Hunting for Glueballs in Electron-Positron Annihilation

We calculate the cross section for the exclusive production of $J^{PC}=0^{++}$ glueballs ${\mathcal{G}}_0$ in association with the $J/\psi$ in $e^{+}{e}^{-}$ annihilation using the perturbative QCD factorization formalism. The required long-distance matrix element for the glueball is bounded by CUSB data from a search for resonances in radiative ${\rm Y}$ decay. The cross section for $e^{+}{e}^{-}\to J/\psi +{\mathcal{G}}_0$ at $\sqrt{s}=10.6\mathrm{G}\mathrm{e}\mathrm{V}$ is similar to exclusive charmonium-pair production $e^{+}{e}^{-}\to J/\psi +h$ for $h={\eta }_c$ and ${\chi }_{c0}$, and is larger by a factor of 2 than that for $h={\eta }_c(2S)$. As the subprocesses ${\gamma }^{*}\to (c\overline{c})(c\overline{c})$ and ${\gamma }^{*}\to (c\overline{c})(gg)$ are of the same nominal order in perturbative QCD, it is possible that some portion of the anomalously large signal observed by Belle in $e^{+}{e}^{-}\to J/\psi X$ may actually be due to the production of charmonium-glueball $J/\psi {\mathcal{G}}_J$ pairs.

Figure 1

Feynman diagram for ${\gamma }^{*}\to H+{\mathcal{G}}_J$.