Based on 448.1×106 ψ(3686) events collected with the BESIII detector, the decays ψ(3686)→γχcJ,χcJ→γγ(J=0,1,2) are studied. The decay branching fractions of χc0,2→γγ are measured to be B(χc0→γγ)=(1.93±0.08±0.05±0.05)×10-4 and B(χc2→γγ)=(3.10±0.09±0.07±0.11)×10-4, which correspond to two-photon decay widths of Γγγ(χc0)=2.03±0.08±0.06±0.13 keV and Γγγ(χc2)=0.60±0.02±0.01±0.04 keV with a ratio of R=Γγγ(χc2)/Γγγ(χc0)=0.295±0.014±0.007±0.027, where the uncertainties are statistical, systematic and associated with the uncertainties of B(ψ(3686)→γχc0,2) and the total widths Γ(χc0,2), respectively. For the forbidden decay of χc1→γγ, no signal is observed, and an upper limit on the two-photon width is obtained to be Γγγ(χc1)<5.3 eV at the 90% confidence level. The ratio of the two-photon widths between helicity-zero and helicity-Two components in the decay χc2→γγ is also measured to be f0/2=Γγγλ=0(χc2)/Γγγλ=2(χc2)=(0.0±0.6±1.2)×10-2, where the uncertainties are statistical and systematic, respectively.
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