For the first time we search for the eta(c2) (1D) in e(+) e(-) -> gamma eta(c2)(1D) at root 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(c20) (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(-) -> gamma eta(c2) (1D) and branching fraction for eta c2(1D) -> gamma h(c) (1P) is determined to be so e(+)e(-)-> gamma c(2) (1D)gamma B eta(c2()1D)-> gamma h(c) (1P)) < 4.9 fb at root s near 10.6 GeV.