Two-photon width of the charmonium state ${\chi }_{c2}$

The two-photon width of ${\chi }_{c2}({}^{3}P_2)$ state of charmonium has been measured using $14.4{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ data taken at $\sqrt{s}=9.46–11.30\mathrm{GeV}$ with the CLEO III detector. The $\gamma \gamma$-fusion reaction studied is $e^{+}{e}^{-}\to e^{+}{e}^{-}\gamma \gamma$, $\gamma \gamma \to {\chi }_{c2}\to \gamma J/\psi \to \gamma e^{+}{e}^{-}({\mu }^{+}{\mu }^{-})$. We measure ${\Gamma }_{\gamma \gamma }({\chi }_{c2})\mathcal{B}({\chi }_{c2}\to \gamma J/\psi )\mathcal{B}(J/\psi \to e^{+}{e}^{-}+{\mu }^{+}{\mu }^{-})=13.2\pm 1.4(\mathrm{stat})\pm 1.1(\mathrm{syst})\mathrm{eV}$, and obtain ${\Gamma }_{\gamma \gamma }({\chi }_{c2})=559\pm 57(\mathrm{stat})\pm 48(\mathrm{syst})\pm 36(\mathrm{br})\mathrm{eV}$. This result is in excellent agreement with the result of $\gamma \gamma$-fusion measurement by Belle and is consistent with that of the $\overline{p}p\to {\chi }_{c2}\to \gamma \gamma$ measurement, when they are both reevaluated using the recent CLEO result for the radiative decay ${\chi }_{c2}\to \gamma J/\psi$.

Figure 1

Distributions of $E/p$ (left) and $p_{\mathrm{tot}}^{\perp }$ (right) in data (points) and in the signal MC (histograms). Vertical dashed lines indicate the $E/p$ cuts for electrons and muons.

Figure 2

Comparison of the background subtracted data (points) and the signal MC (histograms) distributions of $|\cos {\Theta }_{\gamma }^{l\gamma }|$, $|\cos {\Theta }_{l^{+}}^l|$ and $\Delta \varphi$. ${\Theta }_{\gamma }^{l\gamma }$ is the polar angle of the photon in the $l^{+}{l}^{-}\gamma$ rest frame, ${\Theta }_{l^{+}}^l$ is the polar angle of the positive lepton in the $l^{+}{l}^{-}$ rest frame, and $\Delta \varphi$ is the azimuthal angle difference between the momenta of the two leptons in the laboratory frame.

Figure 3

Scatter plot of the $\Delta M=M(\gamma l^{+}{l}^{-})-M(l^{+}{l}^{-})$ with respect to the two lepton effective mass in data. Top and bottom horizontal shaded bands are the areas defined as the $J/\psi$ sideband regions, and the middle band is the area defined as the $J/\psi$ signal region.

Figure 4

$\Delta M=M(\gamma l^{+}{l}^{-})-M(l^{+}{l}^{-})$ mass difference distributions for $e^{+}{e}^{-}$ channel (a), ${\mu }^{+}{\mu }^{-}$ channel (b), and the sum (c). The solid line curves are results of fit to the data points using the background indicated by the dashed line curves.