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

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