Pseudoconformal equation of state in compact-star matter from topology change and hidden symmetries of QCD

  • Yong-Liang MaEmail author
  • Hyun Kyu Lee
  • Won-Gi Paeng
  • Mannque Rho


We construct a new effective field theory approach to the equation of state (EoS), dubbed pseudo-confomal model “PCM”, for nuclear and compact star matter entirely in terms of effective hadron degrees of freedom. The possible transition at n ∼(2–4)n0 (where n0 is the normal nuclear matter density) from hadron degrees of freedom to strongly-coupled quark degrees of freedom, giving rise to a soft-to-hard changeover in the EoS that can accommodate the massive stars observed, is effectuated by the topology change at n1/2 ≳ 2n0 from skyrmions to half-skyrmions without involving local order-parameter fields. The mechanism exploits possible emergence of hidden scale and local symmetries of QCD at high density, leading to a precocious “pseudo-conformal” sound velocity vs2 = 1/3 (in unit of c = 1) for n ≳ 3n0. The resulting prediction signals a drastic departure from standard nuclear many-body theory in the density regime involved in the massive stars. We suggest that the tidal deformability implemented in gravitational waves coming from coalescing neutron stars in LIGO/Virgo-type observations could pin down the location of the topology change density n1/2.


equation of state compact star tidal deformability conformal sound velocity 


  1. 1.
    W. G. Paeng, T. T. S. Kuo, H. K. Lee, Y. L. Ma, and M. Rho, Phys. Rev. D 96, 014031 (2017), arXiv: 1704.02775.ADSCrossRefGoogle Scholar
  2. 2.
    S. Nadkarni, H. B. Nielsen, and I. Zahed, Nucl. Phys. B 253, 308 (1985); M. Rho, Phys. Rep. 240, 1 (1994).ADSCrossRefGoogle Scholar
  3. 3.
    W. G. Paeng, H. K. Lee, M. Rho, and C. Sasaki, Phys. Rev. D 88, 105019 (2013), arXiv: 1303.2898.ADSCrossRefGoogle Scholar
  4. 4.
    M. Harada, and K. Yamawaki, Phys. Rep. 381, 1 (2003).ADSCrossRefGoogle Scholar
  5. 5.
    K. Yamawaki, arXiv: 1803.07271.Google Scholar
  6. 6.
    O. Catà, R. J. Crewther, and L. C. Tunstall, arXiv: 1803.08513.Google Scholar
  7. 7.
    Y. L. Li, Y. L. Ma, and M. Rho, Phys. Rev. C 98, 044318 (2018).ADSCrossRefGoogle Scholar
  8. 8.
    B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. Lett. 119, 161101 (2017), arXiv: 1710.05832.ADSCrossRefGoogle Scholar
  9. 9.
    Y. L. Ma, and M. Rho, Sci. China-Phys. Mech. Astron. 60, 032001 (2017), arXiv: 1612.06600.ADSCrossRefGoogle Scholar
  10. 10.
    G. Baym, T. Hatsuda, T. Kojo, P. D. Powell, Y. Song, and T. Takatsuka, Rep. Prog. Phys. 81, 056902 (2018), arXiv: 1707.04966.ADSCrossRefGoogle Scholar
  11. 11.
    H. K. Lee, B. Y. Park, and M. Rho, Phys. Rev. C 83, 025206 (2011), arXiv: 1005.0255; [Erratum-ibid. Phys. Rev. C 84, 059902 (2011)].ADSCrossRefGoogle Scholar
  12. 12.
    J. W. Holt, G. E. Brown, T. T. S. Kuo, J. D. Holt, and R. Machleidt, Phys. Rev. Lett. 100, 062501 (2008), arXiv: 0710.0310.ADSCrossRefGoogle Scholar
  13. 13.
    C. DeTar, and T. Kunihiro, Phys. Rev. D 39, 2805 (1989).ADSCrossRefGoogle Scholar
  14. 14.
    M. Rho, New Phys.-Sae Mulli 66, 1465 (2016); M. Rho, Int. J. Mod. Phys. A 32, 1747012 (2017).CrossRefGoogle Scholar
  15. 15.
    I. Tews, J. Carlson, S. Gandolfi, and S. Reddy, Astrophys. J. 860, 149 (2018), arXiv: 1801.01923.ADSCrossRefGoogle Scholar
  16. 16.
    B. P. Abbott, et al. (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. X 9, 011001 (2019), arXiv: 1805.11579.Google Scholar
  17. 17.
    H. Dong, T. T. S. Kuo, H. K. Lee, R. Machleidt, and M. Rho, Phys. Rev. C 87, 054332 (2013), arXiv: 1207.0429.ADSCrossRefGoogle Scholar
  18. 18.
    N. B. Zhang, and B. A. Li, arXiv: 1807.07698.Google Scholar
  19. 19.
    B. A. Li, and L. W. Chen, Phys. Rev. C 72, 064611 (2005).ADSCrossRefGoogle Scholar
  20. 20.
    M. B. Tsang, Y. Zhang, P. Danielewicz, M. Famiano, Z. Li, W. G. Lynch, Z. Y. Sun, F. Amorini, L. Andronenko, M. Andronenko, G. Cardella, M. Chatterje, P. Dinh, E. Galichet, H. Hua, E. Laguidara, G. Lanzalone, H. Liu, F. Lu, C. Maiolino, A. Pagano, S. Piantelli, M. Papa, S. Pirrone, G. Politi, F. Porto, F. Rizzo, P. Russotto, D. Santonocito, and G. Verde, Int. J. Mod. Phys. E 19, 1631 (2010).ADSCrossRefGoogle Scholar
  21. 21.
    J. Piekarewicz, arXiv: 1812.04438.Google Scholar
  22. 22.
    P. Zhang, K. Kimm, L. Zou, and Y. M. Cho, arXiv: 1704.05975; S. B. Gudnason, and M. Nitta, Phys. Rev. D 91, 085040 (2015).Google Scholar
  23. 23.
    D. K. Hong, M. Rho, and I. Zahed, Phys. Lett. B 468, 261 (1999).ADSCrossRefGoogle Scholar
  24. 24.
    M. G. Alford, G. Baym, K. Fukushima, T. Hatsuda, and M. Tachibana, Phys. Rev. D 99, 036004 (2019).ADSCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Yong-Liang Ma
    • 1
    Email author
  • Hyun Kyu Lee
    • 2
  • Won-Gi Paeng
    • 3
  • Mannque Rho
    • 4
  1. 1.Center for Theoretical Physics and College of PhysicsJilin UniversityChangchunChina
  2. 2.Department of PhysicsHanyang UniversitySeoulKorea
  3. 3.Rare Isotope Science ProjectInstitute for Basic ScienceDaejeonKorea
  4. 4.Institut de Physique ThéoriqueCEA SaclayGif-sur-Yvette cédexFrance

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