Nonet symmetry in η, η^{\prime} and B\to Kη,Kη^{\prime} decays

Abstract

The nonet symmetry scheme seems to describe rather well the masses and $η-η^{\prime}$ mixing angle of the ground state pseudo-scalar mesons. It is expected that nonet symmetry should also be valid for the matrix elements of the pseudo-scalar densitty operators which play an important role in charmless two-body B decays with $η$ or $η^{\prime}$ in the final state. Starting from the divergences of the SU(3) octet and singlet axial vector currents, we show that nonet symmetry for the pseudo-scalar mass term implies nonet symmetry for the pseudo-scalar density operators. In this nonet symmetry scheme, we find that the branching ratio $B\to PP,PV$, with $η$ in the final state agrees well with data, while those with $η'$ are underestimated, but by increasing the $B\to η'$ form factor by $40-50%$, one could explain the tree-dominated $B^{-}\to π^{-}η'$ and $B^{-}\to ρ^{-}η'$ measured branching ratios. With this increased form factor and with only a moderate annihilation contribution, we are able to obtain $62\times 10^{-6}$ for the penguin-dominated $B^{-}\to K^{-}η'$ branching ratios, quite close to the measured value. This supports the predicted value for the $B\to η'$ form factor in PQCD and light-cone sum rules approach. A possible increase by 15% of $<0|\bar{s} iγ_5 s|s\bar{s}>$ for $η_{0} $ would bring the predicted $B^{-}\to K^{-}η'$ branching ratio to $69.375\times 10^{-6}$, very close to experiment.