Article,
Nonet symmetry in \eta, \eta^\prime and BK\eta,K\eta^\prime decays
(Jan 17, 2008)
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. 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 \$\eta\$ or \$\eta^\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 \$BPP,PV\$, with \$\eta\$ in the final state agrees
well with data, while those with \$\eta'\$ are underestimated, but by increasing
the \$B\eta'\$ form factor by \$40-50\%\$, one could explain the tree-dominated
\$B^-\pi^-\eta'\$ and \$B^-\rho^-\eta'\$ measured branching ratios.
With this increased form factor and with only a moderate annihilation
contribution, we are able to obtain \$6210^-6\$ for the
penguin-dominated \$B^-K^-\eta'\$ branching ratios, quite close to the
measured value. This supports the predicted value for the \$B\eta'\$ form
factor in PQCD and light-cone sum rules approach. A possible increase by 15\% of
\$<0|s i\gamma\_5 s|ss>\$ for \$\eta\_0 \$ would bring the predicted
\$B^-K^-\eta'\$ branching ratio to \$69.37510^-6\$, very close to
experiment.
