# Form factors of two-hadron states from a covariant finite-volume formalism

## Abstract

Here we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $$\textbf 2 + \mathcal J \to \textbf 2$$ transition amplitudes. Furthermore, we give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $$\mathcal J$$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $G$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $$\pi \pi + \mathcal J \to \pi \pi$$ amplitude in the $$\rho$$ channel, for which the single-pion form factor, $$F_\pi(Q^2)$$, as well as the scattering phase, $$\delta_{\pi\pi}$$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 1557352

- Alternate Identifier(s):
- OSTI ID: 1557629

- Report Number(s):
- JLAB-THY-18-2878; DOE/OR/-23177-4598; arXiv:1812.10504

Journal ID: ISSN 2470-0010; PRVDAQ; 034511

- Grant/Contract Number:
- AC05-06OR23177; SC0019229; SC0010300

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 100 Journal Issue: 3; Journal ID: ISSN 2470-0010

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., and Ortega-Gama, Felipe G. Form factors of two-hadron states from a covariant finite-volume formalism. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.034511.
```

```
Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., & Ortega-Gama, Felipe G. Form factors of two-hadron states from a covariant finite-volume formalism. United States. doi:10.1103/PhysRevD.100.034511.
```

```
Baroni, Alessandro, Briceño, Raúl A., Hansen, Maxwell T., and Ortega-Gama, Felipe G. Thu .
"Form factors of two-hadron states from a covariant finite-volume formalism". United States. doi:10.1103/PhysRevD.100.034511.
```

```
@article{osti_1557352,
```

title = {Form factors of two-hadron states from a covariant finite-volume formalism},

author = {Baroni, Alessandro and Briceño, Raúl A. and Hansen, Maxwell T. and Ortega-Gama, Felipe G.},

abstractNote = {Here we develop a Lorentz-covariant version of the previously derived formalism for relating finite-volume matrix elements to $\textbf 2 + \mathcal J \to \textbf 2$ transition amplitudes. Furthermore, we give various details relevant for the implementation of this formalism in a realistic numerical lattice QCD calculation. Particular focus is given to the role of single-particle form factors in disentangling finite-volume effects from the triangle diagram that arise when $\mathcal J$ couples to one of the two hadrons. This also leads to a new finite-volume function, denoted $G$, the numerical evaluation of which is described in detail. As an example we discuss the determination of the $\pi \pi + \mathcal J \to \pi \pi$ amplitude in the $\rho$ channel, for which the single-pion form factor, $F_\pi(Q^2)$, as well as the scattering phase, $\delta_{\pi\pi}$, are required to remove all power-law finite-volume effects. The formalism presented here holds for local currents with arbitrary Lorentz structure, and we give specific examples of insertions with up to two Lorentz indices.},

doi = {10.1103/PhysRevD.100.034511},

journal = {Physical Review D},

number = 3,

volume = 100,

place = {United States},

year = {2019},

month = {8}

}

DOI: 10.1103/PhysRevD.100.034511

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