# 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. https://doi.org/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

Works referenced in this record:

##
Multiquark States

journal, October 2018

- Karliner, Marek; Rosner, Jonathan L.; Skwarnicki, Tomasz
- Annual Review of Nuclear and Particle Science, Vol. 68, Issue 1

##
Hadronic molecules

journal, February 2018

- Guo, Feng-Kun; Hanhart, Christoph; Meißner, Ulf-G.
- Reviews of Modern Physics, Vol. 90, Issue 1

##
Nonstandard heavy mesons and baryons: Experimental evidence

journal, February 2018

- Olsen, Stephen Lars; Skwarnicki, Tomasz; Zieminska, Daria
- Reviews of Modern Physics, Vol. 90, Issue 1

##
Bounds on the width, mass difference and other properties of $X(3872)\to {\pi}^{+}{\pi}^{-}J/\psi $ decays

journal, September 2011

- Choi, S. -K.; Olsen, S. L.; Trabelsi, K.
- Physical Review D, Vol. 84, Issue 5

##
Production of the bottom analogs and the spin partner of the X(3872) at hadron colliders

journal, September 2014

- Guo, Feng-Kun; Meißner, Ulf-G.; Wang, Wei
- The European Physical Journal C, Vol. 74, Issue 9

##
Observation of a Narrow Charmoniumlike State in Exclusive ${B}^{\pm}\to {K}^{\pm}{\pi}^{+}{\pi}^{-}J/\psi $ Decays

journal, December 2003

- Choi, S. -K.; Olsen, S. L.; Abe, K.
- Physical Review Letters, Vol. 91, Issue 26

##
Universality in few-body systems with large scattering length

journal, June 2006

- Braaten, Eric; Hammer, H. -W.
- Physics Reports, Vol. 428, Issue 5-6

##
Measurements of ψ(2S) and X(3872) → J/ψπ + π − production in pp collisions at s = 8 $$ \sqrt{s}=8 $$ TeV with the ATLAS detector

journal, January 2017

- Aaboud, M.; Aad, G.; Abbott, B.
- Journal of High Energy Physics, Vol. 2017, Issue 1

##
The X(3872) Meson and "Exotic" Spectroscopy at cdf ii — or not? —

journal, February 2006

- Bauer, G.
- International Journal of Modern Physics A, Vol. 21, Issue 05

##
Comment on ‘Note on *X* (3872) production at hadron colliders and its molecular structure’

journal, October 2018

- Esposito, A.; Grinstein, B.; Maiani, L.
- Chinese Physics C, Vol. 42, Issue 11

##
Review of Particle Physics

journal, August 2018

- Tanabashi, M.; Hagiwara, K.; Hikasa, K.
- Physical Review D, Vol. 98, Issue 3

##
Measurement of the X(3872) production cross section via decays to J/ψπ + π − in pp collisions at $ \sqrt{s}=7 $ TeV

journal, April 2013

- Chatrchyan, S.; Khachatryan, V.; Sirunyan, A. M.
- Journal of High Energy Physics, Vol. 2013, Issue 4

##
Observation of the Narrow State $X\left(3872\right)\to J/\psi {\pi}^{+}{\pi}^{-}$ in $\overline{p}p$ Collisions at $\sqrt{s}=1.96\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{T}\mathrm{e}\mathrm{V}$

journal, August 2004

- Acosta, D.; Affolder, T.; Ahn, M. H.
- Physical Review Letters, Vol. 93, Issue 7

##
Exotics: Heavy pentaquarks and tetraquarks

journal, November 2017

- Ali, Ahmed; Lange, Jens Sören; Stone, Sheldon
- Progress in Particle and Nuclear Physics, Vol. 97

##
Note on *X* (3872) production at hadron colliders and its molecular structure

journal, November 2017

- Albaladejo, Miguel; Guo, Feng-Kun; Hanhart, Christoph
- Chinese Physics C, Vol. 41, Issue 12

##
Observation of X(3872) production in pp collisions at $\sqrt{s}=7\mbox{~TeV}$

journal, May 2012

- Aaij, R.; Abellan Beteta, C.; Adeva, B.
- The European Physical Journal C, Vol. 72, Issue 5

##
Determination of the $X(3872)$ Meson Quantum Numbers

journal, May 2013

- Aaij, R.; Abellan Beteta, C.; Adeva, B.
- Physical Review Letters, Vol. 110, Issue 22

##
Is the $X(3872)$ Production Cross Section at $\sqrt{s}\mathbf{=}1.96\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{TeV}$ Compatible with a Hadron Molecule Interpretation?

journal, October 2009

- Bignamini, C.; Grinstein, B.; Piccinini, F.
- Physical Review Letters, Vol. 103, Issue 16

##
Bound state and continuum production in large momentum transfer reactions

journal, August 1996

- Fäldt, Göran; Wilkin, Colin
- Physics Letters B, Vol. 382, Issue 3

##
Observation of a Near-Threshold ${D}^{0}{\overline{D}}^{0}{\pi}^{0}$ Enhancement in $B\to {D}^{0}{\overline{D}}^{0}{\pi}^{0}K$ Decay

journal, October 2006

- Gokhroo, G.; Majumder, G.; Abe, K.
- Physical Review Letters, Vol. 97, Issue 16

##
Heavy-quark QCD exotica

journal, March 2017

- Lebed, Richard F.; Mitchell, Ryan E.; Swanson, Eric S.
- Progress in Particle and Nuclear Physics, Vol. 93

##
Multiquark resonances

journal, January 2017

- Esposito, A.; Pilloni, A.; Polosa, A. D.
- Physics Reports, Vol. 668

##
Exotic hadrons with heavy flavors: *X* , *Y* , *Z* , and related states

journal, June 2016

- Hosaka, Atsushi; Iijima, Toru; Miyabayashi, Kenkichi
- Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 6

##
The hidden-charm pentaquark and tetraquark states

journal, June 2016

- Chen, Hua-Xing; Chen, Wei; Liu, Xiang
- Physics Reports, Vol. 639

##
Production of the $X(3872)$ at the Tevatron and the LHC

journal, June 2010

- Artoisenet, Pierre; Braaten, Eric
- Physical Review D, Vol. 81, Issue 11

##
Observation and Properties of the $X(3872)$ Decaying to $J/\psi {\pi}^{+}{\pi}^{-}$ in $p\overline{p}$ Collisions at $\sqrt{s}=1.96\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{T}\mathrm{e}\mathrm{V}$

journal, October 2004

- Abazov, V. M.; Abbott, B.; Abolins, M.
- Physical Review Letters, Vol. 93, Issue 16

##
The *XYZ* states revisited

journal, July 2018

- Yuan, Chang-Zheng
- International Journal of Modern Physics A, Vol. 33, Issue 21

##
Exotics: Heavy pentaquarks and tetraquarks

text, January 2017

- Ali, Ahmed; Lange, Jens Sören; Stone, Sheldon
- Deutsches Elektronen-Synchrotron, DESY, Hamburg