We calculate the cross section for $e^{+}{e}^{-}$ annihilation into $D^{*0}{\overline{D}}^0+\gamma$ at center-of-mass energies near the $D^{*0}{\overline{D}}^{*0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm-meson molecule. The Dalitz plot has a ${\overline{D}}^{*0}$ resonance band in the squared invariant mass $t$ of ${\overline{D}}^0\gamma$. In the limit as the decay width of the $D^{*0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of $D^{*0}{\overline{D}}^0$ from a charm-meson triangle singularity. At the physical value of the $D^{*0}$ width, the narrow band reduces to a shoulder. Thus, the triangle singularity cannot be observed directly as a peak in a differential cross section as a function of $u$. It may however be observed indirectly as a local minimum in the $t$ distribution for events with $u$ below the triangle singularity. The minimum is produced by the Schmid cancellation between triangle loop diagrams and a tree diagram. The observation of this minimum would support the identification of $X(3872)$ as a weakly bound charm-meson molecule.

• Received 27 April 2020
• Accepted 18 May 2020

DOI:https://doi.org/10.1103/PhysRevD.101.096020

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society