Equation of state and thermodynamic properties of isospin imbalanced strongly interacting matter

Lu Qi; Chen Wei-Jie; Lu Zhen-Yan; Xu Ying; Li Xiang-Qian

doi:10.7498/aps.70.20210132

Abstract

The effects of temperature and baryon chemical potential on equation of state and thermodynamics of isospin imbalanced QCD matter are investigated in the framework of two-flavor Nambu−Jona-Lasinio model. The equation of state at zero temperature and baryon chemical potential as well as the isospin density and normalized pressure at finite temperature are shown to be consistent with the lattice data. We also find that the energy per isospin increases monotonically with the increase of isospin density at vanishing temperature and baryon chemical potential, while it first decreases and then increases with the augment of isospin density, behaving as a non-symmetric parabolic curve. Finally, we compute the sound velocity and find that it is discontinuous at the phase transition point for finite temperature and/or baryon chemical potential. In particular, the sound velocity in the superfluid phase is distinctly larger than that in the ordinary nuclear matter and quark matter, while the temperature and baryon chemical potential included in the superfluid phase makes the equation of state softer and the sound velocity slower.

Keywords:

Authors and contacts

1.
School of Physics and Electronic Science, Hunan University of Science and Technology, Xiangtan 411201, China
2.
College of Physics and Optoelectronic Engineering, Taiyuan University of Technology, Taiyuan 030024, China

Corresponding author: Lu Zhen-Yan, luzhenyan@hnust.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11947135), the Natural Science Foundation of Hunan Province, China (Grant Nos. 2018JJ2111, 2020JJ4284), the Scientific Research Project of Hunan University of Science and Technology, China (Grant No. E52059), and the Natural Science Foundation for Young Scientists of Shanxi Province, China (Grant No. 201901D211110)

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References

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Cited By

图 1 温度$T=0.124$ GeV时, 归一化同位旋密度$n_{\rm I}/T^3$ (上板面) 和归一化压强$\Delta P/T^4$ (下板面) 随同位旋化学势的变化关系. 蓝色实心圆表示取自文献[54]的格点数据

Figure 1. Normalized isospin density $n_{\rm I}/T^3$ (upper panel) and normalized pressure $\Delta P/T^4$ (lower panel) as functions of $\mu_{\rm I}/m_\pi$ at fixed $T=0.124$ GeV. The blue circles are taken from Ref.[54] for comparison.

DownLoad: Full-Size Img PowerPoint

图 2 不同重子化学势和温度下手征凝聚σ和pion凝聚Π随同位旋化学势变化关系

Figure 2. Chiral and pion condensates as functions of $\mu_{\rm I}/m_\pi$ at different baryon chemical potentials and temperatures.

DownLoad: Full-Size Img PowerPoint

图 3 不同重子化学势和温度下平均同位旋能量随同位旋密度的变化关系. 曲线的标记方式与图2相同

Figure 3. Energy per isospin as a function of the isospin density. Conventions for colors and symbols are the same used in Fig. 2.

DownLoad: Full-Size Img PowerPoint

图 4 不同重子化学势和温度下归一化同位旋密度$n_{\rm I}/m_\pi^3$随同位旋化学势的变化关系. 曲线的标记方式与图2相同

Figure 4. Normalized isospin density as a function of isospin chemical potential at various baryon chemical potentials and temperatures. Conventions for colors and lines are the same used in Fig. 2.

DownLoad: Full-Size Img PowerPoint

图 5 同位旋非对称物质热力学量分别随(a)同位旋化学势和(b)重子化学势变化得到的状态方程. 图(a)内插图的橙色阴影区域表示取自文献[40]的格点数据

Figure 5. The equation of state obtained with the variation of (a) isospin and (b) baryon chemical potentials respectively, while the orange shaded area denotes the lattice data taken from Ref.[40].

DownLoad: Full-Size Img PowerPoint

图 6 不同重子化学势和温度下声速平方随同位旋化学势的变化关系. 曲线的标记方式与图2相同

Figure 6. Sound velocity as a function of $\mu_{\rm I}/m_\pi$ at zero temperature at various baryon chemical potentials and temperatures. Conventions for colors and lines are the same used in Fig. 2.

DownLoad: Full-Size Img PowerPoint

map

[1]	Graf T, Schaffner-Bielich J, Fraga E S 2016 Phys. Rev. D 93 085030 Google Scholar
[2]	Xu J F, Peng G X, Lu Z Y, Cui S S 2015 Sci. China Phys. Mech. Astron. 58 042001 Google Scholar
[3]	Xu J F, Peng G X, Liu F, Hou D F, Chen L W 2015 Phys. Rev. D 92 025025 Google Scholar
[4]	Allton C, Ejiri S, Hands S, Kaczmarek O, Karsch F, Laermann E, Schmidt C 2003 Phys. Rev. D 68 014507 Google Scholar
[5]	Borsanyi S, Endrodi G, Fodor Z, Katz S D, Krieg S, Ratti C, Szabo K K 2012 JHEP 08 053 Google Scholar
[6]	Bazavov A, Ding H T, Hegde P, Kaczmarek O, Karsch F, Laermann E, Maezawa Y, Mukherjee S, Ohno H, Petreczky P, Sandmeyer H, Steinbrecher P, Schmidt C, Sharma S, Soeldner W, Wagner M 2017 Phys. Rev. D 95 054504 Google Scholar
[7]	Gasser J, Leutwyler H 1985 Nucl. Phys. B 250 465 Google Scholar
[8]	Balkin R, Serra J, Springmann K, Weiler A 2020 JHEP 07 221 Google Scholar
[9]	Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 122 345 Google Scholar
[10]	Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 124 246 Google Scholar
[11]	Hatsuda T, Kunihiro T 1994 Phys. Rep. 247 221 Google Scholar
[12]	Schaefer B J, Pawlowski J M, Wambach J 2007 Phys. Rev. D 76 074023 Google Scholar
[13]	Li X, Fu W J, Liu Y X 2019 Phys. Rev. D 99 074029 Google Scholar
[14]	沈婉萍, 尤仕佳, 毛鸿 2019 68 181101 Google Scholar Shen W P, You S J, Mao H 2019 Acta Phys. Sin. 68 181101 Google Scholar
[15]	Xu S S, Cui Z F, Wang B, Shi Y M, Yang Y C, Zong H S 2015 Phys. Rev. D 91 056003 Google Scholar
[16]	Gao F, Liu Y X 2016 Phys. Rev. D 94 094030 Google Scholar
[17]	Contant R, Huber M Q 2020 Phys. Rev. D 101 014016 Google Scholar
[18]	Peng G X, Chiang H C, Yang J J, Li L, Liu B 2000 Phys. Rev. C 61 015201 Google Scholar
[19]	Wen X J, Zhong X H, Peng G X, Shen P N, Ning P Z 2005 Phys. Rev. C 72 015204 Google Scholar
[20]	Xia C J, Peng G X, Chen S W, Lu Z Y, Xu J F 2014 Phys. Rev. D 89 105027 Google Scholar
[21]	Chu P C, Chen L W 2014 Astrophys. J. 780 135 Google Scholar
[22]	Chu P C, Zhou Y, Li X H, Zhang Z 2019 Phys. Rev. D 100 103012 Google Scholar
[23]	Peshier A, Kampfer B, Soff G 2000 Phys. Rev. C 61 045203 Google Scholar
[24]	Wen X J, Feng Z Q, Li N, Peng G X 2009 J. Phys. G 36 025011 Google Scholar
[25]	Cao J, Jiang Y, Sun W M, Zong H S 2012 Phys. Lett. B 711 65 Google Scholar
[26]	Son D T, Stephanov M A 2001 Phys. Rev. Lett. 86 592 Google Scholar
[27]	Kogut J B, Sinclair D K 2002 Phys. Rev. D 66 034505 Google Scholar
[28]	Kogut J B, Sinclair D K 2002 Phys. Rev. D 66 014508 Google Scholar
[29]	Kogut J B, Sinclair D K 2004 Phys. Rev. D 70 094501 Google Scholar
[30]	He L Y, Jin M, Zhuang P F 2005 Phys. Rev. D 71 116001 Google Scholar
[31]	He L Y, Jin M, Zhuang P F 2005 Phys. Lett. B 615 93 Google Scholar
[32]	Warringa H J, Boer D, Andersen J O 2005 Phys. Rev. D 72 014015 Google Scholar
[33]	Adhikari P, Andersen J O, Kneschke P 2019 Eur. Phys. J. C 79 874 Google Scholar
[34]	Adhikari P, Andersen J O 2020 JHEP 06 170 Google Scholar
[35]	Wu Z, Ping J, Zong H 2017 Chin. Phys. C 41 124106 Google Scholar
[36]	Xiong J, Jin M, Li J 2009 J. Phys. G 36 125005 Google Scholar
[37]	Xia T, He L, Zhuang P 2013 Phys. Rev. D 88 056013 Google Scholar
[38]	Mammarella A, Mannarelli M 2015 Phys. Rev. D 92 085025 Google Scholar
[39]	Mao S 2014 Phys. Rev. D 89 116006 Google Scholar
[40]	Brandt B B, Endrodii G, Fraga E S, Hippert M, Schaffner-Bielich J, Schmalzbauer S 2018 Phys. Rev. D 98 094510 Google Scholar
[41]	Chao J, Huang M, Radzhabov A 2020 Chin. Phys. C 44 034105 Google Scholar
[42]	Mannarelli M 2019 Particles 2 411 Google Scholar
[43]	Lu Z Y, Xia C J, Ruggieri M 2020 Eur. Phys. J. C 80 46 Google Scholar
[44]	Gatto R, Ruggieri M 2012 Phys. Rev. D 85 054013 Google Scholar
[45]	Borsanyi S, Fodor Z, Guenther J, Kampert K H, Katz S D, Kawanai T, Kovacs T G, Mages S W, Pasztor A, Pittler F, Redondo J, Ringwald A, Szabo K K 2016 Nature 539 69 Google Scholar
[46]	Lu Z Y, Du M L, Guo F K, Meißner U G, Vonk T 2020 JHEP 05 001 Google Scholar
[47]	Grilli C G, Hardy E, Pardo V J, Villadoro G 2016 JHEP 01 034 Google Scholar
[48]	Lu Z Y, Ruggieri M 2019 Phys. Rev. D 100 014013 Google Scholar
[49]	李昂, 胡金牛, 鲍世绍, 申虹, 徐仁新 2019 原子核物理评论 36 1 Google Scholar Li A, Hu J N, Bao S S, Shen H, Xu R X 2019 Nucl. Phys. Rev. 36 1 Google Scholar
[50]	Gorenstein M I, Yang S N 1995 Phys. Rev. D 52 5206 Google Scholar
[51]	Lu Z Y, Peng G X, Xu J F, Zhang S P 2016 Sci. China Phys. Mech. Astron. 59 662001 Google Scholar
[52]	Wen X J, Su S Z, Yang D H, Peng G X 2012 Phys. Rev. D 86 034006 Google Scholar
[53]	Zhuang P, Hufner J, Klevansky S P 1994 Nucl. Phys. A 576 525 Google Scholar
[54]	Brandt B B, EndrHodi G, Schmalzbauer S 2018 EPJ Web Conf. 175 07020 Google Scholar
[55]	Avancini S S, Bandyopadhyay A, Duarte D C, Farias R L S 2019 Phys. Rev. D 100 116002 Google Scholar
[56]	Farhi E, Jaffe R L 1984 Phys. Rev. D 30 2379 Google Scholar
[57]	Lu Z Y, Peng G X, Zhang S P, Ruggieri M, Greco V 2016 Nucl. Sci. Tech. 27 148 Google Scholar
[58]	Carignano S, Lepori L, Mammarella A, Mannarelli M, Pagliaroli G 2017 Eur. Phys. J. A 53 35 Google Scholar
[59]	Di Clemente F, Mannarelli M, Tonelli F 2020 Phys. Rev. D 101 103003 Google Scholar
[60]	Demorest P, Pennucci T, Ransom S, Roberts M, Hessels J 2010 Nature 467 1081 Google Scholar
[61]	Antoniadis J, Freire P, Wex N, et al. 2013 Science 340 6131 Google Scholar
[62]	Linares M, Shahbaz T, Casares J 2018 Astrophys. J. 859 54 Google Scholar
[63]	Cromartie H T, Fonseca E, Ransom S M, et al. 2019 Nature Astron. 4 72 Google Scholar
[64]	Reed B, Horowitz C 2020 Phys. Rev. C 101 045803 Google Scholar
[65]	Carignano S, Mammarella A, Mannarelli M 2016 Phys. Rev. D 93 051503 Google Scholar

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