A global $SU(3)/U(3)$ flavor symmetry analysis for $B\to PP$ with $η-η'$ Mixing

Abstract: A large number of new experimental data on $B$ decay into two light pesudoscalar ($P$) mesons have been collected by the LHCb collaboration. Besides confirming information on $B_{u,d} \to PP$ decays obtained earlier by B-factories at KEK and SLAC, new information on $B_s\to PP$ and also more decay modes with $P$ being $\eta$ or $\eta'$ have been obtained. Using these new data, we perform a global fit for $B \to PP$ to determine decay amplitudes in the framework of $SU(3)/U(3)$ flavor symmetry. We find that $SU(3)$ flavor symmetry can explain data well. The annihilation amplitudes are found to be small as expected. Several CP violating relations predicted by $SU(3)$ flavor symmetry are in good agreement with data. Current available data can give constraints on the amplitudes which induce $P = \eta,\;\eta'$ decays in the framework of $U(3)$ flavor symmetry, and can also determine the $\eta-\eta'$ mixing angle $\theta$ with $\theta = (-18.4\pm1.2)^\circ$. Several $B \to PP$ decay modes which have not been measured are predicted with branching ratios accessible at the LHCb. These decays can provide further tests for the framework of $SU(3)/U(3)$ flavor symmetry for $B$ decays.