Formation of the $\eta_c$ in Two-Photon Collisions at LEP
The two-photon width $\Gamma_{\gamma\gamma}$ of the $\eta_c$ meson has been measured with the L3 detector at LEP. The $\eta_c$ is studied in the decay modes $\pi^+\pi^-\pi^+\pi^-$, $\pi^+\pi^-$K$^+$K$^-$, K$_s^0$K$^\pm\pi^\mp$, K$^+$K$^-\pi^{0}$, $\pi^+\pi^-\eta$, $\pi^+\pi^-\eta'$, and $\rho^+\rho^-$ using an integrated luminosity of 140 pb$^{-1}$ at $\sqrt{s} \simeq 91$ GeV and of 52 pb$^{-1}$ at $\sqrt{s} \simeq 183$ GeV. The result is $\Gamma_{\gamma\gamma}(\eta_c) = 6.9 \pm 1.7 (stat.) \pm 0.8 (sys.) \pm 2.0$(BR) keV. The $Q^2$ dependence of the $\eta_c$ cross section is studied for $Q^2 < 9$ GeV$^{2}$. It is found to be better described by a Vector Meson Dominance model form factor with a J-pole than with a $\rho$-pole. In addition, a signal of $29 \pm 11$ events is observed at the $\chi_c0$ mass. Upper limits for the two-photon widths of the $\chi_c0$, $\chi_c2$, and $\eta_c'$ are also given.