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Unraveling K(1690) as a pseudoscalar udd¯s¯ tetraquark state

Jin-Peng Zhang1, Xu-Liang Chen1, Zi-Xi Ou-Yang2, Xiang Yu1, Wei Chen1,3,*, and Jia-Jun Wu2,3

  • *Contact author: chenwei29@mail.sysu.edu.cn
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Phys. Rev. D 112, 094047 – Published 24 November, 2025

DOI: https://doi.org/10.1103/fv87-6bcr

Abstract

The recently observed K(1690) has been identified as a supernumerary pseudoscalar resonance signal in the strange-meson spectrum predicted by quark model calculations. It is the best candidate of a strange cryptoexotic state. In this work, we systematically study the hadron masses of udd¯s¯ tetraquark states with JP=0− in the method of QCD sum rules. For ten interpolating currents, we calculate the correlation functions up to dimension-8 nonperturbative condensates. To calculate the trigluon condensate, we comprehensively consider the contributions from different operators with and without covariant derivatives. The infrared safety can be guaranteed for the completely calculated trigluon condensate by properly addressing the IR divergences in Feynman diagrams. It is demonstrated that the trigluon condensate provides significant contributions to the sum-rule analyses in these light tetraquark systems. Our results support the interpretation of K(1690) resonance to be a pseudoscalar udd¯s¯ tetraquark state.

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References (48)

  1. M. Gell-Mann, A schematic model of baryons and mesons, Phys. Lett. 8, 214 (1964).
  2. G. Zweig, An SU(3) model for strong interaction symmetry and its breaking. Version 2 (1964), pp. 22–101, 10.17181/CERN-TH-412.
  3. H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, The hidden-charm pentaquark and tetraquark states, Phys. Rep. 639, 1 (2016).
  4. R. F. Lebed, R. E. Mitchell, and E. S. Swanson, Heavy-quark QCD exotica, Prog. Part. Nucl. Phys. 93, 143 (2017).
  5. A. Esposito, A. Pilloni, and A. D. Polosa, Multiquark resonances, Phys. Rep. 668, 1 (2017).
  6. F.-K. Guo, C. Hanhart, U.-G. Meißner, Q. Wang, Q. Zhao, and B.-S. Zou, Hadronic molecules, Rev. Mod. Phys. 90, 015004 (2018); 94, 029901(E) (2022).
  7. Y.-R. Liu, H.-X. Chen, W. Chen, X. Liu, and S.-L. Zhu, Pentaquark and tetraquark states, Prog. Part. Nucl. Phys. 107, 237 (2019).
  8. N. Brambilla, S. Eidelman, C. Hanhart, A. Nefediev, C.-P. Shen, C. E. Thomas, A. Vairo, and C.-Z. Yuan, The XYZ states: Experimental and theoretical status and perspectives, Phys. Rep. 873, 1 (2020).
  9. H.-X. Chen, W. Chen, X. Liu, Y.-R. Liu, and S.-L. Zhu, An updated review of the new hadron states, Rep. Prog. Phys. 86, 026201 (2023).
  10. L. Meng, B. Wang, G.-J. Wang, and S.-L. Zhu, Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules, Phys. Rep. 1019, 1 (2023).
  11. M.-Z. Liu, Y.-W. Pan, Z.-W. Liu, T.-W. Wu, J.-X. Lu, and L.-S. Geng, Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions, Phys. Rep. 1108, 1 (2025).
  12. Z.-G. Wang, Review of the QCD sum rules for exotic states, Front. Phys. 21, 016300 (2026).
  13. H. C. Pekeler, Recent spectroscopy highlights from COMPASS, Proc. Sci. HQL2023 (2024) 041.
  14. S. Wallner, Strange-meson spectroscopy with COMPASS, Nuovo Cimento Soc. Ital. Fis. 47C, 149 (2024).
  15. G. D. Alexeev et al., Spectroscopy of strange mesons and first observation of a strange crypto-exotic state with JP=0−, arXiv:2504.09470.
  16. D. Ebert, R. N. Faustov, and V. O. Galkin, Mass spectra and Regge trajectories of light mesons in the relativistic quark model, Phys. Rev. D 79, 114029 (2009).
  17. S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D 32, 189 (1985).
  18. C.-Q. Pang, J.-Z. Wang, X. Liu, and T. Matsuki, A systematic study of mass spectra and strong decay of strange mesons, Eur. Phys. J. C 77, 861 (2017).
  19. J. Oudichhya, K. Gandhi, and A. K. Rai, Kaon and strangeonium spectrum in Regge phenomenology, Phys. Rev. D 108, 014034 (2023).
  20. U. Taboada-Nieto, P. G. Ortega, D. R. Entem, F. Fernández, and J. Segovia, Kaon spectrum revisited: Bound states of high energy and spin, Eur. Phys. J. A 59, 40 (2023).
  21. S. Navas et al., Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  22. S. R. Cotanch, I. J. General, and P. Wang, QCD Coulomb gauge approach to exotic hadrons, Eur. Phys. J. A 31, 656 (2007).
  23. I. J. General, P. Wang, S. R. Cotanch, and F. J. Llanes-Estrada, Light 1−+ exotics: Molecular resonances, Phys. Lett. B 653, 216 (2007).
  24. C. Lodha and A. K. Rai, Probing kaons as light-strange tetraquarks through spectral and decay dynamics, arXiv:2505.01195.
  25. C.-K. Jiao, W. Chen, H.-X. Chen, and S.-L. Zhu, The possible JPC=0−− exotic state, Phys. Rev. D 79, 114034 (2009).
  26. Z.-R. Huang, W. Chen, T. G. Steele, Z.-F. Zhang, and H.-Y. Jin, Investigation of the light four-quark states with exotic JPC=0−−, Phys. Rev. D 95, 076017 (2017).
  27. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, QCD and resonance physics. Theoretical foundations, Nucl. Phys. B147, 385 (1979).
  28. L. J. Reinders, H. Rubinstein, and S. Yazaki, Hadron properties from QCD sum rules, Phys. Rep. 127, 1 (1985).
  29. Xu-Liang Chen, Peng-Fei Yang, and Wei Chen, Discontinuities of banana integrals in dispersion relation representation, Chin. Phys. Lett. 41, 111101 (2024).
  30. T. Zhong, X.-G. Wu, Z.-G. Wang, T. Huang, H.-B. Fu, and H.-Y. Han, Revisiting the pion leading-twist distribution amplitude within the QCD background field theory, Phys. Rev. D 90, 016004 (2014).
  31. K.-C. Yang, W. Y. P. Hwang, E. M. Henley, and L. S. Kisslinger, QCD sum rules and neutron proton mass difference, Phys. Rev. D 47, 3001 (1993).
  32. A. G. Grozin, Methods of calculation of higher power corrections in QCD, Int. J. Mod. Phys. A 10, 3497 (1995).
  33. W. Chen, R. T. Kleiv, T. G. Steele, B. Bulthuis, D. Harnett, J. Ho, T. Richards, and S.-L. Zhu, Mass spectrum of heavy quarkonium hybrids, J. High Energy Phys. 09 (2013) 019.
  34. S.-H. Li, Z.-S. Chen, Y.-X. Chen, and H.-Y. Jin, QCD sum rule analysis of 0+ four-quark states, arXiv:2410.09847.
  35. D. J. Broadhurst and S. C. Generalis, Can mass singularities be minimally subtracted?, Phys. Lett. 142B, 75 (1984).
  36. H. Y. Jin, J. G. Korner, and T. G. Steele, Improved determination of the mass of the 1−+ light hybrid meson from QCD sum rules, Phys. Rev. D 67, 014025 (2003).
  37. Z.-R. Huang, H.-Y. Jin, and Z.-F. Zhang, New predictions on the mass of the 1−+ light hybrid meson from QCD sum rules, J. High Energy Phys. 04 (2015) 004.
  38. S. Narison, QCD condensates and αs from τ-decay: Summary, J. Subatomic Part. Cosmol. 3, 100038 (2025).
  39. A. Di Giacomo, K. Fabricius, and G. Paffuti, Trilinear gluon condensation parameter from lattice QCD, Phys. Lett. 118B, 129 (1982).
  40. M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, QCD and resonance physics: Applications, Nucl. Phys. B147, 448 (1979).
  41. S. Narison, Gluon condensates and m¯b(m¯b) from QCD-exponential moments at higher orders, Phys. Lett. B 707, 259 (2012).
  42. S. Narison, Gluon condensates and precise m¯c,b from QCD-moments and their ratios to order αs3 and ⟨ G4⟩, Phys. Lett. B 706, 412 (2012).
  43. M. Nielsen, F. S. Navarra, and S. H. Lee, New charmonium states in QCD sum rules: A concise review, Phys. Rep. 497, 41 (2010).
  44. S. N. Nikolaev and A. V. Radyushkin, Method for computing higher gluonic power corrections to QCD charmonium sum rules, Phys. Lett. 110B, 476 (1982); 116B, 469(E) (1982).
  45. S. N. Nikolaev and A. V. Radyushkin, Vacuum corrections to QCD charmonium sum rules: Basic formalism and O (G3) results, Nucl. Phys. B213, 285 (1983).
  46. R.-H. Wu, Y.-S. Zuo, C. Meng, Y.-Q. Ma, and K.-T. Chao, NLO effects for Ω QQQ baryons in QCD Sum Rules, Chin. Phys. C 45, 093103 (2021).
  47. F.-K. Guo, X.-H. Liu, and S. Sakai, Threshold cusps and triangle singularities in hadronic reactions, Prog. Part. Nucl. Phys. 112, 103757 (2020).
  48. G. D. Alexeev et al., Triangle singularity as the origin of the a1(1420), Phys. Rev. Lett. 127, 082501 (2021).

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Phys. Rev. D 112, 094047– Published 24 November, 2025
  • Received 10 July 2025
  • Accepted 6 November 2025
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