Bounding the effect of penguin diagrams in (formula)

A clean determination of the angle (Formula presented) of the unitary triangle from (Formula presented) decays requires an isospin analysis. If the (Formula presented) and (Formula presented) decay rates are small it may be hard to carry out this analysis. Here we show that an upper bound on the error on (Formula presented) due to penguin diagram effects can be obtained using only the measured rate (Formula presented) and an upper bound on the combined rate (Formula presented). Since no (Formula presented) 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.