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

We present a search for the decay $X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^0$ in the $(772\pm 11)\times {10}^6$ $\mathrm{{\rm Y}}(4S)\to B\bar{B}$ 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, $\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^0)<1.3\mathrm{\%}$; if $M({\pi }^{+}{\pi }^{-})$ is concentrated near the mass of the $D^0{\bar{D}}^0$ pair in the process $X(3872)\to D^0{\bar{D}}^{\ast 0}+c\mathrm{.}c\mathrm{.}\to D^0{\bar{D}}^0{\pi }^0\to {\pi }^{+}{\pi }^{-}{\pi }^0$, $\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^0)<1.2\times {10}^{-3}$.