Diagnostic for New Physics in B → Πk Decays

A recent analysis of B → πK decays concludes that present data do not clearly indicate whether (i) the standard model (or ∆I = 0 new physics) is sufficient, or (ii) ∆I = 1 new physics is needed. We show that these two possibilities can be distinguished by whether a sum rule relating the CP asymmetries of the four B → πK decays is valid. If case (i) is favored, the sum rule holds, and one predicts ACP (π K) = −0.15, while in case (ii) fits to new physics involving large values of a colorsuppressed tree amplitude entail ACP (π K) = −0.03. The current experimental average ACP (π K) = −0.01 ± 0.10 must be measured a factor of at least three times more precisely in order to distinguish between the two cases.