Reducing the error on α in B→ππ,ρρ,ρπ

Theoretical errors in the extraction of α from B→(π+π−,ρ+ρ−,ρ±π∓) decays are usually given in terms of upper bounds on |αeff−α| obtained from isospin or from SU(3) relations, where αeff is measured through CP asymmetries. We show that mild assumptions about magnitudes and strong phases of penguin and tree amplitudes (|P/T|⩽1 and |δ|⩽π/2) in B→ππ and B→ρρ, imply αeff>α, thus reducing by a factor two the error in α. Similarly, the assumptions |p±/t±|⩽1,|δ−|⩽π/2⩽|δ+| in B→ρπ lead to a cancellation between two terms in αeff−α. Current data support these conditions, which are justified by both QCD-factorization and flavor SU(3).