Rate and CP-asymmetry sum rules in $B \to K \pi$

Abstract

The observed violation of $A_{CP}(B^0 \to K^+ \pi^-) = A_{CP}(B^+ \to K^+ \pi^0)$ has been recently mentioned as a puzzle for the standard model. We point out that while this violation may be accounted for by a large color-suppressed tree amplitude, a sum rule involving three or four $B\to K\pi$ CP asymmetries should hold. The current experimental status of these sum rules and of a sum rule for $B\to K\pi$ decay rates is presented.