Bounding the penguin effects in determinations of α from B⁰(t) → π⁺π^-

In the absence of QCD penguin contributions a measurement of the time-dependent asymmetry in the decay B⁰;(t) → π⁺π^- gives directly the weak angle α. Several bounds have been proposed in the literature on the magnitude of the penguin effects on this determination, the prototype of which is the isospin bound of Grossman and Quinn. We point out that large strong final state interactions could cause these bounds to overestimate the real penguin effect. A new flavor SU(3) bound is proposed, requiring only the charge-averaged branching ratios for B⁰ → π⁺π^- and B_s → K⁺K^-, which exactly takes into account all relevant amplitudes and electroweak penguin effects. This bound on the penguin-induced error on the determination of the weak phase α holds even without knowledge of direct CP asymmetry in the π⁺π^- channel.