Study of ${\chi }_{bJ}(2P)\to \omega \mathrm{{\rm Y}}(1S)$ at Belle

We report a study of the hadronic transitions ${\chi }_{bJ}(2P)\to \omega \mathrm{{\rm Y}}(1S)$, with $\omega \to {\pi }^{+}{\pi }^{-}{\pi }^0$, using $28.2\times {10}^6\mathrm{{\rm Y}}(3S)$ mesons recorded by the Belle detector. We present the first evidence for the near–threshold transition ${\chi }_{b0}(2P)\to \omega \mathrm{{\rm Y}}(1S)$, the analog of the near-threshold charm sector decay ${\chi }_{c1}(3872)\to \omega J\mathrm{/}\psi$, with a branching fraction of $\mathcal{B}({\mathcal{\chi }}_{\mathcal{b}\mathcal{0}}(\mathcal{2}\mathcal{P})\to \mathcal{\omega }\mathcal{{\rm Y}}(\mathcal{1}\mathcal{S}))=(\mathcal{0.55}\pm \mathcal{0.19}\pm \mathcal{0.07})\mathcal{\%}$. We also obtain branching fractions of $\mathcal{B}({\mathcal{\chi }}_{\mathcal{b}\mathcal{1}}(\mathcal{2}\mathcal{P})\to \mathcal{\omega }\mathcal{{\rm Y}}(\mathcal{1}\mathcal{S}))=(\mathcal{2.39}{}_{-\mathcal{0.19}}^{+\mathcal{0.20}}\pm \mathcal{0.24})\mathcal{\%}$ and $\mathcal{B}({\mathcal{\chi }}_{\mathcal{b}\mathcal{2}}(\mathcal{2}\mathcal{P})\to \mathcal{\omega }\mathcal{{\rm Y}}(\mathcal{1}\mathcal{S}))=(\mathcal{0.47}{}_{-\mathcal{0.12}}^{+\mathcal{0.13}}\pm \mathcal{0.06})\mathcal{\%}$, confirming the measurement of the $\omega$ transitions of the $J=1,2P$–wave states. The ratio for the $J=2$ to $J=1$ transitions is also measured and found to differ by 3.3 standard deviations from the expected value in the QCD multipole expansion.