First search for the $eta_{c2}(1D)$ in $B$ decays at Belle

The first dedicated search for the $eta_{c2}(1D)$ is carried out using the decays $B^+ rightarrow eta_{c2}(1D) K^+$, $B^0 rightarrow eta_{c2}(1D) K^0_S$, $B^0 rightarrow eta_{c2}(1D) pi^- K^+$, and $B^+ rightarrow eta_{c2}(1D) pi^+ K^0_S$ with $eta_{c2}(1D) to h_c gamma$. No significant signal is found. For the $eta_{c2}(1D)$ mass range between $3795$ and $3845 mathrm{MeV}/c^2$, the branching-fraction upper limits are determined to be $mathcal{B}(B^+ rightarrow eta_{c2}(1D) K^+) times mathcal{B}(eta_{c2}(1D) to h_c gamma) < 3.7 times 10^{-5}$, $mathcal{B}(B^0 rightarrow eta_{c2}(1D) K^0_S) times mathcal{B}(eta_{c2}(1D) to h_c gamma) < 3.5 times 10^{-5}$, $mathcal{B}(B^0 rightarrow eta_{c2}(1D) pi^- K^+) times mathcal{B}(eta_{c2}(1D) to h_c gamma) < 1.0 times 10^{-4}$, and $mathcal{B}(B^+ rightarrow eta_{c2}(1D) pi^+ K^0_S) times mathcal{B}(eta_{c2}(1D) to h_c gamma) < 1.1 times 10^{-4}$ at 90% C. L. The analysis is based on the 711 $mathrm{fb}^{-1}$ data sample collected on the $Upsilon(4S)$ resonance by the Belle detector, which operated at the KEKB asymmetric-energy $e^+ e^-$ collider.