# Stability of tetrons

## Abstract

We consider the interactions in a mesonic system, referred here to as ‘tetron’, consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally ${Q}_{a}{Q}_{b}{\overline{q}}_{c}{\overline{q}}_{d}$, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors ${N}_{c}$, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large ${N}_{c}$ limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable $bb\overline{u}\overline{d}$ tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of Minnesota, Minneapolis, MN (United States); Univ. of Alberta, Edmonton, AB (Canada)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Natural Sciences and Engineering Research Council of Canada (NSERC)

- OSTI Identifier:
- 1418381

- Alternate Identifier(s):
- OSTI ID: 1499155

- Grant/Contract Number:
- SC0011842

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 778 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Czarnecki, Andrzej, Leng, Bo, and Voloshin, M. B. Stability of tetrons. Netherlands: N. p., 2018.
Web. doi:10.1016/j.physletb.2018.01.034.
```

```
Czarnecki, Andrzej, Leng, Bo, & Voloshin, M. B. Stability of tetrons. Netherlands. doi:10.1016/j.physletb.2018.01.034.
```

```
Czarnecki, Andrzej, Leng, Bo, and Voloshin, M. B. Thu .
"Stability of tetrons". Netherlands. doi:10.1016/j.physletb.2018.01.034.
```

```
@article{osti_1418381,
```

title = {Stability of tetrons},

author = {Czarnecki, Andrzej and Leng, Bo and Voloshin, M. B.},

abstractNote = {We consider the interactions in a mesonic system, referred here to as ‘tetron’, consisting of two heavy quarks and two lighter antiquarks (which may still be heavy in the scale of QCD), i.e. generally QaQbq¯cq¯d, and study the existence of bound states below the threshold for decay into heavy meson pairs. At a small ratio of the lighter to heavier quark masses an expansion parameter arises for treatment of the binding in such systems. We find that in the limit where all the quarks and antiquarks are so heavy that a Coulomb-like approximation can be applied to the gluon exchange between all of them, such bound states arise when this parameter is below a certain critical value. We find the parametric dependence of the critical mass ratio on the number of colors Nc, and confirm this dependence by numerical calculations. In particular there are no stable tetrons when all constituents have the same mass. We discuss an application of a similar expansion in the large Nc limit to realistic systems where the antiquarks are light and their interactions are nonperturbative. In this case our findings are in agreement with the recent claims from a phenomenological analysis that a stable bbu¯d¯ tetron is likely to exist, unlike those where one or both bottom quarks are replaced by the charmed quark.},

doi = {10.1016/j.physletb.2018.01.034},

journal = {Physics Letters B},

number = C,

volume = 778,

place = {Netherlands},

year = {2018},

month = {3}

}

DOI: 10.1016/j.physletb.2018.01.034

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

_{c}= 3. The state with the symmetry w

_{++}(circles) is bound more strongly thanmore »

Works referencing / citing this record:

##
Mass spectrum of the hidden-charm pentaquarks in the compact diquark model

journal, October 2019

- Ali, Ahmed; Ahmed, Ishtiaq; Aslam, M. Jamil
- Journal of High Energy Physics, Vol. 2019, Issue 10

##
Mass spectrum of the hidden-charm pentaquarks in the compact diquark model

journal, October 2019

- Ali, Ahmed; Ahmed, Ishtiaq; Aslam, M. Jamil
- Journal of High Energy Physics, Vol. 2019, Issue 10

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*