If $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^{+}{e}^{-}$ annihilation by the creation of $D^{*0}{\overline{D}}^{*0}$ from a virtual photon followed by the rescattering of the $P$-wave charm-meson pair into the $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^{+}{e}^{-}\to X\gamma$ about 2.2 MeV above the $D^{*0}{\overline{D}}^{*0}$ threshold. We predict the normalized cross section in the region of the peak. We show that the absorptive contribution to the cross section for $e^{+}{e}^{-}\to D^{*0}{\overline{D}}^{*0}\to X\gamma$, which was calculated previously by Dubynskiy and Voloshin, does not give a good approximation to the peak from the triangle singularity.

• Received 17 September 2019

DOI:https://doi.org/10.1103/PhysRevD.101.014021

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Published by the American Physical Society