  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.

High Energy Physics - Phenomenology