First evidence of $X(3872)\to \ddot{I}{€}^0\ddot{I}{‡}_{c0}(1P)$ and search for $X(3915)\to \ddot{I}{€}^0\ddot{I}{‡}_{c1}(1P)$

Abstract

We search for the pionic transitions $X(3872)\to \ddot{I}{€}^0\ddot{I}{‡}_{cJ}(1P)$ $(J=0,1,2)$ and $X(3915)\to \ddot{I}{€}^0\ddot{I}{‡}_{c1}$ in $B^{+}\to \ddot{I}{€}^0\ddot{I}{‡}_{cJ}{K}^{+}$ decays using the Belle and Belle~II data samples collected at the $\hat{I}\yen (4S)$ resonance, corresponding to integrated luminosities of $711{\mathrm{fb}}^{-1}$ and $492{\mathrm{fb}}^{-1}$, respectively. We report the first evidence for the decay $X(3872)\to \ddot{I}{€}^0\ddot{I}{‡}_{c0}$ with a significance of $3.4\ddot{I}ƒ$, including systematic uncertainties. We measure the product of branching fractions $\mathcal{B}(B^{+}\to X(3872)K^{+})\times \mathcal{B}(X(3872)\to \ddot{I}{€}^0\ddot{I}{‡}_{c0})=(20.0\pm 6.8\pm 2.3)\times 10^{-6}$ and the branching fraction ratio $\mathcal{B}(X(3872)\to \ddot{I}{€}^0\ddot{I}{‡}_{c0})/\mathcal{B}(X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}J/\ddot{I}ˆ)=2.3\pm 0.8\pm 0.4$, 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 $\ddot{I}{€}^0\ddot{I}{‡}_{c1}$ and $\ddot{I}{€}^0\ddot{I}{‡}_{c2}$ modes are $7.5\times 10^{-6}$ and $15.3\times 10^{-6}$, respectively. The corresponding upper limits on the branching fraction ratios relative to the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}J/\ddot{I}ˆ$ decay are $0.9$ and $1.8$. The measured branching fractions for $X(3872)\to \ddot{I}{€}^0\ddot{I}{‡}_{cJ}$ are consistent with several theoretical predictions based on the hadronic molecular interpretation of the $X(3872)$. No significant signal is seen for the $X(3915)\to \ddot{I}{€}^0\ddot{I}{‡}_{c1}$ decay, and we set the 90\% credibility upper limit of $\mathcal{B}(B^{+}\to X(3915)K^{+})\times \mathcal{B}(X(3915)\to \ddot{I}{€}^0\ddot{I}{‡}_{c1})<6.6\times 10^{-6}$, while the decays for $J=0$ and 2 are forbidden by parity conservation.

9 pages, 2 figures