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 P-wave charm-meson pair into the $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^{+}{e}^{-}\to X\gamma$ 2.2 MeV above the $D^{\ast 0}{\bar{D}}^{\ast 0}$ threshold. We predict the normalized cross section in the region of the peak. We show that the absorptive contribution to the cross section for $e^{+}{e}^{-}\to D^{\ast 0}{\bar{D}}^{\ast 0}\to X\gamma$, which was calculated previously by Dubynskiy and Voloshin, does not give a good approximation to the peak from the triangle singularity.

Comments: 26 pages, 11 figures. arXiv admin note: text overlap with arXiv:1904.12915