Two-photon widths of the $χ_{c0, 2}$ states and helicity analysis for $χ_{c2}\arγγ$}
Based on a data sample of 106 M $ψ^{\prime}$ events collected with the BESIII detector, the decays $ψ^{\prime}\arγχ_{c0, 2}$,$χ_{c0, 2}\arγγ$ are studied to determine the two-photon widths of the $χ_{c0, 2}$ states. The two-photon decay branching fractions are determined to be ${\cal B}(χ_{c0}\arγγ) = (2.24\pm 0.19\pm 0.12\pm 0.08)\times 10^{-4}$ and ${\cal B}(χ_{c2}\arγγ) = (3.21\pm 0.18\pm 0.17\pm 0.13)\times 10^{-4}$. From these, the two-photon widths are determined to be $Γ_{γγ}(χ_{c0}) = (2.33\pm0.20\pm0.13\pm0.17)$ keV, $Γ_{γγ}(χ_{c2}) = (0.63\pm0.04\pm0.04\pm0.04)$ keV, and $\cal R$ $=Γ_{γγ}(χ_{c2})/Γ_{γγ}(χ_{c0})=0.271\pm 0.029\pm 0.013\pm 0.027$, where the uncertainties are statistical, systematic, and those from the PDG ${\cal B}(ψ^{\prime}\arγχ_{c0,2})$ and $Γ(χ_{c0,2})$ errors, respectively. The ratio of the two-photon widths for helicity $λ=0$ and helicity $λ=2$ components in the decay $χ_{c2}\arγγ$ is measured for the first time to be $f_{0/2} =Γ^{λ=0}_{γγ}(χ_{c2})/Γ^{λ=2}_{γγ}(χ_{c2}) = 0.00\pm0.02\pm0.02$.