We study three-body nonleptonic decays $B\to VVP$ by introducing two-meson distribution amplitudes for the vector-pseudoscalar pair, such that the analysis is simplified into the one for two-body decays. The twist-2 and twist-3 $\varphi K$ two-meson distribution amplitudes, associated with longitudinally and transversely polarized $\varphi$ mesons, are constrained by the experimental data of the $\tau \to \varphi K\nu$ and $B\to \varphi K\gamma$ branching ratios. We then predict the $B\to \varphi K\gamma$ and $B\to \varphi \varphi K$ decay spectra in the $\varphi K$ invariant mass. Since the resonant contribution in the $\varphi K$ channel is negligible, the above decay spectra provide a clean test for the application of two-meson distribution amplitudes to three-body $B$ meson decays.

• Received 3 May 2004

DOI:https://doi.org/10.1103/PhysRevD.70.054006