Constraints on the $\eta \eta'$ decay rate of a scalar glueball from gauge/gravity duality

Predictions of glueball decay rates in the holographic Witten-Sakai-Sugimoto model for low-energy QCD can be uniquely extended to include finite quark masses up to an as yet undetermined parameter in the coupling of glueballs to the nonanomalous part of the pseudoscalar mass terms. The assumption of a universal coupling of glueballs to mass terms of the full nonet of pseudoscalar mesons leads to flavor asymmetries in the decay rates of scalar glueballs that agree well with experimental data for the glueball candidate $f_0(1710)$ and implies a vanishing decay rate into $\eta\eta'$ pairs, for which only upper bounds for the $f_0(1710)$ meson are known at present from experiment. Relaxing this assumption, the holographic model gives a tight correlation between the decay rates into pairs of pseudo-Goldstone bosons of same type and $\eta\eta'$ pairs. If $\Gamma(G\to KK)/\Gamma(G\to\pi\pi)$ is kept within the range reported currently by the Particle Data Group for the $f_0(1710)$ meson, the rate $\Gamma(G\to\eta\eta')/\Gamma(G\to\pi\pi)$ is predicted to be $\lesssim 0.04$. The corresponding situation for $f_0(1500)$ is also discussed, which however is found to be much less compatible with the interpretation of a largely unmixed glueball.