Flavor-Singlet B-Decay Amplitudes in QCD Factorization

TL;DR

This work assesses whether flavor-singlet amplitudes can explain exclusive B decays to η or η′ in QCD factorization. By incorporating three gluon–related mechanisms—the $b\to s gg$ charm-loop contribution, soft spectator scattering involving two gluons, and singlet weak annihilation—the authors show that singlet effects exist at leading power but are generally subdominant to penguin interference, with radiative $\alpha_s$ corrections playing a crucial role. The η–η′ mixing is treated in the FKS scheme to reduce hadronic uncertainties to a few parameters, and the analysis finds that constructive or destructive interference among penguin amplitudes largely accounts for the observed pattern, including the enhanced $Kη′$ mode, albeit with large residual uncertainties from weak annihilation and the gluonic content of the η^(′). Overall, factorization remains a useful framework for singlet final states, provided one allows for a non-local $B\to K^{(*)}$ form factor to capture soft spectator effects.

Abstract

Exclusive hadronic B-meson decays into two-body final states consisting of a light pseudoscalar or vector meson along with an eta or eta' meson are of great phenomenological interest. Their theoretical analysis involves decay mechanisms that are unique to flavor-singlet states, such as their coupling to gluons or their ``intrinsic charm'' content. These issues are studied systematically in the context of QCD factorization and the heavy-quark expansion. Theory can account for the experimental data on the B->K^{(*)} eta^{(')} branching fractions, albeit within large uncertainties.

Figures (5)

• Figure 1: Two-gluon emission from a quark loop. A second diagram with the two gluons crossed is implied.
• Figure 2: Contributions to the $b\to s gg$ amplitude that are power suppressed in the heavy-quark limit.
• Figure 3: Spectator-scattering contributions to the $B\to K^{(*)}\eta^{(\prime)}$ decay amplitudes. The shaded blob represents the $\eta^{(\prime)} g^* g^*$ form factor.
• Figure 4: Representative singlet annihilation diagrams.
• Figure 5: Leading two-gluon contribution to the $B\to\eta^{(\prime)}$ form factor. The dot represents the insertion of the current.