Observation of the charmonium decay $η_c\toγγ$ in $J/ψ\toγη_c$
Using $(2712.4\pm14.3)\times10^{6}$ $ψ(3686)$ events collected with the BESIII detector at the BEPCII collider, the decay $η_c\toγγ$ in $J/ψ\toγη_c$ is observed. We determine the product branching fraction $\mathcal{B}(J/ψ\toγη_c)\times\mathcal{B}(η_c\toγγ)=(5.23\pm0.26_{\rm{stat.}}\pm0.30_{\rm{syst.}})\times10^{-6}$. This result is consistent with the LQCD calculation $(5.34\pm0.16)\times10^{-6}$ from HPQCD in 2023. By using the world-average values of $\mathcal{B}(J/ψ\toγη_c)$ and the total decay width of $η_c$, the partial decay width $Γ(η_c\toγγ)$ is determined to be $(11.30\pm0.56_{\rm{stat.}}\pm0.66_{\rm{syst.}}\pm1.14_{\rm{ref.}})~\rm{keV}$, which deviates from the corresponding world-average value by $3.4σ$.