Revisiting $X(3872)\to D^0 \bar{D}^0 \pi^0$ in XEFT

TL;DR

This paper revisits the decay process of X(3872) into D0, anti-D0, and pi0 using effective field theory, analyzing how rescattering effects influence decay width and pion energy distribution, revealing insights into its molecular structure.

Contribution

It incorporates rescattering diagrams into the decay analysis and studies the pion energy distribution's shape and sensitivity to binding energy, providing new insights into the X(3872)'s nature.

Findings

Rescattering effects significantly affect decay width predictions.

Pion energy distribution shape is sensitive to binding energy.

Distribution shape can reveal the molecular nature of X(3872).

Abstract

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 $X(3872)$.