## Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD

## Abstract

We present the first determination of ρπ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 ρπ, we calculate partial-wave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and D-wave channels with J ^{P} = 1 ^{+}. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that m _{π} ~700 MeV, ensuring that the ρ is stable against strong decay. Furthermore, this work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.

- Authors:

- Univ. of Cambridge, Cambridge (United Kingdom)
- College of William and Mary, Williamsburg, VA (United States); Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
- Trinity College, Dublin (Ireland)

- 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) (SC-26)

- Contributing Org.:
- for the Hadron Spectrum collaboration

- OSTI Identifier:
- 1462038

- Report Number(s):
- JLAB-THY-18-2643; DOE/OR/23177-4345; arXiv:1802.05580; DAMTP-2018-6

Journal ID: ISSN 1029-8479; PII: 8577; TRN: US1902093

- Grant/Contract Number:
- AC05-06OR23177

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Lattice field theory simulation; QCD Phenomenology

### Citation Formats

```
Woss, Antoni J., Thomas, Christopher E., Dudek, Jozef J., Edwards, Robert G., and Wilson, David J. Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD. United States: N. p., 2018.
Web. doi:10.1007/JHEP07(2018)043.
```

```
Woss, Antoni J., Thomas, Christopher E., Dudek, Jozef J., Edwards, Robert G., & Wilson, David J. Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD. United States. doi:10.1007/JHEP07(2018)043.
```

```
Woss, Antoni J., Thomas, Christopher E., Dudek, Jozef J., Edwards, Robert G., and Wilson, David J. Fri .
"Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD". United States. doi:10.1007/JHEP07(2018)043. https://www.osti.gov/servlets/purl/1462038.
```

```
@article{osti_1462038,
```

title = {Dynamically-coupled partial-waves in ρπ isospin-2 scattering from lattice QCD},

author = {Woss, Antoni J. and Thomas, Christopher E. and Dudek, Jozef J. and Edwards, Robert G. and Wilson, David J.},

abstractNote = {We present the first determination of ρπ scattering, incorporating dynamically-coupled partial-waves, using lattice QCD, a first-principles numerical approach to QCD. Considering the case of isospin-2 ρπ, we calculate partial-wave amplitudes with J ≤ 3 and determine the degree of dynamical mixing between the coupled S and D-wave channels with JP = 1+. The analysis makes use of the relationship between scattering amplitudes and the discrete spectrum of states in the finite volume lattice. Constraints on the scattering amplitudes are provided by over one hundred energy levels computed on two lattice volumes at various overall momenta and in several irreducible representations of the relevant symmetry groups. The spectra follow from variational analyses of matrices of correlations functions computed with large bases of meson-meson operators. Calculations are performed with degenerate light and strange quarks tuned to the physical strange quark mass so that mπ ~700 MeV, ensuring that the ρ is stable against strong decay. Furthermore, this work demonstrates the successful application of techniques, opening the door to calculations of scattering processes that incorporate the effects of dynamically-coupled partial-waves, including those involving resonances or bound states.},

doi = {10.1007/JHEP07(2018)043},

journal = {Journal of High Energy Physics (Online)},

number = 7,

volume = 2018,

place = {United States},

year = {2018},

month = {7}

}

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Works referenced in this record:

##
Three-particle quantization condition in a finite volume: 2. General formalism and the analysis of data

journal, October 2017

- Hammer, Hans-Werner; Pang, Jin-Yi; Rusetsky, Akaki
- Journal of High Energy Physics, Vol. 2017, Issue 10, 31 p.