# Estimates of the $X\left(3872\right)$ cross section at a hadron collider

## Abstract

The claim that the $X(3872)$ meson cannot be a charm-meson molecule because its prompt production cross section at hadron colliders is too large is based on an upper bound in terms of a cross section for producing charm-meson pairs. Assuming $$X$$ is sufficiently weakly bound, we derive an equality between the $$X$$ cross section and a charm-meson pair cross section that takes into account the threshold enhancement from the $$X$$ resonance. The cross section for producing $$X$$ is equal to that for producing $$D^{*0} \bar{D}^0$$ integrated up to a relative momentum $$k_\mathrm{max} = 7.7\,\gamma_X$$, where $$\gamma_X$$ is the binding momentum of $$X$$. We also derive an order-of-magnitude estimate of the $$X$$ cross section in terms of a naive charm-meson pair cross section that does not take into account the threshold enhancement, such as that produced by a Monte Carlo event generator. The cross section for producing $$X$$ can be approximated by the naive cross section for producing $$D^{*0} \bar{D}^0$$ integrated up to a relative momentum $$k_\mathrm{max}$$ of order $$(m_\pi^2 \gamma_X)^{1/3}$$. The estimates of the prompt $$X$$ cross section at hadron colliders are consistent with the cross sections observed at the Tevatron and the LHC.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

- OSTI Identifier:
- 1607574

- Alternate Identifier(s):
- OSTI ID: 1602459

- Grant/Contract Number:
- SC0011726; PHY-1607190

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 9; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

## Citation Formats

```
Braaten, Eric, He, Li-Ping, and Ingles, Kevin. Estimates of the X(3872) cross section at a hadron collider. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.094024.
```

```
Braaten, Eric, He, Li-Ping, & Ingles, Kevin. Estimates of the X(3872) cross section at a hadron collider. United States. https://doi.org/10.1103/PhysRevD.100.094024
```

```
Braaten, Eric, He, Li-Ping, and Ingles, Kevin. Fri .
"Estimates of the X(3872) cross section at a hadron collider". United States. https://doi.org/10.1103/PhysRevD.100.094024.
```

```
@article{osti_1607574,
```

title = {Estimates of the X(3872) cross section at a hadron collider},

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

abstractNote = {The claim that the $X(3872)$ meson cannot be a charm-meson molecule because its prompt production cross section at hadron colliders is too large is based on an upper bound in terms of a cross section for producing charm-meson pairs. Assuming $X$ is sufficiently weakly bound, we derive an equality between the $X$ cross section and a charm-meson pair cross section that takes into account the threshold enhancement from the $X$ resonance. The cross section for producing $X$ is equal to that for producing $D^{*0} \bar{D}^0$ integrated up to a relative momentum $k_\mathrm{max} = 7.7\,\gamma_X$, where $\gamma_X$ is the binding momentum of $X$. We also derive an order-of-magnitude estimate of the $X$ cross section in terms of a naive charm-meson pair cross section that does not take into account the threshold enhancement, such as that produced by a Monte Carlo event generator. The cross section for producing $X$ can be approximated by the naive cross section for producing $D^{*0} \bar{D}^0$ integrated up to a relative momentum $k_\mathrm{max}$ of order $(m_\pi^2 \gamma_X)^{1/3}$. The estimates of the prompt $X$ cross section at hadron colliders are consistent with the cross sections observed at the Tevatron and the LHC.},

doi = {10.1103/PhysRevD.100.094024},

journal = {Physical Review D},

number = 9,

volume = 100,

place = {United States},

year = {2019},

month = {11}

}

https://doi.org/10.1103/PhysRevD.100.094024

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