$B\to K\eta ,K{\eta }^{\prime }$ 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 $B\to K^{\ast }\pi$ and $B\to K^{\ast }\eta$ decay for which the measured branching ratios are much bigger than the QCDF predictions.

Talk given at QCD08, the 14th International QCD Conference, 7-12th July 2008, Montpellier (France), LaTeX, 7 pages

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