$B\to \pi \rho$, $\pi \omega$ Decays in Perturbative QCD Approach

Abstract

We calculate the branching ratios and CP asymmetries for $B^0 \to \pi^+\rho^-$, $B^0 \to \rho^+\pi^-$, $B^+ \to \rho^+\pi^0$, $B^+ \to \pi^+\rho^0$, $B^0 \to \pi^0\rho^0$, $B^+ \to \pi^+\omega$ and $B^0 \to \pi^0\omega$ decays, in a perturbative QCD approach. In this approach, we calculate non-factorizable and annihilation type contributions, in addition to the usual factorizable contributions. Our result is in agreement with the measured branching ratio of $B^0/\bar B^0 \to \pi^\pm\rho^\mp$, $B^\pm \to \pi^\pm\rho^0$, $\pi^\pm \omega$ by CLEO and BABAR collaboration. We also predict large CP asymmetries in these decays. These channels are useful to determine the CKM angle $\phi_2$.