Charmless Two-Body B Meson Decays In Factorization Assisted Topological Amplitude Approach

We analyze charmless two-body non-leptonic $B$ decays under the framework of factorization assisted topological amplitude approach. Unlike the conventional flavor diagram approach, we consider flavor $SU(3)$ breaking effect assisted by factorization hypothesis for topological diagram amplitudes of different decay modes, by factorizing out the corresponding decay constants and form factors. The non-perturbative parameters of topology diagram magnitudes $\chi$ and strong phase $\phi$ are universal that can be extracted by $\chi^2$ fit from current abundant experimental data of charmless $B$ decays. The number of free parameters and the $\chi^2$ per degree of freedom are both reduced comparing with previous analysis. With these best fitted parameters, we predict branching fractions and $CP$ asymmetry parameters of nearly 100 $B_{u,d}$ and $B_s$ decay modes. The long-standing $\pi \pi$ and $\pi K$-$CP$ puzzles are solved simultaneously.