Diagnostic for new physics in $B\to \pi K$ decays

Abstract

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

10 pages, no figures. Submitted to Physics Letters B. Slight clarification added

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