Charmless decaysB→ππ,πKandKKin broken SU(3) symmetry

Charmless $B$ decay modes $B\to \pi \pi ,\pi K$ and $KK$ are systematically investigated with and without flavor SU(3) symmetry. Independent analyses on $\pi \pi$ and $\pi K$ modes both favor a large ratio between color-suppressed tree ($C$) and tree $(T)$ diagram, which suggests that they are more likely to originate from long distance effects. The sizes of QCD penguin diagrams extracted individually from $\pi \pi$, $\pi K$ and $KK$ modes are found to follow a pattern of SU(3) breaking in agreement with the naive factorization estimates. Global fits to these modes are done under various scenarios of SU(3) relations. The results show good determinations of weak phase $\gamma$ in consistency with the standard model (SM), but a large electroweak penguin $(P_{\mathrm{EW}})$ relative to $T+C$ with a large relative strong phase is favored, which requires a big enhancement of color-suppressed electroweak penguin ($P_{\mathrm{EW}}^C$) compatible in size but destructively interfering with $P_{\mathrm{EW}}$ within the SM, or implies new physics. The possibilities of sizable contributions from nonfactorizable diagrams such as $W$ exchange ($E$), annihilation ($A$), and penguin-annihilation diagrams ($P_A$) are investigated. The implications to the branching ratios and $CP$ violations in $KK$ modes are discussed.