. Taking into account the B-meson production in the first generation of B factories and recent measurements from CLEO, this method could bring the best measurement of $gamma$ in the next years.
A model for the $B^pm to pi^-pi^+pi^pm$ decay amplitude is proposed to study the large CP violation observed at the high mass region of the Dalitz plane. A short distance $ b to u $ amplitude with the weak phase $gamma$ is considered together with the contribution of a hadronic charm loop and a s-wave $Dbar{D}to pipi$ rescattering. In the model, the $chi_c^0$ appears as a narrow resonant state of the $Dbar D$ system below threshold. It is introduced in an unitary two channel S-matrix model of the coupled $Dbar D$ and $pipi$ channels, where the $chi_c^0$ complex pole in $Dbar D$ channel shows its signature in the off-diagonal matrix element and in the associated $Dbar{D}to pipi$ transition amplitude. The strong phase of the resulting decay amplitude has a sharp sign change at the $Dbar D$ threshold, changing the sign of the CP asymmetry, as it is observed in the data. We conclude that the hadronic charm loop and rescattering mechanism are relevant to the broadening of the CP asymmetry around the $chi_c^0$ resonance in the $pipi$ channel. This novel mechanism provides a possible interpretation of the CP asymmetry defier experimental result presented by the LHCb collaboration for the $B^pm to pi^-pi^+pi^pm$ decay in the high mass region.
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