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In the absence of the QCD penguin contributions a measurement of thetime-dependent asymmetry in the decay $B^0(t)\to \pi^+\pi^-$ gives directly theweak angle $\alpha$. Several bounds have been proposed in the literature on themagnitude of the penguin effects on this determination, the prototype of whichis the isospin bound of Grossman and Quinn. It is pointed out that large strongfinal state interactions could cause these bounds to overestimate the realpenguin effect. A new flavor SU(3) bound is proposed, requiring only thecharge-averaged branching ratios for $B^0\to \pi^+\pi^-$ and $B_s\to K^+K^-$,which exactly takes into account all relevant amplitudes and electroweakpenguin effects. This bound on the penguin-induced error on the determinationof the weak phase $\alpha$ holds even without a knowledge of the direct CPasymmetry in the $\pi^+\pi^-$ channel.Comment: 10 pages ReVTeX with 3 included eps figure

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Bounding the penguin effects in determinations of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>B</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mn /><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mn /><mml:mo>→</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:…

Bounding the penguin effects in determinations ofαfromB0(t)→π