$B\to K\eta,K\eta^{\prime}$ Decays

Abstract

The nonet symmetry scheme seems to describe rather well the masses and $\eta-\eta^{\prime}$ mixing angle of the ground state pseudo-scalar mesons and is thus expected to be also a good approximation for the matrix elements of the pseudo-scalar density operators which play an important role in charmless two-body B decays with $\eta$ or $\eta^{\prime}$ in the final state. In this talk, I would like to report on a recent work on the $B^{-}\to K^{-}\eta, K^{-}\eta^{\prime}$ decay using nonet symmetry for the matrix elements of pseudo-scalar density operators. We find that the branching ratio $B\to PP$, with an $\eta$ meson in the final state agrees well with data, while those with an $\eta^{\prime}$ meson are underestimated by $20-30%$. This could be considered as a more or less successful prediction for QCDF, considering the theoretical uncertainties involved. This could also indicate that an additional power-suppressed terms could bring the branching ratio close to experiment, as with the $B\to K^{*}\pi$ and $B\to K^{*}\eta$ decay for which the measured branching ratios are much bigger than the QCDF predictions.