Search for the $η_{c2}(1D)$ in $e^+e^-\toγη_{c2}(1D)$ at $\sqrt{s}$ near 10.6 GeV at Belle
For the first time we search for the $η_{c2}(1D)$ in $e^+e^-\toγη_{c2}(1D)$ at $\sqrt{s}$ = 10.52, 10.58, and 10.867 GeV with data samples of 89.5 fb$^{-1}$, 711 fb$^{-1}$, and 121.4 fb$^{-1}$, respectively, accumulated with the Belle detector at the KEKB asymmetric energy electron-positron collider. No significant $η_{c2}(1D)$ signal is observed in the mass range between 3.8 and 3.88 GeV/$c^2$. The upper limit at 90\% confidence level on the product of the Born cross section for $e^+e^- \to γη_{c2}(1D)$ and branching fraction for $η_{c2}(1D)\to γh_c(1P)$ is determined to be $σ(e^+e^- \to γη_{c2}(1D)){\cal B}(η_{c2}(1D)\to γh_c(1P))$ $<$ 4.9 fb at $\sqrt{s}$ near 10.6 GeV.