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

Abstract

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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• On Puzzles and Non-Puzzles in B -> pi pi, pi K Decays
• CP asymmetries in three-body B+- decays to charged pions and kaons
• Benchmarks for the New-Physics Search through CP Violation in B^0->pi^0 K_S
• Hints for the scale of new CP-violating physics from B-CP anomalies
• B_s -> phi rho^0 and B_s -> phi pi^0 as a handle on isospin-violating New Physics
• Resolving B-CP Puzzles in QCD Factorization
• Constraining the mixing matrix for Standard Model with four generations: time dependent and semi-leptonic CP asymmetries in $B_d^0$, $B_s$ and $D^0$
• Implications for CP asymmetries of improved data on $B\to K^0{\pi }^0$
• Searching For New Physics With B to K pi Decays
• Analytic Resolution of Puzzle in $B\to K\pi$ decays
• Diagnostic for new physics in $B\to \pi K$ decays
• Demise of CKM & its aftermath
• CP Asymmetries in B->K pi, K*pi, rho K Decays
• Isospin of new physics in $|\Delta S|=1$ charmless B decays
• CP violation in beauty decays
• Implications of final state interactions in B-decays