Search for the $eta_{c2}(1D)$ in $e^+e^-togammaeta_{c2}(1D)$ at $sqrt{s}$ near 10.6 GeV at Belle

For the first time we search for the $eta_{c2}(1D)$ in $e^+e^-togammaeta_{c2}(1D)$ 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 $eta_{c2}(1D)$ 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 $e^+e^- to gammaeta_{c2}(1D)$ and branching fraction for $eta_{c2}(1D)to gamma h_c(1P)$ is determined to be $sigma(e^+e^- to gammaeta_{c2}(1D)){cal B}(eta_{c2}(1D)to gamma h_c(1P))$ $<$ 4.9 fb at $sqrt{s}$ near 10.6 GeV.