# Self-consistent mean field approximation and application in three-flavor NJL model

• In this study, we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio (NJL) model and compare it with the two-flavor NJL model. The self-consistent mean field approximation introduces a new parameter, $\alpha$, that cannot be fixed in advance by the mean field approach itself. Due to the lack of experimental data, the parameter, $\alpha$, is undetermined. Hence, it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation. $\alpha$ affects numerous properties of the chiral phase transitions, such as the position of the phase transition point and the order of phase transition. Additionally, increasing $\alpha$ will decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero. Finally, we observed that $\alpha$ affects the equation of state (EOS) of the quark matter, and the sound velocity can be calculated to determine the stiffness of the EOS, which provides a good basis for studying the neutron star mass-radius relationship.
•  [1] J. R. Oppenheimer and G. M. Volkoff, Physical Review, 55: 374 (1939) doi: 10.1103/PhysRev.55.374 [2] Y. Nambu and G. Jona-Lasinio, Physical Review, 122: 345 (1961) doi: 10.1103/PhysRev.122.345 [3] Y. Nambu and G. Jona-Lasinio, Physical Review, 124: 246 (1961) doi: 10.1103/PhysRev.124.246 [4] S. P. Klevansky, Reviews of Modern Physics, 64: 649 (1992) doi: 10.1103/RevModPhys.64.649 [5] M. Buballa, Physics Reports, 407: 205 (2005) [6] T. Kunihiro and T. Hatsuda, Progress of Theoretical Physics, 71: 1332 (1984) doi: 10.1143/PTP.71.1332 [7] T. Hatsuda and T. Kunihiro, Prog. Theor. Phys., 74: 765 (1985) doi: 10.1143/PTP.74.765 [8] F. Wang, Y. Cao, and H. Zong, Chinese Physics C, 43: 084102 (2019) doi: 10.1088/1674-1137/43/8/084102 [9] P. Demorest, T. Pennucci, S. Ransom et al., nature, 467: 1081 (2010) doi: 10.1038/nature09466 [10] J. Antoniadis, P. C. Freire, N. Wex et al., Science, 340: 1233232 (2013) doi: 10.1126/science.1233232 [11] E. Fonseca, T. T. Pennucci, J. A. Ellis et al., The Astrophysical Journal, 832: 167 (2016) doi: 10.3847/0004-637X/832/2/167 [12] H. Cromartie, E. Fonseca, S. M. Ransom et al., arXiv: 1904.06759 (2019) [13] B. P. Abbott, R. Abbott, T. Abbott et al., Physical Review Letters, 119: 161101 (2017) doi: 10.1103/PhysRevLett.119.161101 [14] H. Gao, Z. Cao, S. Ai et al., The Astrophysical Journal Letters, 851: L45 (2017) doi: 10.3847/2041-8213/aaa0c6 [15] A. Bauswein, O. Just, H.-T. Janka et al., The Astrophysical Journal Letters, 850: L34 (2017) doi: 10.3847/2041-8213/aa9994 [16] J.-E. Christian, A. Zacchi, and J. Schaffner-Bielich, Physical Review D, 99: 023009 (2019) doi: 10.1103/PhysRevD.99.023009 [17] A. Bauswein, N.-U. F. Bastian, D. Blaschke et al., arXiv: 1904.01306 (2019) [18] T. Zhao, W. Zheng, F. Wang et al., Physical Review D, 100: 043018 (2019) doi: 10.1103/PhysRevD.100.043018 [19] Z.-F. Cui, F.-Y. Hou, Y.-M. Shi et al., Annals of Physics, 358: 172 (2015) doi: 10.1016/j.aop.2015.03.025 [20] M. Halasz, A. Jackson, R. Shrock et al., Physical Review D, 58: 096007 (1998) doi: 10.1103/PhysRevD.58.096007 [21] H.-S. Zong and W.-M. Sun, Physical Review D, 78: 054001 (2008) doi: 10.1103/PhysRevD.78.054001 [22] H.-S. Zong and W.-M. Sun, International Journal of Modern Physics A, 23: 3591 (2008) doi: 10.1142/S0217751X08040457 [23] Y. Yan, J. Cao, X.-L. Luo et al., Physical Review D, 86: 114028 (2012) doi: 10.1103/PhysRevD.86.114028 [24] O. Benvenuto and G. Lugones, Physical Review D, 51: 1989 (1995) [25] C. C. Moustakidis, T. Gaitanos, C. Margaritis et al., Physical Review C, 95: 045801 (2017) doi: 10.1103/PhysRevC.95.045801 [26] P. Bedaque and A. W. Steiner, Physical Review Letters, 114: 031103 (2015) doi: 10.1103/PhysRevLett.114.031103 [27] I. Tews, J. Margueron, and S. Reddy, Physical Review C, 98: 045804 (2018) doi: 10.1103/PhysRevC.98.045804 [28] Q. Wang, T. Zhao, and H. Zong, arXiv: 1908.01325 (2019) [29] Q. Wang, C. Shi, and H.-S. Zong, Physical Review D, 100: 123003 (2019) doi: 10.1103/PhysRevD.100.123003

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Zi-Xiong Yu, Tong Zhao and ong-Shi Zong. New self-consistent mean field approximation and its application in three-flavor NJL model[J]. Chinese Physics C. doi: 10.1088/1674-1137/44/7/074104
Zi-Xiong Yu, Tong Zhao and ong-Shi Zong. New self-consistent mean field approximation and its application in three-flavor NJL model[J]. Chinese Physics C.
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## Self-consistent mean field approximation and application in three-flavor NJL model

###### Corresponding author: Hong-Shi Zong, zonghs@nju.edu.cn
• 1. Department of physics, Nanjing University, Nanjing 210093, China
• 2. Department of physics, AnHui Normal University, Wuhu 241000, China
• 3. Nanjing Proton Source Research and Design Center, Nanjing 210093, China

Abstract: In this study, we apply a self-consistent mean field approximation of the three-flavor Nambu–Jona-Lasinio (NJL) model and compare it with the two-flavor NJL model. The self-consistent mean field approximation introduces a new parameter, $\alpha$, that cannot be fixed in advance by the mean field approach itself. Due to the lack of experimental data, the parameter, $\alpha$, is undetermined. Hence, it is regarded as a free parameter and its influence on the chiral phase transition of strong interaction matter is studied based on this self-consistent mean field approximation. $\alpha$ affects numerous properties of the chiral phase transitions, such as the position of the phase transition point and the order of phase transition. Additionally, increasing $\alpha$ will decrease the number densities of different quarks and increase the chemical potential at which the number density of the strange quark is non-zero. Finally, we observed that $\alpha$ affects the equation of state (EOS) of the quark matter, and the sound velocity can be calculated to determine the stiffness of the EOS, which provides a good basis for studying the neutron star mass-radius relationship.

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