Diagnostic for new physics in $B \to πK$ decays

Abstract

A recent analysis of $B \to πK$ decays concludes that present data do not clearly indicate whether (i) the standard model (or $ΔI=0$ new physics) is sufficient, or (ii) $ΔI=1$ 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 $B \to πK$ decays is valid. If case (i) is favored, the sum rule holds, and one predicts $A_{CP}(π^0 K^0) = -0.15$, while in case (ii) fits to new physics involving large values of a color-suppressed tree amplitude entail $A_{CP}(π^0 K^0) = -0.03$. The current experimental average $A_{CP}(π^0 K^0) = -0.01 \pm 0.10$ must be measured a factor of at least three times more precisely in order to distinguish between the two cases.