# Quark-Mass Dependence of Elastic $πK$ Scattering from QCD

## Abstract

We present a determination of the isospin-½ elastic $πK$ scattering amplitudes in $S$ and $P$ partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the $P$-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the $S$-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $$κ/K_{0}^{*}$$(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP); Royal Society–Science Foundation Ireland University; Science and Technology Facilities Council (STFC); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); National Science Foundation (NSF); State of Illinois

- Contributing Org.:
- Hadron Spectrum Collaboration

- OSTI Identifier:
- 1545442

- Alternate Identifier(s):
- OSTI ID: 1608409

- Report Number(s):
- JLAB-THY-19-2911; DOE/OR/23177-4665; arXiv:1904.03188

Journal ID: ISSN 0031-9007; PRLTAO; 042002

- Grant/Contract Number:
- AC05-06OR23177; SC0019229; SC0018416; AC05-00OR22725; AC02-05CH11231; UF160419; ST/P000681/1; OCI-0725070; ACI-1238993

- Resource Type:
- Published Article

- Journal Name:
- Physical Review Letters

- Additional Journal Information:
- Journal Name: Physical Review Letters Journal Volume: 123 Journal Issue: 4; Journal ID: ISSN 0031-9007

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Wilson, David J., Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Thomas, Christopher E., and for the Hadron Spectrum Collaboration. Quark-Mass Dependence of Elastic $πK$ Scattering from QCD. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.123.042002.
```

```
Wilson, David J., Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Thomas, Christopher E., & for the Hadron Spectrum Collaboration. Quark-Mass Dependence of Elastic $πK$ Scattering from QCD. United States. doi:https://doi.org/10.1103/PhysRevLett.123.042002
```

```
Wilson, David J., Briceño, Raúl A., Dudek, Jozef J., Edwards, Robert G., Thomas, Christopher E., and for the Hadron Spectrum Collaboration. Wed .
"Quark-Mass Dependence of Elastic $πK$ Scattering from QCD". United States. doi:https://doi.org/10.1103/PhysRevLett.123.042002.
```

```
@article{osti_1545442,
```

title = {Quark-Mass Dependence of Elastic $πK$ Scattering from QCD},

author = {Wilson, David J. and Briceño, Raúl A. and Dudek, Jozef J. and Edwards, Robert G. and Thomas, Christopher E. and for the Hadron Spectrum Collaboration},

abstractNote = {We present a determination of the isospin-½ elastic $πK$ scattering amplitudes in $S$ and $P$ partial waves using lattice quantum chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV, at a single lattice spacing. Below the first inelastic threshold, the $P$-wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the $S$-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a $κ/K_{0}^{*}$(700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.},

doi = {10.1103/PhysRevLett.123.042002},

journal = {Physical Review Letters},

number = 4,

volume = 123,

place = {United States},

year = {2019},

month = {7}

}

DOI: https://doi.org/10.1103/PhysRevLett.123.042002

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