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Roles of U(1) axial anomaly effects in cold and dense two-color QCD with 2+2 flavors

Manato Sakai1 and Daiki Suenaga2,3

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Phys. Rev. D 112, 114042 – Published 26 December, 2025

DOI: https://doi.org/10.1103/mxq2-25x1

Abstract

We explore phase structures and hadron mass spectra in cold and dense two-color quantum chromodynamics (QCD) with 2+2 flavors where the sign problem disappears. We particularly focus on U(1) axial anomaly effects. We employ an Nf=2+2 linear sigma model based on the SU(8) Pauli-Gürsey symmetry to describe negative-parity as well as positive-parity hadrons, for which low-energy excitations are appropriately described particularly in the baryon superfluid phase with light diquark condensates. As a result, the strange chiral condensate is found to be enhanced in the superfluid phase owing to the flavor-mixing structure of U(1) axial anomaly effects. We also confirm this enhancement by means of the Nambu–Jona-Lasinio model. Besides, our present analysis predicts the existence of a novel superfluid phase where heavy diquarks condense in dense regime. The topological susceptibility with 2+2 flavors from the viewpoints of the anomaly effects and chiral-symmetry restoration is investigated. Furthermore, we derive a complete inverse mass hierarchy for negative-parity diquarks with sufficient anomaly effects. Our findings are expected to provide future lattice simulations with useful information on flavor-symmetry violation from the U(1) axial anomaly aspects in cold and dense two-color QCD medium.

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References (57)

  1. Gordon Baym, Tetsuo Hatsuda, Toru Kojo, Philip D. Powell, Yifan Song, and Tatsuyuki Takatsuka, From hadrons to quarks in neutron stars: A review, Rep. Prog. Phys. 81, 056902 (2018).
  2. Mark G. Alford, Andreas Schmitt, Krishna Rajagopal, and Thomas Schäfer, Color superconductivity in dense quark matter, Rev. Mod. Phys. 80, 1455 (2008).
  3. Gert Aarts, Introductory lectures on lattice QCD at nonzero baryon number, J. Phys. Conf. Ser. 706, 022004 (2016).
  4. Keitaro Nagata, Finite-density lattice QCD and sign problem: Current status and open problems, Prog. Part. Nucl. Phys. 127, 103991 (2022).
  5. Shin Muroya, Atsushi Nakamura, Chiho Nonaka, and Tetsuya Takaishi, Lattice QCD at finite density: An introductory review, Prog. Theor. Phys. 110, 615 (2003).
  6. Tamer Boz, Pietro Giudice, Simon Hands, and Jon-Ivar Skullerud, Dense two-color QCD towards continuum and chiral limits, Phys. Rev. D 101, 074506 (2020).
  7. P. V. Buividovich, D. Smith, and L. von Smekal, Electric conductivity in finite-density SU(2) lattice gauge theory with dynamical fermions, Phys. Rev. D 102, 094510 (2020).
  8. N. Astrakhantsev, V. V. Braguta, E. M. Ilgenfritz, A. Yu. Kotov, and A. A. Nikolaev, Lattice study of thermodynamic properties of dense QC2D, Phys. Rev. D 102, 074507 (2020).
  9. Kei Iida, Etsuko Itou, Kotaro Murakami, and Daiki Suenaga, Lattice study on finite density QC2D towards zero temperature, J. High Energy Phys. 10 (2024) 022.
  10. Victor V. Braguta, Phase diagram of dense two-color QCD at low temperatures, Symmetry 15, 1466 (2023).
  11. J. B. Kogut, Misha A. Stephanov, D. Toublan, J. J. M. Verbaarschot, and A. Zhitnitsky, QCD—like theories at finite baryon density, Nucl. Phys. B582, 477 (2000).
  12. J. T. Lenaghan, F. Sannino, and K. Splittorff, The Superfluid and conformal phase transitions of two color QCD, Phys. Rev. D 65, 054002 (2002).
  13. Gao-feng Sun, Lianyi He, and Pengfei Zhuang, BEC-BCS crossover in the Nambu-Jona-Lasinio model of QCD, Phys. Rev. D 75, 096004 (2007).
  14. Tomas Brauner, Kenji Fukushima, and Yoshimasa Hidaka, Two-color quark matter: U(1)A restoration, superfluidity, and quarkyonic phase, Phys. Rev. D 80, 074035 (2009); 81, 119904(E) (2010).
  15. Masayasu Harada, Chiho Nonaka, and Tetsuro Yamaoka, Masses of vector bosons in two-color dense QCD based on the hidden local symmetry, Phys. Rev. D 81, 096003 (2010).
  16. Nils Strodthoff, Bernd-Jochen Schaefer, and Lorenz von Smekal, Quark-meson-diquark model for two-color QCD, Phys. Rev. D 85, 074007 (2012).
  17. Shotaro Imai, Hiroshi Toki, and Wolfram Weise, Quark-hadron matter at finite temperature and density in a two-color PNJL model, Nucl. Phys. A913, 71 (2013).
  18. Dyana C. Duarte, P. G. Allen, R. L. S. Farias, Patricia H. A. Manso, Rudnei O. Ramos, and N. N. Scoccola, BEC-BCS crossover in a cold and magnetized two color NJL model, Phys. Rev. D 93, 025017 (2016).
  19. Romain Contant and Markus Q. Huber, Dense two-color QCD from Dyson-Schwinger equations, Phys. Rev. D 101, 014016 (2020).
  20. Daiki Suenaga and Toru Kojo, Gluon propagator in two-color dense QCD: Massive Yang-Mills approach at one-loop, Phys. Rev. D 100, 076017 (2019).
  21. T. G. Khunjua, K. G. Klimenko, and R. N. Zhokhov, The dual properties of chiral and isospin asymmetric dense quark matter formed of two-color quarks, J. High Energy Phys. 06 (2020) 148.
  22. Daiki Suenaga, Kotaro Murakami, Etsuko Itou, and Kei Iida, Probing the hadron mass spectrum in dense two-color QCD with the linear sigma model, Phys. Rev. D 107, 054001 (2023).
  23. Nirmalendu Acharyya, Prasanjit Aich, Arkajyoti Bandyopadhyay, and Sachindeo Vaidya, Matrix model of two-color one-flavor QCD: The ultrastrong coupling regime, Phys. Rev. D 110, 054016 (2024).
  24. J. B. Kogut, Misha A. Stephanov, and D. Toublan, On two color QCD with baryon chemical potential, Phys. Lett. B 464, 183 (1999).
  25. Mamiya Kawaguchi and Daiki Suenaga, Fate of the topological susceptibility in two-color dense QCD, J. High Energy Phys. 08 (2023) 189.
  26. Daiki Suenaga, Kotaro Murakami, Etsuko Itou, and Kei Iida, Mass spectrum of spin-one hadrons in dense two-color QCD: Novel predictions by extended linear sigma model, Phys. Rev. D 109, 074031 (2024).
  27. Mamiya Kawaguchi and Daiki Suenaga, Sound velocity peak induced by the chiral partner in dense two-color QCD, Phys. Rev. D 109, 096034 (2024).
  28. G. Fejos and D. Suenaga, Chiral symmetry restoration in QC2D from an effective model using the functional renormalization group, Phys. Rev. D 111, 076018 (2025).
  29. Gergely Fejős and Daiki Suenaga, Enhancement of axial anomaly effects in hot two-color QCD: FRG approach in the linear sigma model, arXiv:2506.14010.
  30. Daiki Suenaga, Chiral effective model of cold and dense two-color QCD: The linear sigma model approach, Symmetry 17, 124 (2025).
  31. Thomas Schäfer and Frank Wilczek, Continuity of quark and hadron matter, Phys. Rev. Lett. 82, 3956–3959 (1999).
  32. Hiroaki Abuki, Gordon Baym, Tetsuo Hatsuda, and Naoki Yamamoto, The NJL model of dense three-flavor matter with axial anomaly: The low temperature critical point and BEC-BCS diquark crossover, Phys. Rev. D 81, 125010 (2010).
  33. M. Kobayashi and T. Maskawa, Chiral symmetry and eta-x mixing, Prog. Theor. Phys. 44, 1422 (1970).
  34. M. Kobayashi, H. Kondo, and T. Maskawa, Symmetry breaking of the chiral U(3) ⊗ U(3) and the quark model, Prog. Theor. Phys. 45, 1955 (1971).
  35. Gerard ’t Hooft, Computation of the quantum effects due to a four-dimensional pseudoparticle, Phys. Rev. D 14, 3432 (1976); 18, 2199(E) (1978).
  36. Gerard ’t Hooft, Symmetry breaking through Bell-Jackiw anomalies, Phys. Rev. Lett. 37, 8 (1976).
  37. Masayasu Harada, Yan-Rui Liu, Makoto Oka, and Kei Suzuki, Chiral effective theory of diquarks and the UA(1) anomaly, Phys. Rev. D 101, 054038 (2020).
  38. Kenji Fukushima, Characteristics of the eigenvalue distribution of the Dirac operator in dense two-color QCD, J. High Energy Phys. 07 (2008) 083.
  39. W. Pauli, On the conservation of the lepton charge, Nuovo Cimento 6, 204 (1957).
  40. Feza Gürsey, Relation of charge independence and baryon conservation to Pauli’s transformation, Nuovo Cimento 7, 411 (1958).
  41. Edward Witten, Baryons in the 1/n expansion, Nucl. Phys. B160, 57 (1979).
  42. Claudia Ratti and Wolfram Weise, Thermodynamics of two-colour QCD and the Nambu Jona-Lasinio model, Phys. Rev. D 70, 054013 (2004).
  43. Simon Hands, Peter Sitch, and Jon-Ivar Skullerud, Hadron spectrum in a two-colour baryon-rich medium, Phys. Lett. B 662, 405 (2008).
  44. Kotaro Murakami, Daiki Suenaga, Kei Iida, and Etsuko Itou, Measurement of hadron masses in 2-color finite density QCD, Proc. Sci. LATTICE2022 (2023) 154 [arXiv:2211.13472].
  45. S. Navas et al. (Particle Data Group), Review of particle physics, Phys. Rev. D 110, 030001 (2024).
  46. Toru Kojo, Daiki Suenaga, and Ryuji Chiba, Isospin QCD as a Laboratory for Dense QCD, Universe 10, 293 (2024).
  47. Mamiya Kawaguchi, Shinya Matsuzaki, and Akio Tomiya, Analysis of nonperturbative flavor violation at chiral crossover criticality in QCD, Phys. Rev. D 103, 054034 (2021).
  48. Varouzhan Baluni, CP violating effects in QCD, Phys. Rev. D 19, 2227 (1979).
  49. Tetsuo Hatsuda and Teiji Kunihiro, QCD phenomenology based on a chiral effective Lagrangian, Phys. Rep. 247, 221 (1994).
  50. Michael Buballa, NJL model analysis of quark matter at large density, Phys. Rep. 407, 205 (2005).
  51. Daiki Suenaga and Makoto Oka, Axial anomaly effect on the chiral-partner structure of diquarks at high temperature, Phys. Rev. D 108, 014030 (2023).
  52. Daiki Suenaga and Makoto Oka, Fate of Σc, Ξc’ and Ωc baryons at high temperature with chiral-symmetry restoration, Phys. Rev. D 111, 074032 (2025).
  53. A. V. Manohar, M. B. Wise, T. Ericson, and P. Y. Landshoff, Heavy Quark Physics, Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology (Cambridge University Press, Cambridge, England, 2000).
  54. Yuki Fujimoto, Toru Kojo, and Larry D. McLerran, Momentum shell in quarkyonic matter from explicit duality: A dual model for cold, dense QCD, Phys. Rev. Lett. 132, 112701 (2024).
  55. Yuki Fujimoto, Toru Kojo, and Larry McLerran, Quarkyonic matter pieces together the hyperon puzzle, arXiv:2410.22758.
  56. Ryuji Chiba and Toru Kojo, Sound velocity peak and conformality in isospin QCD, Phys. Rev. D 109, 076006 (2024).
  57. Ryuji Chiba, Toru Kojo, and Daiki Suenaga, Thermal effects on sound velocity peak and conformality in isospin QCD, Phys. Rev. D 110, 054037 (2024).

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Phys. Rev. D 112, 114042– Published 26 December, 2025
  • Received 9 October 2025
  • Accepted 4 December 2025
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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.

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