Role of ρ-ω interference in semileptonic B →π^+ π^- ℓν̅_ℓ decays

It is long known that interference effects play an important role in understanding the shape of the π^+π^- spectrum of resonances near the threshold. In this manuscript we investigate the role of the ρ-ω interference in the study of semileptonic B →π^+ π^- ℓν̅_ℓ decays. We determine for the first time the strong phase between B →ρ^0 ℓν̅_ℓ and B →ωℓν̅_ℓ from a recent Belle measurement of the m_ππ spectrum of B →π^+ π^- ℓν̅_ℓ. We find ϕ_ρ-ω = ( -46_-67^+155)xb0 and extract the branching fraction of ℬ(B →ρ^0 ℓν̅_ℓ) = (1.41_-0.38^+0.49) × 10^-4. In addition, we set a limit on the S-wave component within a mass window ranging from 2 m_π to 1.02 GeV of 0.51 × 10^-4 at 90% CL. We also determine the absolute value of the Cabibbo-Kobayashi-Maskawa matrix element of |V_ub|_ρ-ω = ( 3.03^+0.49_-0.44) × 10^-3, which takes into account the ρ-ω interference.