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.

29 pages and 15 figures

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• Fully charmed tetraquarks from LHC to FCC: Natural stability from fragmentation
• Hadronic decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Bottomoniumlike states in proton collisions: Fragmentation and resummation
• Exotic tetraquarks at the HL-LHC with JETHAD: A high-energy viewpoint
• Possible precise measurements of the $X(3872)$ mass with the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ reactions
• Fragmentation of fully heavy tetraquarks: The TQ4Q1.1 functions as a case study
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• The role of triangle singularity in isospin breaking process $J/\psi \to \Lambda \bar{\Lambda }\pi$ and the possible evidence of ${\Sigma }^{\ast }({\frac{1}{2}}^{-})$ states
• Study of $e^{+}{e}^{-}\to \omega X(3872)$ and $\gamma X(3872)$ from 4.66 to 4.95 GeV
• Tetraquark-Jet Systems at the High-Luminosity LHC
• All-charm tetraquarks at hadron colliders: A high-precision fragmentation perspective