## Yukawa bound states of a large number of fermions

## Abstract

Here, we consider the bound state problem for a field theory that contains a Dirac fermion χ that Yukawa couples to a (light) scalar field Φ. We are interested in bound states with a large number N of χ particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic χ’s are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic χ particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and χ mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such χ particles.

- Authors:

- California Inst. of Technology, Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics

- Publication Date:

- Research Org.:
- California Inst. of Technology, Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1455179

- Grant/Contract Number:
- SC0011632; SC0010255

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTRONOMY AND ASTROPHYSICS; Beyond Standard Model; Cosmology of Theories beyond the SM; Statistical Methods

### Citation Formats

```
Wise, Mark B., and Zhang, Yue. Yukawa bound states of a large number of fermions. United States: N. p., 2015.
Web. doi:10.1007/JHEP02(2015)023.
```

```
Wise, Mark B., & Zhang, Yue. Yukawa bound states of a large number of fermions. United States. doi:10.1007/JHEP02(2015)023.
```

```
Wise, Mark B., and Zhang, Yue. Tue .
"Yukawa bound states of a large number of fermions". United States. doi:10.1007/JHEP02(2015)023. https://www.osti.gov/servlets/purl/1455179.
```

```
@article{osti_1455179,
```

title = {Yukawa bound states of a large number of fermions},

author = {Wise, Mark B. and Zhang, Yue},

abstractNote = {Here, we consider the bound state problem for a field theory that contains a Dirac fermion χ that Yukawa couples to a (light) scalar field Φ. We are interested in bound states with a large number N of χ particles. A Fermi gas model is used to numerically determine the dependence of the radius R of these bound states on N and also the dependence of the binding energy on N. Since scalar interactions with relativistic χ’s are suppressed two regimes emerge. For modest values of N the state is composed of non-relativistic χ particles. In this regime as N increases R decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as N increases. As a result, for fixed Yukawa coupling and χ mass, there is a minimum sized state that occurs roughly at the value of N where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such χ particles.},

doi = {10.1007/JHEP02(2015)023},

journal = {Journal of High Energy Physics (Online)},

number = 2,

volume = 2015,

place = {United States},

year = {2015},

month = {2}

}

*Citation information provided by*

Web of Science

Web of Science