Charmless $\overrightarrow{B}\mathrm{PP}$ decays using flavor SU(3) symmetry

The decays of B mesons to a pair of charmless pseudoscalar (P) mesons are analyzed within a framework of flavor SU(3). Symmetry breaking is taken into account in tree (T) amplitudes through ratios of decay constants; exact SU(3) is assumed elsewhere. Acceptable fits to $\overrightarrow{B}\pi \pi$ and $\overrightarrow{B}K\pi$ branching ratios and CP asymmetries are obtained with tree, color-suppressed $\mathrm{}\left(C\right),$ penguin $\mathrm{}\left(P\right),$ and electroweak penguin ${(P}_{\mathrm{EW}})$ amplitudes. Crucial additional terms for describing processes involving $\eta$ and ${\eta }^{\prime }$ include a large flavor-singlet penguin amplitude (S) as proposed earlier and a penguin amplitude $P_{\mathrm{tu}}$ associated with intermediate t and u quarks. For the $B^{+}\to {\pi }^{+}{\eta }^{\prime }$ mode a term $S_{\mathrm{tu}}$ associated with intermediate t and u quarks also may be needed. Values of the weak phase $\gamma$ are obtained consistent with an earlier analysis of $\overrightarrow{B}\mathrm{VP}$ decays, where V denotes a vector meson, and with other analyses of CKM parameters.