Using $9.9{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected by the BESIII detector at center-of-mass energies between 4.15 and 4.30 GeV, we search for the processes $e^{+}{e}^{-}\to \gamma X(3872)$ with $X(3872)\to {\pi }^0{\chi }_{c0}$ and $X(3872)\to \pi \pi {\chi }_{c0}$. We set upper limits (at 90% C.L.) of $\frac{\mathcal{B}(X(3872)\to {\pi }^0{\chi }_{c0})}{\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )}<3.6$, $\frac{\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}{\chi }_{c0})}{\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )}<0.56$, and $\frac{\mathcal{B}(X(3872)\to {\pi }^0{\pi }^0{\chi }_{c0})}{\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )}<1.7$. Combined with the BESIII measurement of $X(3872)\to {\pi }^0{\chi }_{c1}$, we also set an upper limit of $\frac{\mathcal{B}(X(3872)\to {\pi }^0{\chi }_{c0})}{\mathcal{B}(X(3872)\to {\pi }^0{\chi }_{c1})}<4.5$.

• Received 2 February 2022
• Accepted 8 April 2022

DOI:https://doi.org/10.1103/PhysRevD.105.072009

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Published by the American Physical Society