Pseudoscalar glueball mass from $\eta$-${\eta }^{\prime }$-$G$ mixing

Abstract

We deduce the mass of the pseudoscalar glueball $G$ from an $\eta$-${\eta }^{\prime }$-$G$ mixing formalism based on the anomalous Ward identity for transition matrix elements. With the inputs from the recent KLOE experiment, we find a solution for the pseudoscalar glueball mass around $(1.4\pm 0.1)$ GeV, which is fairly insensitive to a range of inputs with or without Okubo-Zweig-Iizuka-rule violating effects. This affirms that $\eta (1405)$, having a large production rate in the radiative $J/\Psi$ decay and not seen in $\gamma \gamma$ reactions, is indeed a leading candidate for the pseudoscalar glueball. Other relevant quantities including the anomaly and pseudoscalar density matrix elements are obtained. The decay widths for $G\to \gamma \gamma$, ${\ell }^{+}{\ell }^{-}$ are also predicted.

Comments: 12 pages no figure, version to appear in PRD