Further Search for the Two-Photon Production of the Glueball Candidate $f_J\left(2220\right)$

The CLEO II detector at the $e^{+}{e}^{-}$ storage ring CESR has been used to search for two-photon production of the $f_J\left(2220\right)$ decaying into ${\pi }^{+}{\pi }^{-}$. No evidence for a signal is found in $4.77{\mathrm{fb}}^{-1\mathrm{}}$ of data and a 95% C.L. upper limit on $[{\Gamma }_{\gamma \gamma }{B}_{{\pi }^{+}{\pi }^{-}}{]}_{f_J\left(2220\right)}$ of 2.5 eV is set. If this result is combined with the BES Collaboration's measurement of $f_J\left(2220\right)\to {\pi }^{+}{\pi }^{-}$ in radiative $J/\psi$ decay and the recent CLEO result for $[{\Gamma }_{\gamma \gamma }{B}_{K_S^0{K}_S^0}{]}_{f_J\left(2220\right)}$, a $95\%$ C.L. lower limit on the stickiness of 102 is obtained. This result for the stickiness provides further support for a substantial neutral parton content in the $f_J\left(2220\right)$.