Bounding the effect of penguin diagrams in a_CP(B⁰→ π⁺π^-)

A clean determination of the angle α of the unitary triangle from B → π π decays requires an isospin analysis. If the B → π⁰π⁰ and B̄ → π⁰π⁰ decay rates are small it may be hard to carry out this analysis. Here we show that an upper bound on the error on sin 2α due to penguin diagram effects can be obtained using only the measured rate B (B ± → π^±π⁰) and an upper bound on the combined rate B(B → π⁰π0) + B(B̄ → π⁰π⁰). Since no b flavor tagging is needed to measure this combined rate, the bound that can be achieved may be significantly better than any approach which requires separate flavor-tagged neutral pion information.