Limit on the Two-Photon Production of the Glueball Candidate $f_J\left(2220\right)$ at the Cornell Electron Storage Ring

We use the CLEO detector at the Cornell $e^{+}{e}^{-}$ storage ring, CESR, to search for the two-photon production of the glueball candidate $f_J\left(2220\right)$ in its decay to $K_s{K}_s$. We present a restrictive upper limit on the product of the two-photon partial width and the $K_s{K}_s$ branching fraction, $({\gamma }_{\gamma \gamma }{B}_{K_s{K}_s}{)}_{f_{J\left(2220\right)}}$. We use this limit to calculate a lower limit on the stickiness, which is a measure of the two-gluon coupling relative to the two-photon coupling. This limit on stickiness indicates that the $f_J\left(2220\right)$ has substantial glueball content.