Glueball production via gluonic penguin $$B$$ B decays

Abstract

We study glueball \(G\) production in gluonic penguin decay \(B\rightarrow G + X_s\), using the next-to-leading order \(b\rightarrow s g^*\) gluonic penguin interaction and effective couplings of a glueball to two perturbative gluons. Subsequent decays of a scalar glueball are described by using techniques of effective chiral Lagrangians to incorporate the interaction between a glueball and pseudoscalar mesons. Mixing effects between the pure glueball with other mesons are considered. Identifying the \(f_0(1710)\) as a scalar glueball, we find that both the top and the charm penguin are important and obtain a sizable branching ratio for \(B\rightarrow f_0(1710) + X_s\) of order \(1.3\times 10^{-4}(f/0.07\,\text{ GeV }^{-1})^2\), where the effective coupling strength \(f\) is estimated to be \(0.07\) GeV\(^{-1}\) using experimental data for the branching ratio of \(f_0(1710) \rightarrow K \overline{K}\) based on a chiral Lagrangian estimate. An alternative perturbative QCD based estimation of \(f\) is a factor of 20 larger, which would imply a much enhanced branching ratio. Glueball production from this rare semi-inclusive \(B\) decay can be probed at the LHCb and Belle II to narrow down the allowed parameter space. A similar branching ratio is expected for the pseudoscalar glueball. We also briefly comment on the case of vector and tensor glueballs.