Gluonic contribution toB→η(′)form factors

Abstract

We calculate the flavor-singlet contribution to the $B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}$ transition form factors from the gluonic content of the ${\ensuremath{\eta}}^{(\ensuremath{'})}$ meson in the large-recoil region using the perturbative QCD approach. The formulation for the $\ensuremath{\eta}\mathrm{\text{\ensuremath{-}}}{\ensuremath{\eta}}^{\ensuremath{'}}$ mixing in the quark-flavor and singlet-octet schemes is compared, and employed to determine the chiral enhancement scales associated with the two-parton twist-3 ${\ensuremath{\eta}}^{(\ensuremath{'})}$ meson distribution amplitudes. It is found that the gluonic contribution is negligible (around 5%) in the $B\ensuremath{\rightarrow}\ensuremath{\eta}$ form factors, but reaches 10%--40% in the $B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}$ ones. Its impact on the accommodation of the measured $B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{(\ensuremath{'})}K$ branching ratios in the perturbative QCD and QCD-improved factorization approaches is elaborated.