# Relativistic, model-independent, multichannel $2\to 2$ transition amplitudes in a finite volume

## Abstract

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $$\rho$$-meson form factor, in which the unstable nature of the $$\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.

- Authors:

- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Johannes Gutenberg-Univ. Mainz, Mainz (Germany)

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1262312

- Alternate Identifier(s):
- OSTI ID: 1262447

- Report Number(s):
- JLAB-THY-15-2140; DOE/OR/23177-3556; arXiv:1509.08507

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 94; 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; finite volume

### Citation Formats

```
Briceno, Raul A., and Hansen, Maxwell T.
```*Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume*. United States: N. p., 2016.
Web. doi:10.1103/PhysRevD.94.013008.

```
Briceno, Raul A., & Hansen, Maxwell T.
```*Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume*. United States. doi:10.1103/PhysRevD.94.013008.

```
Briceno, Raul A., and Hansen, Maxwell T. Wed .
"Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume". United States. doi:10.1103/PhysRevD.94.013008. https://www.osti.gov/servlets/purl/1262312.
```

```
@article{osti_1262312,
```

title = {Relativistic, model-independent, multichannel 2→2 transition amplitudes in a finite volume},

author = {Briceno, Raul A. and Hansen, Maxwell T.},

abstractNote = {We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of the $\rho$-meson form factor, in which the unstable nature of the $\rho$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.},

doi = {10.1103/PhysRevD.94.013008},

journal = {Physical Review D},

issn = {2470-0010},

number = 1,

volume = 94,

place = {United States},

year = {2016},

month = {7}

}

*Citation information provided by*

Web of Science

Web of Science