Decays ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{cJ}(J=0,1,2)\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi$ are studied using $(448.1\pm 2.9)\times {10}^6\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}(3686)$ events collected with the BESIII detector in 2009 and 2012. In addition to the previously established ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c0}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi$, the first observation of ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c1}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi$ is reported in this paper. The measured product branching fractions are $\mathcal{B}(\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}(3686)\to \mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}{\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c0})\times \mathcal{B}({\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c0}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi )=(13.83\pm 0.70\pm 1.01)\times {10}^{-6}$ and $\mathcal{B}(\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}(3686)\to \mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}{\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c1})\times \mathcal{B}({\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c1}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi )=(2.67\pm 0.31\pm 0.27)\times {10}^{-6}$, and the absolute branching fractions are $\mathcal{B}({\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c0}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi )=(13.84\pm 0.70\pm 1.08)\times {10}^{-5}$ and $\mathcal{B}({\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c1}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi )=(2.80\pm 0.32\pm 0.30)\times {10}^{-5}$. We also find strong evidence for ${\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c2}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi$ with a statistical significance of $4.8\mathrm{<ruby><rb>\sigma </rb><rt>しぐま</rt></ruby>}$, and the corresponding product and absolute branching fractions are measured to be $\mathcal{B}(\mathrm{<ruby><rb>\psi </rb><rt>ぷさい</rt></ruby>}(3686)\to \mathrm{<ruby><rb>\gamma </rb><rt>がんま</rt></ruby>}{\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c2})\times \mathcal{B}({\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c2}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi )=(0.91\pm 0.23\pm 0.12)\times {10}^{-6}$ and $\mathcal{B}({\mathrm{<ruby><rb>\chi </rb><rt>かい</rt></ruby>}}_{c2}\to \mathrm{<ruby><rb>\omega </rb><rt>おめが</rt></ruby>}\varphi )=(1.00\pm 0.25\pm 0.14)\times {10}^{-5}$. Here, the first errors are statistical and the second ones systematic.

• Received 23 October 2018

DOI:https://doi.org/10.1103/PhysRevD.99.012015

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