# Charm-meson triangle singularity in ${e}^{+}{e}^{-}$ annihilation into ${D}^{*0}{\overline{D}}^{0}+\gamma $

## Abstract

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

- Authors:

- Publication Date:

- Research Org.:
- The Ohio State Univ., Columbus, OH (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); Natural Science Foundation of Shandong Province; Fundamental Research Funds of Shandong University

- OSTI Identifier:
- 1631077

- Alternate Identifier(s):
- OSTI ID: 1782849

- Grant/Contract Number:
- SC0011726; ZR2019QA012

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 101 Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Braaten, Eric, He, Li-Ping, Ingles, Kevin, and Jiang, Jun. Charm-meson triangle singularity in e + e − annihilation into D * 0 D ¯ 0 + γ. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.096020.
```

```
Braaten, Eric, He, Li-Ping, Ingles, Kevin, & Jiang, Jun. Charm-meson triangle singularity in e + e − annihilation into D * 0 D ¯ 0 + γ. United States. https://doi.org/10.1103/PhysRevD.101.096020
```

```
Braaten, Eric, He, Li-Ping, Ingles, Kevin, and Jiang, Jun. Thu .
"Charm-meson triangle singularity in e + e − annihilation into D * 0 D ¯ 0 + γ". United States. https://doi.org/10.1103/PhysRevD.101.096020.
```

```
@article{osti_1631077,
```

title = {Charm-meson triangle singularity in e + e − annihilation into D * 0 D ¯ 0 + γ},

author = {Braaten, Eric and He, Li-Ping and Ingles, Kevin and Jiang, Jun},

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

doi = {10.1103/PhysRevD.101.096020},

journal = {Physical Review D},

number = 9,

volume = 101,

place = {United States},

year = {2020},

month = {5}

}

https://doi.org/10.1103/PhysRevD.101.096020

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