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Using a total of $9.0~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data withcenter-of-mass energies between 4.15 and 4.30 GeV collected by the BESIIIdetector, we search for the processes $e^+e^-\to \gamma X(3872)$ with$X(3872)\to\pi^0\chi_{cJ}$ for $J=0,1,2$. We report the first observation of$X(3872)\to\pi^{0}\chi_{c1}$, a new decay mode of the $X(3872)$, with astatistical significance of more than 5$\sigma$. Normalizing to the previouslyestablished process $e^+e^-\to \gamma X(3872)$ with$X(3872)\to\pi^+\pi^-J/\psi$, we find ${\cal B}(X(3872) \to \pi^0\chi_{c1})/{\cal B}(X(3872) \to \pi^+\pi^- J/\psi) =0.88^{+0.33}_{-0.27}\pm0.10$, where the first error is statistical and thesecond is systematic. We set 90% confidence level upper limits on thecorresponding ratios for the decays to $\pi^0\chi_{c0}$ and $\pi^0\chi_{c2}$ of19 and 1.1, respectively.

Observation of the decay $X(3872) \to \pi^0 \chi_{c1}(1P)$