On the Short Distance Part of the QCD Anomaly Contribution to the b --> s eta' Amplitude

Abstract

In addressing the B --> eta' K puzzle, there has been a considerable hope in the literature to resolve it by the QCD anomaly contribution to the b --> s eta' amplitude. This contribution corresponds to the electroweak b --> s g* g* transition followed by the off-shell gluon fusion g* g* --> eta'. In the present paper we perform a critical reassessment of this issue. We show that for the hard virtual gluons in a loop there is a well defined short distance amplitude corresponding to a remnant of the QCD anomaly. However, we find that it cannot account for the measured amplitude. In addition, we point out that the reduction of the gluon fusion vertex for the off-shell gluons is compensated by an absence of the claimed suppression in the electroweak vertex, and that some nonperturbative contributions related to the QCD anomaly may still be viable in explaining the physical B --> eta' K amplitude.

11 pages, 4 figures, LaTeX + elsart.cls, to appear in Phys. Lett. B

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Cited by in corpus (8)

• Gluonic contribution to $B\to {\eta }^{(\prime )}$ form factors
• ${\eta }_c$ mixing effects on charmonium and $B$ meson decays
• Okubo-Zweig-Iizuka-rule violation and B\to η^{(\prime)}K branching ratios
• QCD anomalies in hadronic weak decays
• The B^- -> phi phi K^- decay rate with phi phi invariant mass below charm treshold
• On the Singlet Penguin in B --> K eta' decay
• On the color suppressed contribution to $\bar{B_{d}^0} \rightarrow \, π^0 π^{0}
• Soft end-point and mass corrections to the eta' g*g* vertex function