- Open Access
Coupled-channel scattering of , , and in isospin-1 from lattice QCD
Phys. Rev. D 112, 114511 – Published 22 December, 2025
DOI: https://doi.org/10.1103/xz5r-p533
Abstract
The first coupled-channel determination of two-body and scattering amplitudes in isospin-1 from lattice quantum chromodynamics (QCD) is presented. Using three lattice volumes at , finite-volume energies relevant for the channels of interest are determined. Through the Lüscher formalism, these energies are used to constrain amplitudes of coupled , , and scattering. All channels feature weakly repulsive interactions in the -wave, except for a weak attraction in . No amplitude singularities corresponding to physical states are found. Some of these amplitudes will be a necessary component of future lattice QCD analyses of and scattering, taking into account three-body and left-hand cut effects.
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References (76)
- S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024).
- D. Johnson, I. Polyakov, T. Skwarnicki, and M. Wang, Annu. Rev. Nucl. Part. Sci. 74, 583 (2024).
- R. Aaij et al. (LHCb Collaboration), Nat. Phys. 18, 751 (2022).
- R. Aaij et al. (LHCb Collaboration), Nat. Commun. 13, 3351 (2022).
- H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, Rep. Prog. Phys. 86, 026201 (2023).
- M. Neubert, Phys. Rep. 245, 259 (1994).
- L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Phys. Rep. 1019, 1 (2023).
- M. Albaladejo, Phys. Lett. B 829, 137052 (2022).
- P. G. Ortega, J. Segovia, D. R. Entem, and F. Fernandez, Phys. Lett. B 841, 137918 (2023); 847, 138308(E) (2023).
- G. Yang, J. Ping, and J. Segovia, Phys. Rev. D 101, 014001 (2020).
- M. Luscher, Nucl. Phys. B354, 531 (1991).
- K. Rummukainen and S. A. Gottlieb, Nucl. Phys. B450, 397 (1995).
- P. F. Bedaque, Phys. Lett. B 593, 82 (2004).
- C. h. Kim, C. T. Sachrajda, and S. R. Sharpe, Nucl. Phys. B727, 218 (2005).
- S. He, X. Feng, and C. Liu, J. High Energy Phys. 07 (2005) 011.
- M. Lage, U.-G. Meissner, and A. Rusetsky, Phys. Lett. B 681, 439 (2009).
- Z. Fu, Phys. Rev. D 85, 014506 (2012).
- L. Leskovec and S. Prelovsek, Phys. Rev. D 85, 114507 (2012).
- M. Gockeler, R. Horsley, M. Lage, U. G. Meissner, P. E. L. Rakow, A. Rusetsky, G. Schierholz, and J. M. Zanotti, Phys. Rev. D 86, 094513 (2012).
- M. T. Hansen and S. R. Sharpe, Phys. Rev. D 86, 016007 (2012).
- R. A. Briceno and Z. Davoudi, Phys. Rev. D 88, 094507 (2013).
- P. Guo, J. Dudek, R. Edwards, and A. P. Szczepaniak, Phys. Rev. D 88, 014501 (2013).
- R. A. Briceno, Phys. Rev. D 89, 074507 (2014).
- P. Junnarkar, N. Mathur, and M. Padmanath, Phys. Rev. D 99, 034507 (2019).
- M. Padmanath and S. Prelovsek, Phys. Rev. Lett. 129, 032002 (2022).
- Y. Lyu, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, and J. Meng, Phys. Rev. Lett. 131, 161901 (2023).
- S. Collins, A. Nefediev, M. Padmanath, and S. Prelovsek, Phys. Rev. D 109, 094509 (2024).
- T. Whyte, D. J. Wilson, and C. E. Thomas (Hadron Spectrum Collaboration), Phys. Rev. D 111, 034511 (2025).
- S. Chen, C. Shi, Y. Chen, M. Gong, Z. Liu, W. Sun, and R. Zhang, Phys. Lett. B 833, 137391 (2022).
- L. Meng, E. Ortiz-Pacheco, V. Baru, E. Epelbaum, M. Padmanath, and S. Prelovsek, Phys. Rev. D 111, 034509 (2025).
- P.-P. Shi, F.-K. Guo, C. Liu, L. Liu, P. Sun, J.-J. Wu, and H. Xing, arXiv:2502.07438.
- Y. Ikeda, B. Charron, S. Aoki, T. Doi, T. Hatsuda, T. Inoue, N. Ishii, K. Murano, H. Nemura, and K. Sasaki, Phys. Lett. B 729, 85 (2014).
- M. T. Hansen, F. Romero-López, and S. R. Sharpe, J. High Energy Phys. 06 (2024) 051.
- S. M. Dawid, F. Romero-López, and S. R. Sharpe, J. High Energy Phys. 01 (2025) 060.
- L. Meng, V. Baru, E. Epelbaum, A. A. Filin, and A. M. Gasparyan, Phys. Rev. D 109, L071506 (2024).
- S. M. Dawid, A. W. Jackura, and A. P. Szczepaniak, Phys. Lett. B 864, 139442 (2025).
- R. Bubna, H.-W. Hammer, F. Müller, J.-Y. Pang, A. Rusetsky, and J.-J. Wu, J. High Energy Phys. 05 (2024) 168.
- A. B. Raposo and M. T. Hansen, J. High Energy Phys. 08 (2024) 075.
- A. B. Raposo, R. A. Briceño, M. T. Hansen, and A. W. Jackura, J. High Energy Phys. 06 (2025) 186.
- F. Gil-Domínguez, A. Giachino, and R. Molina, Phys. Rev. D 111, 016029 (2025).
- S. Prelovsek, E. Ortiz-Pacheco, S. Collins, L. Leskovec, M. Padmanath, and I. Vujmilovic, Phys. Rev. D 112, 014507 (2025).
- R. G. Edwards, B. Joo, and H.-W. Lin, Phys. Rev. D 78, 054501 (2008).
- R. G. Edwards, N. Mathur, D. G. Richards, and S. J. Wallace (Hadron Spectrum Collaboration), Phys. Rev. D 87, 054506 (2013).
- D. J. Wilson, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Phys. Rev. D 109, 114503 (2024).
- J. J. Dudek, R. G. Edwards, and C. E. Thomas, Phys. Rev. D 86, 034031 (2012).
- G. Moir, M. Peardon, S. M. Ryan, C. E. Thomas, and D. J. Wilson, J. High Energy Phys. 10 (2016) 011.
- B. Blossier, M. Della Morte, G. von Hippel, T. Mendes, and R. Sommer, J. High Energy Phys. 04 (2009) 094.
- C. Michael, Nucl. Phys. B259, 58 (1985).
- M. Luscher and U. Wolff, Nucl. Phys. B339, 222 (1990).
- J. J. Dudek, R. G. Edwards, M. J. Peardon, D. G. Richards, and C. E. Thomas, Phys. Rev. D 82, 034508 (2010).
- R. C. Johnson, Phys. Lett. 114B, 147 (1982).
- G. K. C. Cheung, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), J. High Energy Phys. 11 (2017) 033.
- C. E. Thomas, R. G. Edwards, and J. J. Dudek, Phys. Rev. D 85, 014507 (2012).
- D. J. Wilson, J. J. Dudek, R. G. Edwards, and C. E. Thomas, Phys. Rev. D 91, 054008 (2015).
- J. R. Green, A. D. Hanlon, P. M. Junnarkar, and H. Wittig, Phys. Rev. Lett. 127, 242003 (2021).
- J. D. E. Yeo, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), J. High Energy Phys. 07 (2024) 012.
- R. A. Briceno, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Phys. Rev. Lett. 118, 022002 (2017).
- F. Romero-López, S. R. Sharpe, T. D. Blanton, R. A. Briceño, and M. T. Hansen, J. High Energy Phys. 10 (2019) 007.
- A. S. Reiner, Phys. Lett. 28B, 387 (1969).
- A. J. Woss, C. E. Thomas, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Phys. Rev. D 100, 054506 (2019).
- R. A. Briceno, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Phys. Rev. D 97, 054513 (2018).
- C. E. Thomas and F. E. Close, Phys. Rev. D 78, 034007 (2008).
- M. Karliner and J. L. Rosner, Phys. Rev. D 105, 034020 (2022).
- T. Shrimal, S. Collins, P. Jana, M. Padmanath, and S. Prelovsek, Phys. Rev. D 112, 054513 (2025).
- www.hadspec.org.
- R. G. Edwards and B. Joo, Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).
- M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi, Comput. Phys. Commun. 181, 1517 (2010).
- R. Babich, M. A. Clark, and B. Joo, in SC 10 (Supercomputing 2010) New Orleans, Louisiana, 2010 (2010), http://www1.jlab.org/Ul/publications/view-pub.cfm?pub-id=10186.
- K. Clark, B. Joo, A. Strelchenko, M. Cheng, A. Gambhir, and R. Brower, in SC ’10: Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis (IEEE, New Orleans, LA, 2016).
- B. Joó, D. Kalamkar, K. Vaidyanathan, M. Smelyanskiy, K. Pamnany, V. Lee, P. Dubey, and W. Watson, in Supercomputing, edited by J. Kunkel, T. Ludwig, and H. Meuer, Lecture Notes in Computer Science (Springer, Berlin Heidelberg, 2013), Vol. 7905, pp. 40–54, ISBN [Amazon][WorldCat].
- B. Joó, MG_PROTO: A Multigrid Library for QCD, https://github.com/JeffersonLab/mg_proto/.
- J. C. Osborn, R. Babich, J. Brannick, R. C. Brower, M. A. Clark, S. D. Cohen, and C. Rebbi, Proc. Sci. LATTICE2010 (2010) 037 [arXiv:1011.2775].
- R. Babich, J. Brannick, R. C. Brower, M. A. Clark, T. A. Manteuffel, S. F. McCormick, J. C. Osborn, and C. Rebbi, Phys. Rev. Lett. 105, 201602 (2010).
- J. Chen, R. G. Edwards, and W. Mao, in Platform for Advanced Scientific Computing (2023), 10.1145/3592979.3593409.
- www.csd3.cam.ac.uk.
- www.dirac.ac.uk.