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Lattice study of ccu¯s¯ tetraquark channels in D(*)Ds(*) scattering

Tanishk Shrimal1,2,*, Sara Collins3,†, Priyajit Jana4,5, M. Padmanath1,2,‡, and Sasa Prelovsek6,7,§

  • *Contact author: tanishks@imsc.res.in
  • †Contact author: sara.collins@ur.de
  • ‡Contact author: padmanath@imsc.res.in
  • §Contact author: sasa.prelovsek@ijs.si
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Phys. Rev. D 112, 054513 – Published 26 September, 2025

DOI: https://doi.org/10.1103/tdjf-4l5v

Abstract

We present the first lattice quantum chromodynamics (QCD) determination of coupled DDs* and D*Ds scattering amplitudes in the JP=1+ channel and elastic DDs scattering amplitude in the JP=0+ channel. The aim is to investigate whether tetraquarks with flavor ccu¯s¯ exist in the region near threshold. Lattice QCD ensembles from the CLS consortium with mπ∼280  MeV, a∼0.09  fm and L/a=24, 32 are utilized. Finite-volume spectra are determined via variational analysis of two-point correlation matrices, computed using large bases of operators resembling bilocal two-meson structures within the distillation framework. The scattering matrix for partial wave l=0 is determined using lattice eigenenergies from multiple inertial frames following Lüscher’s formalism as well as following the solutions of Lippmann-Schwinger equation in the finite-volume on a plane-wave basis. We observe small nonzero energy shifts in the simulated spectra from the noninteracting scenario in both the channels studied, which points to rather weak nontrivial interactions between the mesons involved. Despite the nonzero energy shifts, the lattice-extracted S-wave amplitudes do not carry signatures of any hadron pole features in the physical amplitudes in the energy region near the threshold.

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References (98)

  1. R. Aaij et al. (LHCb Collaboration), Nat. Phys. 18, 751 (2022).
  2. R. Aaij et al. (LHCb Collaboration), Nat. Commun. 13, 3351 (2022).
  3. J. P. Ader, J. M. Richard, and P. Taxil, Phys. Rev. D 25, 2370 (1982).
  4. J. Carlson, L. Heller, and J. A. Tjon, Phys. Rev. D 37, 744 (1988).
  5. H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, Rep. Prog. Phys. 86, 026201 (2023).
  6. N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, Phys. Rep. 873, 1 (2020).
  7. N. Brambilla et al., arXiv:2203.16583.
  8. A. V. Manohar and M. B. Wise, Nucl. Phys. B399, 17 (1993).
  9. E. J. Eichten and C. Quigg, Phys. Rev. Lett. 119, 202002 (2017).
  10. R. Aaij et al. (LHCb Collaboration), Phys. Rev. Lett. 119, 112001 (2017).
  11. V. Khachatryan et al. (CMS Collaboration), J. High Energy Phys. 05 (2017) 013.
  12. M. Karliner and J. L. Rosner, Phys. Rev. D 105, 034020 (2022).
  13. Q.-F. Lü, D.-Y. Chen, and Y.-B. Dong, Phys. Rev. D 102, 034012 (2020).
  14. C. Deng and S.-L. Zhu, Phys. Rev. D 105, 054015 (2022).
  15. M. Praszalowicz, Phys. Rev. D 106, 114005 (2022).
  16. D. Gamermann, E. Oset, D. Strottman, and M. J. Vicente Vacas, Phys. Rev. D 76, 074016 (2007).
  17. R. Molina, T. Branz, and E. Oset, Phys. Rev. D 82, 014010 (2010).
  18. L. R. Dai, R. Molina, and E. Oset, Phys. Rev. D 105, 016029 (2022); 106, 099902(E) (2022).
  19. D. Gamermann and E. Oset, Eur. Phys. J. A 33, 119 (2007).
  20. S. S. Agaev, K. Azizi, and H. Sundu, Eur. Phys. J. Plus 138, 621 (2023).
  21. R. L. Jaffe, Phys. Rep. 409, 1 (2005).
  22. A. Francis, P. de Forcrand, R. Lewis, and K. Maltman, J. High Energy Phys. 05 (2022) 062.
  23. P. Bicudo, M. Cardoso, A. Peters, M. Pflaumer, and M. Wagner, Phys. Rev. D 96, 054510 (2017).
  24. P. Bicudo, K. Cichy, A. Peters, and M. Wagner, Phys. Rev. D 93, 034501 (2016).
  25. A. Francis, R. J. Hudspith, R. Lewis, and K. Maltman, Phys. Rev. Lett. 118, 142001 (2017).
  26. P. Junnarkar, N. Mathur, and M. Padmanath, Phys. Rev. D 99, 034507 (2019).
  27. L. Leskovec, S. Meinel, M. Pflaumer, and M. Wagner, Phys. Rev. D 100, 014503 (2019).
  28. P. Mohanta and S. Basak, Phys. Rev. D 102, 094516 (2020).
  29. R. J. Hudspith, B. Colquhoun, A. Francis, R. Lewis, and K. Maltman, Phys. Rev. D 102, 114506 (2020).
  30. R. J. Hudspith and D. Mohler, Phys. Rev. D 107, 114510 (2023).
  31. T. Aoki, S. Aoki, and T. Inoue, Phys. Rev. D 108, 054502 (2023).
  32. C. Alexandrou, J. Finkenrath, T. Leontiou, S. Meinel, M. Pflaumer, and M. Wagner, Phys. Rev. D 110, 054510 (2024).
  33. B. Colquhoun, A. Francis, R. J. Hudspith, R. Lewis, K. Maltman, and W. G. Parrott, Phys. Rev. D 110, 094503 (2024).
  34. B. S. Tripathy, N. Mathur, and M. Padmanath, Phys. Rev. D 111, 114504 (2025).
  35. S. Meinel, M. Pflaumer, and M. Wagner, Phys. Rev. D 106, 034507 (2022).
  36. M. Padmanath, A. Radhakrishnan, and N. Mathur, Phys. Rev. Lett. 132, 201902 (2024).
  37. C. Alexandrou, J. Finkenrath, T. Leontiou, S. Meinel, M. Pflaumer, and M. Wagner, Phys. Rev. Lett. 132, 151902 (2024).
  38. A. Radhakrishnan, M. Padmanath, and N. Mathur, Phys. Rev. D 110, 034506 (2024).
  39. G. K. C. Cheung, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), J. High Energy Phys. 11 (2017) 033.
  40. M. Padmanath and S. Prelovsek, Phys. Rev. Lett. 129, 032002 (2022).
  41. S. Chen, C. Shi, Y. Chen, M. Gong, Z. Liu, W. Sun, and R. Zhang, Phys. Lett. B 833, 137391 (2022).
  42. Y. Lyu, S. Aoki, T. Doi, T. Hatsuda, Y. Ikeda, and J. Meng, Phys. Rev. Lett. 131, 161901 (2023).
  43. S. Collins, A. Nefediev, M. Padmanath, and S. Prelovsek, Phys. Rev. D 109, 094509 (2024).
  44. T. Whyte, D. J. Wilson, and C. E. Thomas (Hadron Spectrum Collaboration), Phys. Rev. D 111, 034511 (2025).
  45. P. Bicudo, Phys. Rep. 1039, 1 (2023).
  46. A. Francis, Prog. Part. Nucl. Phys. 140, 104143 (2025).
  47. M. Luscher, Nucl. Phys. B354, 531 (1991).
  48. R. A. Briceno, Phys. Rev. D 89, 074507 (2014).
  49. M.-L. Du, A. Filin, V. Baru, X.-K. Dong, E. Epelbaum, F.-K. Guo, C. Hanhart, A. Nefediev, J. Nieves, and Q. Wang, Phys. Rev. Lett. 131, 131903 (2023).
  50. A. B. a. Raposo and M. T. Hansen, J. High Energy Phys. 08 (2024) 075.
  51. M. T. Hansen, F. Romero-López, and S. R. Sharpe, J. High Energy Phys. 06 (2024) 051.
  52. M. Bruno et al., J. High Energy Phys. 02 (2015) 043.
  53. G. S. Bali, E. E. Scholz, J. Simeth, and W. Söldner (RQCD Collaboration), Phys. Rev. D 94, 074501 (2016).
  54. M. Bruno, T. Korzec, and S. Schaefer, Phys. Rev. D 95, 074504 (2017).
  55. S. Prelovsek, S. Collins, D. Mohler, M. Padmanath, and S. Piemonte, J. High Energy Phys. 06 (2021) 035.
  56. L. Meng, E. Ortiz-Pacheco, V. Baru, E. Epelbaum, M. Padmanath, and S. Prelovsek, Phys. Rev. D 111, 034509 (2025).
  57. M. Peardon, J. Bulava, J. Foley, C. Morningstar, J. Dudek, R. G. Edwards, B. Joo, H.-W. Lin, D. G. Richards, and K. J. Juge (Hadron Spectrum Collaboration), Phys. Rev. D 80, 054506 (2009).
  58. C. Morningstar, J. Bulava, J. Foley, K. J. Juge, D. Lenkner, M. Peardon, and C. H. Wong, Phys. Rev. D 83, 114505 (2011).
  59. S. Piemonte, S. Collins, D. Mohler, M. Padmanath, and S. Prelovsek, Phys. Rev. D 100, 074505 (2019).
  60. R. C. Johnson, Phys. Lett. 114B, 147 (1982).
  61. C. E. Thomas, R. G. Edwards, and J. J. Dudek, Phys. Rev. D 85, 014507 (2012).
  62. M. Padmanath, S. Collins, D. Mohler, S. Piemonte, S. Prelovsek, A. Schäfer, and S. Weishaeupl, Phys. Rev. D 99, 014513 (2019).
  63. S. Prelovsek, U. Skerbis, and C. B. Lang, J. High Energy Phys. 01 (2017) 129.
  64. S. Prelovsek, E. Ortiz-Pacheco, S. Collins, L. Leskovec, M. Padmanath, and I. Vujmilovic, Phys. Rev. D 112, 014507 (2025).
  65. C. Morningstar, J. Bulava, B. Singha, R. Brett, J. Fallica, A. Hanlon, and B. Hörz, Nucl. Phys. B924, 477 (2017).
  66. C. Michael, Nucl. Phys. B259, 58 (1985).
  67. J. R. Green, A. D. Hanlon, P. M. Junnarkar, and H. Wittig, Phys. Rev. Lett. 127, 242003 (2021).
  68. D. J. Wilson, C. E. Thomas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Phys. Rev. D 109, 114503 (2024).
  69. M.-L. Du, V. Baru, X.-K. Dong, A. Filin, F.-K. Guo, C. Hanhart, A. Nefediev, J. Nieves, and Q. Wang, Phys. Rev. D 105, 014024 (2022).
  70. N. S. Dhindsa, N. Mathur, and M. Padmanath, Proc. Sci. LATTICE2024 (2025) 082 [arXiv:2409.10167].
  71. R. A. Briceno, J. J. Dudek, and R. D. Young, Rev. Mod. Phys. 90, 025001 (2018).
  72. L. Meng and E. Epelbaum, J. High Energy Phys. 10 (2021) 051.
  73. L. Meng, V. Baru, E. Epelbaum, A. A. Filin, and A. M. Gasparyan, Phys. Rev. D 109, L071506 (2024).
  74. H. Burkhardt, Dispersion Relation Dynamics: A Phenomenological Introduction to S-matrix Theory (North-Holland Publishing Company, Amsterdam, 1969), https://books.google.co.in/books?id=oFReAAAAIAAJ.
  75. M. Mai and M. Döring, Eur. Phys. J. A 53, 240 (2017).
  76. J. J. Dudek, R. G. Edwards, C. E. Thomas, and D. J. Wilson (Hadron Spectrum Collaboration), Phys. Rev. Lett. 113, 182001 (2014).
  77. J. A. Oller, Prog. Part. Nucl. Phys. 110, 103728 (2020).
  78. A. J. Woss, D. J. Wilson, and J. J. Dudek (Hadron Spectrum Collaboration), Phys. Rev. D 101, 114505 (2020).
  79. D. J. Wilson, J. J. Dudek, R. G. Edwards, and C. E. Thomas, Phys. Rev. D 91, 054008 (2015).
  80. V. Gribov, Strong Interactions of Hadrons at High Energies: Gribov Lectures on Theoretical Physics (Oxford University Press, New York, 2009), 10.1017/9781009290227.
  81. M. E. Peskin and D. V. Schroeder, An Introduction to quantum field theory (Addison-Wesley, Reading, MA, 1995), 10.1201/9780429503559.
  82. S. Mizera, Phys. Rep. 1047, 1 (2024).
  83. M. Mai, C. Culver, A. Alexandru, M. Döring, and F. X. Lee, Phys. Rev. D 100, 114514 (2019).
  84. A. Rodas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Phys. Rev. D 108, 034513 (2023).
  85. A. Rodas, J. J. Dudek, and R. G. Edwards (Hadron Spectrum Collaboration), Phys. Rev. D 109, 034513 (2024).
  86. X.-H. Cao, Q.-Z. Li, Z.-H. Guo, and H.-Q. Zheng, Phys. Rev. D 108, 034009 (2023).
  87. R. A. Briceno, J. J. Dudek, R. G. Edwards, and D. J. Wilson, Phys. Rev. D 97, 054513 (2018).
  88. L. Meng (private communication).
  89. S. Heybrock, B. Joó, D. D. Kalamkar, M. Smelyanskiy, K. Vaidyanathan, T. Wettig, and P. Dubey, in The International Conference for High Performance Computing, Networking, Storage, and Analysis: SC14: HPC Matters (IEEE, New York, 2014), 10.1109/SC.2014.11.
  90. S. Heybrock, M. Rottmann, P. Georg, and T. Wettig, Proc. Sci. LATTICE2015 (2016) 036 [arXiv:1512.04506].
  91. D. Richtmann, S. Heybrock, and T. Wettig, Proc. Sci. LATTICE2015 (2016) 035 [arXiv:1601.03184].
  92. P. Georg, D. Richtmann, and T. Wettig, Proc. Sci. LATTICE2016 (2017) 361 [arXiv:1701.08521].
  93. R. G. Edwards and B. Joo (SciDAC Collaboration, LHPC Collaboration, and UKQCD Collaboration), Nucl. Phys. B, Proc. Suppl. 140, 832 (2005).
  94. www.hpc-rivr.si
  95. eurohpc-ju.europa.eu
  96. www.izum.si
  97. J. Bulava et al. (Baryon Scattering (BaSc) Collaboration), Phys. Rev. Lett. 132, 051901 (2024).
  98. J. Bulava et al. (Baryon Scattering (BaSc) Collaboration), Phys. Rev. D 109, 014511 (2024).

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Phys. Rev. D 112, 054513– Published 26 September, 2025
  • Received 2 May 2025
  • Accepted 18 August 2025
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