# Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions

## Abstract

A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime, and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly-coupled intermediate channels are included. These channels can consist of non-identical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as non-zero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al.~[Phys.Rev. D91 114510 (2015)], and extends the reach of lattice quantum chromodynamics (QCD) to a wide class of new observables beyond meson mixing and rare decays. Applications include Compton scattering of the pion ($$\pi \gamma^\star \to [\pi \pi, K \overline K] \to \pi \gamma^\star$$), kaon ($$K \gamma^\star \to [\pi K, \eta K] \to K \gamma^\star$$) and nucleon ($$N \gamma^\star \to N \pi \to N \gamma^\star$$), as well as double-$$\beta$$ decays, and radiative corrections to the single-$$\beta$$ decay, of QCD-stable hadrons. The framework presented will further facilitate generalization of the result to studies of nuclear amplitudes involving two currents from lattice QCD.

- Authors:

- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Old Dominion Univ., Norfolk, VA (United States)
- Univ. of Maryland, College Park, MD (United States); Inst. of Physical and Chemical Research (RIKEN), Wako (Japan)
- European Organization for Nuclear Research (CERN), Geneva (Switzerland)
- Univ. of South Carolina, Columbia, SC (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of South Carolina, Columbia, SC (United States)

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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

- OSTI Identifier:
- 1596393

- Alternate Identifier(s):
- OSTI ID: 1596629

- Report Number(s):
- JLAB-THY-19-3051; DOE/OR/23177-4779; arXiv:1911.04036; CERN-TH-2019-189; UMD-PP-019-06

Journal ID: ISSN 2470-0010; PRVDAQ

- Grant/Contract Number:
- AC05-06OR23177; de-sc0019229; SC0019647; AC52-06NA25396

- Resource Type:
- Published Article

- Journal Name:
- Physical Review D

- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 1; Journal ID: ISSN 2470-0010

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Briceno, Raul A., Davoudi, Zohreh, Hansen, Maxwell T., Schindler, Matthias R., and Baroni, Alessandro. Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions. United States: N. p., 2020.
Web. doi:10.1103/PhysRevD.101.014509.
```

```
Briceno, Raul A., Davoudi, Zohreh, Hansen, Maxwell T., Schindler, Matthias R., & Baroni, Alessandro. Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions. United States. doi:10.1103/PhysRevD.101.014509.
```

```
Briceno, Raul A., Davoudi, Zohreh, Hansen, Maxwell T., Schindler, Matthias R., and Baroni, Alessandro. Wed .
"Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions". United States. doi:10.1103/PhysRevD.101.014509.
```

```
@article{osti_1596393,
```

title = {Long-range electroweak amplitudes of single hadrons from Euclidean finite-volume correlation functions},

author = {Briceno, Raul A. and Davoudi, Zohreh and Hansen, Maxwell T. and Schindler, Matthias R. and Baroni, Alessandro},

abstractNote = {A relation is presented between single-hadron long-range matrix elements defined in a finite Euclidean spacetime, and the corresponding infinite-volume Minkowski amplitudes. This relation is valid in the kinematic region where any number of two-hadron states can simultaneously go on shell, so that the effects of strongly-coupled intermediate channels are included. These channels can consist of non-identical particles with arbitrary intrinsic spins. The result accommodates general Lorentz structures as well as non-zero momentum transfer for the two external currents inserted between the single-hadron states. The formalism, therefore, generalizes the work by Christ et al.~[Phys.Rev. D91 114510 (2015)], and extends the reach of lattice quantum chromodynamics (QCD) to a wide class of new observables beyond meson mixing and rare decays. Applications include Compton scattering of the pion ($\pi \gamma^\star \to [\pi \pi, K \overline K] \to \pi \gamma^\star$), kaon ($K \gamma^\star \to [\pi K, \eta K] \to K \gamma^\star$) and nucleon ($N \gamma^\star \to N \pi \to N \gamma^\star$), as well as double-$\beta$ decays, and radiative corrections to the single-$\beta$ decay, of QCD-stable hadrons. The framework presented will further facilitate generalization of the result to studies of nuclear amplitudes involving two currents from lattice QCD.},

doi = {10.1103/PhysRevD.101.014509},

journal = {Physical Review D},

number = 1,

volume = 101,

place = {United States},

year = {2020},

month = {1}

}

DOI: 10.1103/PhysRevD.101.014509

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