# Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states

## Abstract

Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide nontrivial checks on the final results and also to explore limiting cases in which more straightforward predictions may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron’s scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite series of leading volume corrections, ismore »

- 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.

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1577391

- Alternate Identifier(s):
- OSTI ID: 1577432

- Report Number(s):
- JLAB-THY-19-3040; DOE/OR/23177-4782; arXiv:1909.10357

Journal ID: ISSN 2470-0010; PRVDAQ

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

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 11; 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

### Citation Formats

```
Briceño, Raúl A., Hansen, Maxwell T., and Jackura, Andrew W. Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states. United States: N. p., 2019.
Web. doi:10.1103/PhysRevD.100.114505.
```

```
Briceño, Raúl A., Hansen, Maxwell T., & Jackura, Andrew W. Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states. United States. doi:10.1103/PhysRevD.100.114505.
```

```
Briceño, Raúl A., Hansen, Maxwell T., and Jackura, Andrew W. Fri .
"Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states". United States. doi:10.1103/PhysRevD.100.114505.
```

```
@article{osti_1577391,
```

title = {Consistency checks for two-body finite-volume matrix elements: Conserved currents and bound states},

author = {Briceño, Raúl A. and Hansen, Maxwell T. and Jackura, Andrew W.},

abstractNote = {Recently, a framework has been developed to study form factors of two-hadron states probed by an external current. The method is based on relating finite-volume matrix elements, computed using numerical lattice QCD, to the corresponding infinite-volume observables. As the formalism is complicated, it is important to provide nontrivial checks on the final results and also to explore limiting cases in which more straightforward predictions may be extracted. In this work we provide examples on both fronts. First, we show that, in the case of a conserved vector current, the formalism ensures that the finite-volume matrix element of the conserved charge is volume independent and equal to the total charge of the two-particle state. Second, we study the implications for a two-particle bound state. We demonstrate that the infinite-volume limit reproduces the expected matrix element and derive the leading finite-volume corrections to this result for a scalar current. Finally, we provide numerical estimates for the expected size of volume effects in future lattice QCD calculations of the deuteron’s scalar charge. We find that these effects completely dominate the infinite-volume result for realistic lattice volumes and that applying the present formalism, to analytically remove an infinite series of leading volume corrections, is crucial to reliably extract the infinite-volume charge of the state.},

doi = {10.1103/PhysRevD.100.114505},

journal = {Physical Review D},

number = 11,

volume = 100,

place = {United States},

year = {2019},

month = {12}

}

DOI: 10.1103/PhysRevD.100.114505

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