Triangle Singularity in the Production of $X(3872)$ and a Photon in $e^{+}{e}^{-}$ Annihilation

Abstract

If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^{+}{e}^{-}$ annihilation by the creation of $D^{\ast 0}{\bar{D}}^{\ast 0}$ from a virtual photon followed by the rescattering of the charm-meson pair into $X$ 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 $D^{\ast 0}{\bar{D}}^{\ast 0}$ threshold. We predict the normalized cross section in the region near the peak. The peak from the triangle singularity may be observable by the BESIII detector.

Comments: 5 pages, 3 figures, published in Phys. Rev. D as Rapid Communication