Direct CP asymmetries of three-body $B$ decays in perturbative QCD

Abstract

We propose a theoretical framework for analyzing three-body hadronic $B$ meson decays based on the perturbative QCD approach. The crucial nonperturbative input is a two-hadron distribution amplitude for final states, whose involved time-like form factor and rescattering phase are fit to relevant experimental data. Together with the short-distance strong phase from the $b$-quark decay kernel, we are able to make predictions for direct CP asymmetries in, for example, the $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ and ${\pi }^{+}{\pi }^{-}{K}^{\pm }$ modes, which are consistent with the LHCb data in various localized regions of phase space. Applications of our formalism to other three-body hadronic and radiative $B$ meson decays are mentioned.

13 pages, 4 figures

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