Based on $448.1\times {10}^6\psi (3686)$ events collected with the BESIII detector, the decays $\psi (3686)\to \gamma {\chi }_{cJ},{\chi }_{cJ}\to \gamma \gamma (J=0,1,2)$ are studied. The decay branching fractions of ${\chi }_{c0,2}\to \gamma \gamma$ are measured to be $\mathcal{B}({\chi }_{c0}\to \gamma \gamma )=(1.93\pm 0.08\pm 0.05\pm 0.05)\times {10}^{-4}$ and $\mathcal{B}({\chi }_{c2}\to \gamma \gamma )=(3.10\pm 0.09\pm 0.07\pm 0.11)\times {10}^{-4}$, which correspond to two-photon decay widths of ${\mathrm{\Gamma }}_{\gamma \gamma }({\chi }_{c0})=2.03\pm 0.08\pm 0.06\pm 0.13\mathrm{keV}$ and ${\mathrm{\Gamma }}_{\gamma \gamma }({\chi }_{c2})=0.60\pm 0.02\pm 0.01\pm 0.04\mathrm{keV}$ with a ratio of $\mathcal{R}={\mathrm{\Gamma }}_{\gamma \gamma }({\chi }_{c2})/{\mathrm{\Gamma }}_{\gamma \gamma }({\chi }_{c0})=0.295\pm 0.014\pm 0.007\pm 0.027$, where the uncertainties are statistical, systematic and associated with the uncertainties of $\mathcal{B}(\psi (3686)\to \gamma {\chi }_{c0,2})$ and the total widths $\mathrm{\Gamma }({\chi }_{c0,2})$, respectively. For the forbidden decay of ${\chi }_{c1}\to \gamma \gamma$, no signal is observed, and an upper limit on the two-photon width is obtained to be ${\mathrm{\Gamma }}_{\gamma \gamma }({\chi }_{c1})<5.3\mathrm{eV}$ at the 90% confidence level. The ratio of the two-photon widths between helicity-zero and helicity-two components in the decay ${\chi }_{c2}\to \gamma \gamma$ is also measured to be $f_{0/2}={\mathrm{\Gamma }}_{\gamma \gamma }^{\lambda =0}({\chi }_{c2})/{\mathrm{\Gamma }}_{\gamma \gamma }^{\lambda =2}({\chi }_{c2})=(0.0\pm 0.6\pm 1.2)\times {10}^{-2}$, where the uncertainties are statistical and systematic, respectively.

• Received 20 September 2017

DOI:https://doi.org/10.1103/PhysRevD.96.092007