## Three-particle systems with resonant subprocesses in a finite volume

## Abstract

In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 90, 116003 (2014); M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015); R. A. Briceño et al., Phys. Rev. D 95, 074510 (2017).]. Here we lift this restriction, by deriving the quantization condition for identical scalar particles with a G-parity symmetry, in the case that the two-particle K matrix has a pole in the kinematic regime of interest. Here, as in earlier work, our result involves intermediate infinite-volume quantities with no direct physical interpretation, and we show how these are related to the physical three-to-three scattering amplitude by integral equations. This work opens the door to study processes such as a _{2}→ρπ→πππ, in which the ρ is rigorously treated as a resonance state.

- Authors:

- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States). Dept. of Physics
- European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theoretical Physics Dept.
- Univ. of Washington, Seattle, WA (United States). Dept. of Physics

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1492914

- Alternate Identifier(s):
- OSTI ID: 1493163

- Report Number(s):
- JLAB-THY-18-2819; DOE/OR/-23177-4553; arXiv:1810.01429; CERN-TH-2018-216

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- SC0011637; AC05-06OR23177

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 1; 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; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

### Citation Formats

```
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R.. Three-particle systems with resonant subprocesses in a finite volume. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.99.014516.
```

```
Briceño, Raúl A., Hansen, Maxwell T., & Sharpe, Stephen R.. Three-particle systems with resonant subprocesses in a finite volume. United States. doi:10.1103/PhysRevD.99.014516.
```

```
Briceño, Raúl A., Hansen, Maxwell T., and Sharpe, Stephen R.. Wed .
"Three-particle systems with resonant subprocesses in a finite volume". United States. doi:10.1103/PhysRevD.99.014516.
```

```
@article{osti_1492914,
```

title = {Three-particle systems with resonant subprocesses in a finite volume},

author = {Briceño, Raúl A. and Hansen, Maxwell T. and Sharpe, Stephen R.},

abstractNote = {In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 90, 116003 (2014); M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015); R. A. Briceño et al., Phys. Rev. D 95, 074510 (2017).]. Here we lift this restriction, by deriving the quantization condition for identical scalar particles with a G-parity symmetry, in the case that the two-particle K matrix has a pole in the kinematic regime of interest. Here, as in earlier work, our result involves intermediate infinite-volume quantities with no direct physical interpretation, and we show how these are related to the physical three-to-three scattering amplitude by integral equations. This work opens the door to study processes such as a2→ρπ→πππ, in which the ρ is rigorously treated as a resonance state.},

doi = {10.1103/PhysRevD.99.014516},

journal = {Physical Review D},

number = 1,

volume = 99,

place = {United States},

year = {2019},

month = {1}

}

DOI: 10.1103/PhysRevD.99.014516