Sum rule for rate and CP asymmetry in $B^+\to K^+π^0$

Details Sum rule for rate and CP asymmetry in $B^+\to K^+π^0$ Sum rule for rate and CP asymmetry in $B^+\to K^+π^0$

2006-10-18

arxiv.org/abs/hep-ph/0610227v3

Phys.Lett.B644:237-240,2007

Physics

High Energy Physics

High Energy Physics - Phenomenology

small correction

Scientific paper

10.1016/j.physletb.2006.11.044

A sum rule relating the ratio $R_c = 2 \Gamma(B^+ \to K^+ \pi^0)/\Gamma(B^+ \to K^0 \pi^+)$ and the CP asymmetry $A_{CP}(B^+ \to K^+\pi^0)$ 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 $B^+ \to K^+ \pi^0$. The measured ratio $A_{CP}(B^+\to K^+\pi^0)/A_{CP}(B^0\to K^+\pi^-)$ rules out a small strong phase difference between a color-suppressed and a color-favored tree amplitude contributing to $B^+\to K^+\pi^0$ as favored by QCD factorization.

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