Improved measurements of two-photon widths of the $χ_{cJ}$ states and helicity analysis for $χ_{c2}\toγγ$

Abstract

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

11 pages, 4 figures, 4 tables