${\mathcal{A}}_{\mathrm{CP}}$ Puzzle: Possible Evidence for Large Strong Phase in $B\to K\pi$ Color-Suppressed Tree Amplitude

Abstract

In QCD Factorization(QCDF), the suppression of the color-suppressed tree amplitude relative to the color-allowed one in $B\to K\pi$ decay implies a direct CP asymmetry in $B^{-}\to K^{-}{\pi }^0$ to be of the same sign and comparable in magnitude to that in ${\bar{B}}^0\to K^{+}{\pi }^{-}$, in contradiction with experiment. This is the $A_{\mathrm{CP}}$ $B\to K\pi$ puzzle. One of the current proposal to solve this puzzle is the existence of a large color-suppressed amplitude with large strong phase which implies also a large negative ${\bar{B}}^0\to {\bar{K}}^0{\pi }^0$ CP asymmetry. In this paper, by an essentially model-independent calculation, we show clearly that the large negative direct CP asymmetry in ${\bar{B}}^0\to {\bar{K}}^0{\pi }^0$ implies a large $C/T$, the ratio of the color-suppressed to the color-allowed tree amplitude and a large negative strong phase for $C$. By adding to the QCDF amplitude an additional color-suppressed term to generate a large $C/T$ and a large strong phase for $C$ and an additional penguin-like contribution, we obtain branching ratios for all $B\to K\pi$ modes and CP asymmetry for ${\bar{B}}^0\to K^{+}{\pi }^{-}$ and $B^{-}\to K^{-}{\pi }^0$ in agreement with experiment, and a large and negative CP asymmetry in ${\bar{B}}^0\to {\bar{K}}^0{\pi }^0$ which could be checked with more precise measurements.

Comments: LaTeX, 7 pages, 5 figures