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

A sum rule relating the ratio Rc=2Γ(B+→K+π0)/Γ(B+→K0π+) and the CP asymmetry ACP(B+→K+π0) is proved to first order in the ratio of tree to penguin amplitudes. The sum rule explains why it is possible to have Rc consistent with 1 together with a small CP asymmetry in B+→K+π0. The measured ratio ACP(B+→K+π0)/ACP(B0→K+π−) rules out a small strong phase difference between a color-suppressed and a color-favored tree amplitude contributing to B+→K+π0 as favored by QCD factorization.