A precise sum rule among four B -> Kpi CP asymmetries

Abstract

A sum rule relation is proposed for direct CP asymmetries in $B\to K\pi$ decays. Leading terms are identical in the isospin symmetry limit, while subleading terms are equal in the flavor SU(3) and heavy quark limits. The sum rule predicts $A_{\rm CP}(B^0\to K^0\pi^0)=-0.17 \pm 0.06$ using current asymmetry measurements for the other three $B\to K\pi$ decays. A violation of the sum rule would be evidence for New Physics in $b\to s\bar qq$ transitions.