First evidence of $X(3872)\to\pi^0\chi_{c0}(1P)$ and search for $X(3915)\to\pi^0\chi_{c1}(1P)$

Abstract

We search for the pionic transitions $X(3872)\to\pi^0\chi_{cJ}(1P)$ $(J = 0,~1,~2)$ and $X(3915)\to\pi^0\chi_{c1}$ in $B^+\to \pi^0\chi_{cJ}K^+$ decays using the Belle and Belle~II data samples collected at the $\Upsilon(4S)$ resonance, corresponding to integrated luminosities of $711~\mathrm{fb}^{-1}$ and $492~\mathrm{fb}^{-1}$, respectively. We report the first evidence for the decay $X(3872)\to\pi^0\chi_{c0}$ with a significance of $3.4\sigma$, including systematic uncertainties. We measure the product of branching fractions ${\cal B}(B^+\to X(3872)K^+)\times{\cal B}(X(3872)\to\pi^0\chi_{c0})=(20.0\pm6.8\pm2.3)\times10^{-6}$ and the branching fraction ratio ${\cal B}(X(3872)\to\pi^0\chi_{c0})/{\cal B}(X(3872)\to\pi^+\pi^-J/\psi)=2.3\pm0.8\pm0.4$, where the first and second uncertainties are statistical and systematic, respectively. The upper limits at 90\% credibility on the products of branching fractions for the $\pi^0\chi_{c1}$ and $\pi^0\chi_{c2}$ modes are $7.5\times10^{-6}$ and $15.3\times10^{-6}$, respectively. The corresponding upper limits on the branching fraction ratios relative to the $\pi^+\pi^-J/\psi$ decay are $0.9$ and $1.8$. The measured branching fractions for $X(3872)\to\pi^0\chi_{cJ}$ are consistent with several theoretical predictions based on the hadronic molecular interpretation of the $X(3872)$. No significant signal is seen for the $X(3915)\to\pi^0\chi_{c1}$ decay, and we set the 90\% credibility upper limit of ${\cal B}(B^+\to X(3915)K^+)\times{\cal B}(X(3915)\to\pi^0\chi_{c1})<6.6\times10^{-6}$, while the decays for $J=0$ and 2 are forbidden by parity conservation.