Improved Measurements of Two-Photon Widths of The χ(cJ) States and Helicity Analysis For χ(c2) → γγ

Based on 448.1 x 10⁶ ψ(3686) events collected with the BESIII detector, the decays ψ(3686) → γ χ(cJ), χ(cJ) → γγ(J = 0, 1, 2) are studied. The decay branching fractions of χ(c0,2) → γγ are measured to be ℬ(χ(c0) → γγ) = (1.93 ± 0.08 ± 0.05 ± 0.05) x 10⁻⁴ and ℬ(χ(c2) → γγ) = (3.10 ± 0.09 ± 0.07 ± 0.11) x 10⁻⁴ which correspond to two-photon decay widths of Γ(γγ)(χ(c0)) = 2.03 ± 0.08 ± 0.06 ± 0.13 keV and Γ(γγ)(χ(c2)) = 0.60 ± 0.02 ± 0.01 ± 0.04 keV with a ratio of R = Γ(γγ)(χ(c2))/Γ(γγ)(χ(c0)) = 0.295 ± 0.014 ± 0.007 ± 0.027, where the uncertainties are statistical, systematic and associated with the uncertainties of ℬ(ψ(3686) → γχ(c2)) and the total widths Γχ(c0,2), respectively. For the forbidden decay of χ(c1) → γγ, no signal is observed, and an upper limit on the two-photon width is obtained to be Γ(γγ)(χ(c1)) < 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 χ(c2) → γγ is also measured to be f(0/2) = Γ(γγ)(λ=0) (χ(c2)) / Γ(γγ)(λ=2) (χ(c2) = (0.0 ± 0.6 ± 1.2) x 10(-2), where the uncertainties are statistical and systematic, respectively.