Massiveness of Glueballs as Origin of the OZI Rule

Abstract

The heaviness of the glueball mass scale is suggested as the source of the OZI rule at low energy. The $J/\psi \to \rho\pi$ decay "anomaly" implies the vector glueball $O$ has mass $m_O \approx m_{J/\psi}$. Such a heavy mass is supported by other glueball studies. Glueball-meson matrix elements turn out to be not suppressed at all at the 1 GeV scale, and a simple and intuitive picture emerges which is consistent with the Gell-Mann-Okubo mass formula as well as the measured sign of $\phi$-$\omega$ mixing. The suppression of glueball mediated $\bar q_iq_i \longleftrightarrow \bar q_jq_j$ transitions and the cancellation mechanism in two-step meson rescatterings are viewed as related by duality. Extensions to the $2^{++}$, $3^{--}$ meson sectors, and failure for $0^{\pm +}$ mesons are also discussed.