Charmless $B\to PP$ decays using flavor SU(3) symmetry

Abstract

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 $B\to \pi \pi$ and $B\to K\pi$ branching ratios and CP asymmetries are obtained with tree, color-suppressed ($C$), penguin ($P$), and electroweak penguin ($P_{EW}$) 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 $P_{tu}$ associated with intermediate $t$ and $u$ quarks. For the $B^{+}\to {\pi }^{+}{\eta }^{\prime }$ mode a term $S_{tu}$ 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 $B\to VP$ decays, where $V$ denotes a vector meson, and with other analyses of CKM parameters.

Comments: 26 pages, 1 figure. To be submitted to Phys. Rev. D. Reference updated