Improving the measurement of the CKM phase ϕ2 = α in B → ππ and B → ρρ decays

CP-violating asymmetries in B→ππ and B→ρρ decays can help specify the weak phase ϕ2=α of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We discuss the impact of improved measurements of these processes such as will be available in the near future, finding special value in better measurement of the time-dependent CP violation parameter S00 in B0→π0π0 and B0→ρ0ρ0. Reducing the errors on B→ρρ measurements by a factor of two can potentially lead to an error in ϕ2=α just above 2°, at which level the ρ width and isospin-breaking corrections must be considered.