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

TL;DR

This paper proposes a method to distinguish between standard model and new physics explanations for $B o ext{pi} K$ decays by testing a sum rule relating CP asymmetries, requiring more precise measurements to identify the correct scenario.

Contribution

It introduces a sum rule test for differentiating standard model and new physics in $B o ext{pi} K$ decays based on CP asymmetry measurements.

Findings

Sum rule holds if standard model is sufficient.

Predicted $A_{CP}( ext{pi}^0 ext{K}^0)$ values differ by scenario.

Current data insufficient to distinguish cases.

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.