Charm-meson Triangle Singularity in $e^{+}{e}^{-}$ Annihilation into $D^{\ast 0}{\bar{D}}^0+\gamma$

Abstract

We calculate the cross section for $e^{+}{e}^{-}$ annihilation into $D^{\ast 0}{\bar{D}}^0+\gamma$ at center-of-mass energies near the $D^{\ast 0}{\bar{D}}^{\ast 0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm meson molecule. The Dalitz plot has a ${\bar{D}}^{\ast 0}$ resonance band in the squared invariant mass $t$ of ${\bar{D}}^0\gamma$. In the limit as the decay width of the $D^{\ast 0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of $D^{\ast 0}{\bar{D}}^0$ from a charm-meson triangle singularity. At the physical value of the $D^{\ast 0}$ 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.

Comments: 29 pages and 15 figures