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

Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures

Y. Aoki1, H. Fukaya2, S. Hashimoto3,4, I. Kanamori1, Y. Nakamura1, C. Rohrhofer2, K. Suzuki5, and D. Ward2 (JLQCD Collaboration)

Phys. Rev. D 111, 114506 – Published 13 June, 2025

DOI: https://doi.org/10.1103/yh8j-q93c

Abstract

We investigate spatial two-point correlation functions of mesonic operators in two-flavor lattice QCD at high temperatures. The simulated temperatures cover the range T∈[147,330]  MeV, where the critical temperature is estimated around 165 MeV. To ensure a good control of the chiral symmetry we employ the Möbius domain-wall fermion action for two degenerate flavors of quarks. With a lattice cutoff a−1∼2.6  GeV, the residual mass is reduced to 0.14 MeV. With the energy spectrum obtained from the screening mass at incremental values of the temperature range, we examine the SU(2)L×SU(2)R chiral symmetry, the anomalous axial U(1), as well as an enhanced symmetry which exchanges the spin degrees of freedom. We also study how the data approaches the perturbative prediction given by twice the Matsubara frequency of free quarks.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (63)

  1. R. D. Pisarski and F. Wilczek, Remarks on the chiral phase transition in chromodynamics, Phys. Rev. D 29, 338 (1984).
  2. D. J. Gross, R. D. Pisarski, and L. G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53, 43 (1981).
  3. D. Diakonov and V. Y. Petrov, Chiral condensate in the instanton vacuum, Phys. Lett. 147B, 351 (1984).
  4. T. R. Morris, D. A. Ross, and C. T. Sachrajda, Higher order quantum corrections in the presence of an instanton background field, Nucl. Phys. B255, 115 (1985).
  5. T. Schäfer and E. V. Shuryak, Instantons in QCD, Rev. Mod. Phys. 70, 323 (1998).
  6. A. Ringwald and F. Schrempp, Confronting instanton perturbation theory with QCD lattice results, Phys. Lett. B 459, 249 (1999).
  7. T. D. Cohen, The high temperature phase of QCD and U(1)-A symmetry, Phys. Rev. D 54, R1867 (1996).
  8. T. D. Cohen, The spectral density of the Dirac operator above T(c) rep, arXiv:nucl-th/9801061.
  9. S. Aoki, H. Fukaya, and Y. Taniguchi, Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature, Phys. Rev. D 86, 114512 (2012).
  10. A. Pelissetto and E. Vicari, Relevance of the axial anomaly at the finite-temperature chiral transition in QCD, Phys. Rev. D 88, 105018 (2013).
  11. T. Kanazawa and N. Yamamoto, Quasi-instantons in QCD with chiral symmetry restoration, Phys. Rev. D 91, 105015 (2015).
  12. T. Sato and N. Yamada, Linking U(2)×U(2) to O(4) model via decoupling, Phys. Rev. D 91, 034025 (2015).
  13. Y. Nakayama and T. Ohtsuki, Conformal bootstrap dashing hopes of emergent symmetry, Phys. Rev. Lett. 117, 131601 (2016).
  14. G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, H. Matsufuru, and J. I. Noaki, Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion formulation, Phys. Rev. D 87, 114514 (2013); 88, 019901(E) (2013).
  15. M. I. Buchoff et al., QCD chiral transition, U(1)A symmetry and the Dirac spectrum using domain wall fermions, Phys. Rev. D 89, 054514 (2014).
  16. V. Dick, F. Karsch, E. Laermann, S. Mukherjee, and S. Sharma, Microscopic origin of UA(1) symmetry violation in the high temperature phase of QCD, Phys. Rev. D 91, 094504 (2015).
  17. B. B. Brandt, A. Francis, H. B. Meyer, O. Philipsen, D. Robaina, and H. Wittig, On the strength of the UA(1) anomaly at the chiral phase transition in Nf=2 QCD, J. High Energy Phys. 12 (2016) 158.
  18. K.-I. Ishikawa, Y. Iwasaki, Y. Nakayama, and T. Yoshie, Nature of chiral phase transition in two-flavor QCD, arXiv:1706.08872.
  19. A. Bazavov et al., Meson screening masses in (2+1)-flavor QCD, Phys. Rev. D 100, 094510 (2019).
  20. O. Kaczmarek, R. Shanker, and S. Sharma, Eigenvalues of the QCD Dirac matrix with improved staggered quarks in the continuum limit, Phys. Rev. D 108, 094501 (2023).
  21. M. Laine and M. Vepsalainen, Mesonic correlation lengths in high temperature QCD, J. High Energy Phys. 02 (2004) 004.
  22. M. Neubert, Heavy quark symmetry, Phys. Rep. 245, 259 (1994).
  23. N. Brambilla, A. Pineda, J. Soto, and A. Vairo, Effective field theories for heavy quarkonium, Rev. Mod. Phys. 77, 1423 (2005).
  24. L. Y. Glozman, SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra, Eur. Phys. J. A 51, 27 (2015).
  25. L. Y. Glozman, SU(2NF) symmetry of QCD at high temperature and its implications, Acta Phys. Pol. B Proc. Suppl. 10, 583 (2017).
  26. L. Y. Glozman, Chiralspin symmetry and QCD at high temperature, Eur. Phys. J. A 54, 117 (2018).
  27. C. B. Lang, Low lying eigenmodes and meson propagator symmetries, Phys. Rev. D 97, 114510 (2018).
  28. M. Catillo, On SU(2)CS-like groups and invariance of the fermionic action in QCD, Int. J. Mod. Phys. A 37, 2250102 (2022).
  29. L. Y. Glozman, O. Philipsen, and R. D. Pisarski, Chiral spin symmetry and the QCD phase diagram, Eur. Phys. J. A 58, 247 (2022).
  30. M. Dalla Brida, L. Giusti, T. Harris, D. Laudicina, and M. Pepe, Non-perturbative thermal QCD at all temperatures: The case of mesonic screening masses, J. High Energy Phys. 04 (2022) 034.
  31. G. Cossu et al. (JLQCD Collaboration), Violation of chirality of the Möbius domain-wall Dirac operator from the eigenmodes, Phys. Rev. D 93, 034507 (2016).
  32. A. Tomiya, G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, and J. Noaki, Evidence of effective axial U(1) symmetry restoration at high temperature QCD, Phys. Rev. D 96, 034509 (2017).
  33. S. Aoki et al. (JLQCD Collaboration), Study of the axial U(1) anomaly at high temperature with lattice chiral fermions, Phys. Rev. D 103, 074506 (2021).
  34. D. B. Kaplan, A method for simulating chiral fermions on the lattice, Phys. Lett. B 288, 342 (1992).
  35. Y. Shamir, Chiral fermions from lattice boundaries, Nucl. Phys. B406, 90 (1993).
  36. V. Furman and Y. Shamir, Axial symmetries in lattice QCD with Kaplan fermions, Nucl. Phys. B439, 54 (1995).
  37. R. C. Brower, H. Neff, and K. Orginos, Mobius fermions, Nucl. Phys. B, Proc. Suppl. 153, 191 (2006).
  38. R. C. Brower, H. Neff, and K. Orginos, The Möbius domain wall fermion algorithm, Comput. Phys. Commun. 220, 1 (2017).
  39. H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417, 141 (1998).
  40. S. Aoki et al. (JLQCD Collaboration), Chiral susceptibility and axial U(1) anomaly near the (pseudo-)critical temperature, Proc. Sci., LATTICE2023 (2024) 184 [arXiv:2401.06459].
  41. N. Mathur, A. Alexandru, Y. Chen, S. J. Dong, T. Draper, I. Horvath, F. X. Lee, K. F. Liu, S. Tamhankar, and J. B. Zhang, Scalar mesons a0(1450) and sigma(600) from lattice QCD, Phys. Rev. D 76, 114505 (2007).
  42. C. Rohrhofer, Y. Aoki, G. Cossu, H. Fukaya, L. Y. Glozman, S. Hashimoto, C. B. Lang, and S. Prelovsek, Approximate degeneracy of J=1 spatial correlators in high temperature QCD, Phys. Rev. D 96, 094501 (2017); 99, 039901(E) (2019).
  43. C. Rohrhofer et al., Symmetries of spatial meson correlators in high temperature QCD, Phys. Rev. D 100, 014502 (2019).
  44. C. Rohrhofer, Y. Aoki, L. Y. Glozman, and S. Hashimoto, Chiral-spin symmetry of the meson spectral function above Tc, Phys. Lett. B 802, 135245 (2020).
  45. T. W. Chiu, Symmetries of meson correlators in high-temperature QCD with physical (u/d, s,c) domain-wall quarks, Phys. Rev. D 107, 114501 (2023).
  46. T. W. Chiu, Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD, Phys. Rev. D 110, 014502 (2024).
  47. T. W. Chiu, Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks, Symmetry 17, 700 (2025).
  48. D. Ward, S. Aoki, Y. Aoki, H. Fukaya, S. Hashimoto, I. Kanamori, T. Kaneko, J. Goswami, and Y. Zhang, Study of symmetries in finite temperature Nf=2 QCD with Möbius domain wall fermions, Proc. Sci., LATTICE2024 (2025) 346 [arXiv:2412.06574].
  49. D. Ward, S. Aoki, Y. Aoki, H. Fukaya, S. Hashimoto, I. Kanamori, T. Kaneko, J. Goswami, and Y. Zhang, Study of chiral symmetry and U(1)A using spatial correlators for Nf=2+1 QCD at finite temperature with domain wall fermions, Proc. Sci., LATTICE2023 (2024) 182.
  50. S. Aoki et al. (JLQCD Collaboration), Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature, Prog. Theor. Exp. Phys. 2022, 023B05 (2022).
  51. S. Aoki et al. (JLQCD Collaboration), Axial U(1) symmetry near the pseudocritical temperature in Nf=2+1 lattice QCD with chiral fermions, Proc. Sci., LATTICE2023 (2024) 185.
  52. J. Goswami et al. (JLQCD Collaboration), Characterizing strongly interacting matter at finite temperature: (2+1)-flavor QCD with Möbius domain wall fermions, Proc. Sci., LATTICE2023 (2024) 187.
  53. G. Cossu, J. Noaki, S. Hashimoto, T. Kaneko, H. Fukaya, P. A. Boyle, and J. Doi, JLQCD IroIro++ lattice code on BG/Q, arXiv:1311.0084.
  54. P. Boyle, A. Yamaguchi, G. Cossu, and A. Portelli, Grid: A next generation data parallel C++ QCD library, arXiv:1512.03487.
  55. S. Ueda, S. Aoki, T. Aoyama, K. Kanaya, H. Matsufuru, S. Motoki, Y. Namekawa, H. Nemura, Y. Taniguchi, and N. Ukita, Development of an object oriented lattice QCD code ‘Bridge++’, J. Phys. Conf. Ser. 523, 012046 (2014).
  56. T. Amagasa, S. Aoki, Y. Aoki, T. Aoyama, T. Doi, K. Fukumura, N. Ishii, K. I. Ishikawa, H. Jitsumoto, H. Kamano et al., Sharing lattice QCD data over a widely distributed file system, J. Phys. Conf. Ser. 664, 042058 (2015).
  57. M. Luscher and P. Weisz, Computation of the action for on-shell improved lattice gauge theories at weak coupling, Phys. Lett. 158B, 250 (1985).
  58. R. Sommer, Scale setting in lattice QCD, Proc. Sci., LATTICE2013 (2014) 015.
  59. C. Morningstar and M. J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69, 054501 (2004).
  60. A. Krasniqi, M. Cè, R. J. Hudspith, and H. B. Meyer, Hot QCD matter around the chiral crossover: A lattice study with -improved Wilson fermions, Phys. Rev. D 110, 114506 (2024).
  61. R. V. Gavai, M. E. Jaensch, O. Kaczmarek, F. Karsch, M. Sarkar, R. Shanker, S. Sharma, S. Sharma, and T. Ueding, Aspects of the chiral crossover transition in (2+1)-flavor QCD with Möbius domain-wall fermions, Phys. Rev. D 111, 034507 (2025).
  62. D. Laudicina, M. Dalla Brida, L. Giusti, T. Harris, and M. Pepe, QCD mesonic screening masses and restoration of chiral symmetry at high T, Proc. Sci., LATTICE2022 (2023) 182.
  63. L. Giusti, T. Harris, D. Laudicina, M. Pepe, and P. Rescigno, Baryonic screening masses in QCD at high temperature, Phys. Lett. B 855, 138799 (2024).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation