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

Understand

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.