Experimental Investigation of the Two-Photon Widths of the ${\chi }_{\mathit{c}0}$ and the ${\chi }_{\mathit{c}2}$ Mesons

Using $12.7{\mathrm{fb}}^{-1\mathrm{}}$ of data collected with the CLEO detector at CESR, we observed two-photon production of the $c\overline{c}$ states ${\chi }_{c0\mathrm{}}$ and ${\chi }_{c2\mathrm{}}$ in their decay to ${\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$. We measured ${\Gamma }_{\gamma \gamma }\left({\chi }_c\right)\times B({\chi }_c\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-})$ to be $75\pm 13\left(\mathrm{stat}\right)\pm 8\left(\mathrm{syst}\right)\mathrm{eV}$ for the ${\chi }_{c0\mathrm{}}$ and $6.4\pm 1.8\left(\mathrm{stat}\right)\pm 0.8\left(\mathrm{syst}\right)\mathrm{eV}$ for the ${\chi }_{c2\mathrm{}}$, implying ${\Gamma }_{\gamma \gamma }\left({\chi }_{c0\mathrm{}}\right)=3.76\mathrm{}\pm 0.65\left(\mathrm{stat}\right)\pm 0.41\left(\mathrm{syst}\right)\pm 1.69\left(\mathrm{br}\right)\mathrm{keV}$ and ${\Gamma }_{\gamma \gamma }\left({\chi }_{c2\mathrm{}}\right)=0.53\mathrm{}\pm 0.15\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right)\pm 0.22\left(\mathrm{br}\right)\mathrm{keV}$. Also, cancellation of dominant experimental and theoretical uncertainties permits a precise comparison of ${\Gamma }_{\gamma \gamma }\left({\chi }_{c0\mathrm{}}\right)/{\Gamma }_{\gamma \gamma }\left({\chi }_{c2\mathrm{}}\right)$, evaluated to be $7.4\pm 2.4\left(\mathrm{stat}\right)\pm 0.5\left(\mathrm{syst}\right)\pm 0.9\left(\mathrm{br}\right)$, with QCD-based predictions.