  The calculation of the decay $X(3872)\to D^0 \bar{D}^0 \pi^0$ in effective
field theory is revisited to include final state $\pi^0 D^0$, $\pi^0
\bar{D}^0$and $D^0\bar{D}^0$ rescattering diagrams. These introduce significant
uncertainty into the prediction for the partial width as a function of the
binding energy. The differential distribution in the pion energy is also
studied for the first time. The normalization of the distribution is again
quite uncertain due to higher order effects but the shape of the distribution
is unaffected by higher order corrections. Furthermore the shape of the
distribution and the location of the peak are sensitive to the binding energy
of $X(3872)$. The shape is strongly impacted by the presence of virtual
$D^{*0}$ graphs which highlights the molecular nature of the $X(3872)$.
  Measurement of the pion energy distribution in the decay $X(3872)\to D^0
\bar{D}^0 \pi^0$ can reveal interesting information about the binding nature of
the $X(3872)$.
