$B\to πρ$, $πω$ Decays in Perturbative QCD Approach

Abstract

We calculate the branching ratios and CP asymmetries for $B^0 \to π^+ρ^-$, $B^0 \to ρ^+π^-$, $B^+ \to ρ^+π^0$, $B^+ \to π^+ρ^0$, $B^0 \to π^0ρ^0$, $B^+ \to π^+ω$ and $B^0 \to π^0ω$ 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 $B^0/\bar B^0 \to π^\pmρ^\mp$, $B^\pm \to π^\pmρ^0$, $π^\pm ω$ by CLEO and BABAR collaboration. We also predict large CP asymmetries in these decays. These channels are useful to determine the CKM angle $ϕ_2$.