Further Analysis of Di-gluon Fusion Mechanism for the decays of $B \to K \eta^{\prime}$

TL;DR

This paper investigates the di-gluon fusion mechanism's role in explaining the large branching ratios of B meson decays to K eta prime, analyzing form factors and comparing with experimental data.

Contribution

It explores various eta prime gluon-gluon form factors and assesses their impact on decay predictions, highlighting the potential significance of di-gluon fusion in B decays.

Findings

Branching ratios for B to K* eta prime are around 10^-5.

Different form factors significantly affect decay rate estimates.

Future experiments can test the importance of di-gluon fusion in these decays.

Abstract

Di-gluon fusion mechanism might account for the large branching ratios of $B\to K \eta^{\prime}$. But because we know little about the effective $\eta^{\prime}gg$ vertex, there are large uncertainties in perturbative QCD estimations. In this paper, we try several kinds of $\eta^{\prime}gg$ form factors and compare the numerical results with the experiment. We find that, though we know little about $\eta^{\prime}gg$ form factor, if di-gluon fusion mechanism is important in $B\to K \eta^{\prime}$, the branching ratios of the decays $B\to K^{\ast} \eta^{\prime}$ would be around $10^{-5}$ which can be tested by future experiments.