Sum rule for rate and CP asymmetry in B+ → K+π0

Abstract A sum rule relating the ratio R c = 2 Γ ( B + → K + π 0 ) / Γ ( B + → K 0 π + ) and the CP asymmetry A CP ( B + → K + π 0 ) is proved to first order in the ratio of tree to penguin amplitudes. The sum rule explains why it is possible to have R c consistent with 1 together with a small CP asymmetry in B + → K + π 0 . The measured ratio A CP ( B + → K + π 0 ) / A CP ( B 0 → K + π − ) rules out a small strong phase difference between a color-suppressed and a color-favored tree amplitude contributing to B + → K + π 0 as favored by QCD factorization.