Search for $X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ at Belle

Abstract

We present a search for the decay $X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$ in the $(772\pm 11)\times 10^6$ $\hat{I}\yen (4S)\to B\bar{B}$ data sample collected at the Belle detector, where the $X(3872)$ is produced in $B^{\pm }\to K^{\pm }X(3872)$ and $B^0\to K_S^{0}X(3872)$ decays. We do not observe a signal, and set 90\% credible upper limits for two different models of the decay processes: if the decay products are distributed uniformly in phase space, $\mathcal{B}(X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)<1.3\%$; if $M(\ddot{I}{€}^{+}\ddot{I}{€}^{-})$ is concentrated near the mass of the $D^0{\bar{D}}^0$ pair in the process $X(3872)\to D^0{\bar{D}}^{\ast 0}+c.c.\to D^0{\bar{D}}^0\ddot{I}{€}^0\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0$, $\mathcal{B}(X(3872)\to \ddot{I}{€}^{+}\ddot{I}{€}^{-}\ddot{I}{€}^0)<1.2\times 10^{-3}$.