Gluonic contribution to $B\to {\eta }^{(\prime )}$ form factors

Abstract

We calculate the flavor-singlet contribution to the $B\to {\eta }^{(\prime )}$ transition form factors from the gluonic content of the ${\eta }^{(\prime )}$ meson in the large-recoil region using the perturbative QCD approach. The formulation for the $\eta$-${\eta }^{\prime }$ 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 ${\eta }^{(\prime )}$ meson distribution amplitudes. It is found that the gluonic contribution is negligible in the $B\to \eta$ form factors, and reaches few percents in the $B\to {\eta }^{\prime }$ ones. Its impact on the accommodation of the measured $B\to {\eta }^{(\prime )}K$ branching ratios in the perturbative QCD and QCD-improved factorization approaches is elaborated.

13 pages, 9 figures, a missing overall coefficient was included into the gluonic contribution. The numerical results were revised accordingly

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