Improved measurements of two-photon widths of the ${\chi }_{cJ}$ states and helicity analysis for ${\chi }_{c2}\to \gamma \gamma$

Based on $448.1\times {10}^6$ $\psi (3686)$ events collected with the BESIII detector, the decays $\psi(3686)\to\gamma\chi_{cJ}, \chi_{cJ} \to \gamma\gamma~(J=0, 1, 2)$arestudied\mathrm{.}Thedecaybranchingfractionsof$\chi_{c0,c2} \to \gamma\gamma$aremeasuredtobe$$\mathcal{B}$(\chi_{c0}\to\gamma\gamma) = (1.93 \pm 0.08 \pm 0.05 \pm 0.05)\times 10^{-4}$and$$\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 $\Gamma_{\gamma\gamma}(\chi_{c0}) = 2.03 \pm 0.08 \pm 0.06 \pm 0.13 ~\rm{keV}$and$\Gamma_{\gamma\gamma}(\chi_{c2}) = 0.60 \pm 0.02 \pm 0.01 \pm 0.04 ~\rm{keV}$witharatioof$$\mathcal{R}$=\Gamma_{\gamma\gamma}(\chi_{c2})/\Gamma_{\gamma\gamma}(\chi_{c0})= 0.295 \pm 0.014 \pm 0.007 \pm 0.027$, where the uncertainties are statistical, systematic and associated with the uncertainties of $\mathcal{B}(\psi (3686)\to \gamma {\chi }_{c0,c2})$ and the total widths $\mathrm{\Gamma }({\chi }_{c0,c2})$, 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 $\Gamma_{\gamma\gamma}(\chi_{c1})<5.3 ~\rm{eV}$ 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 $f_{0/2} = \Gamma^{\lambda=0}{\gamma\gamma}(\chi{c2})/\Gamma^{\lambda=2}{\gamma\gamma}(\chi{c2}) = (0.0 \pm 0.6 \pm 1.2)\times 10^{-2}$, where the uncertainties are statistical and systematic, respectively.