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In a mean-field approximation, we study the in-medium effective potential of the two-flavor quark meson model in the presence of a fermionic vacuum term at a finite temperature and density. There exists a crossover phase transition in the low-density region, and also there is a first-order phase transition in the high-density region accompanied by a critical end point. For the first-order phase transition, when the temperature is close to the critical temperature, the values of surface tension are calculated at various chemical potentials and we find that our results are very close to the results recently found in other chiral models with two flavors. Some consequences and possible applications of our results are also pointed out for the experiments on heavy ion collisions and the evolutions of the compact stars in their early stages.
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Keywords:
- quark-meson model /
- chiral phase transition /
- thermal field theory /
- surface tension
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图 1 在不同夸克化学势密度条件下, σ场的真空期望值随温度的演化行为
Fig. 1. Chiral condensate σ as a function of temperature at various chemical potential.
图 2 (a)
$\mu = 0$ MeV和(b)$\mu = 310$ MeV时, 有效势能随σ场的演化行为Fig. 2. Effective potential as a function of the chiral condensate σ for (a)
$\mu = 0$ MeV and (b)$\mu = 310$ MeV.
图 4
$T = {T_{\rm{c}}}$ 时表面张力与夸克化学势的演化关系Fig. 4. Surface tension as a function of a quark chemical potential when
$T = {T_{\rm{c}}}$ -
[1] Yagi K, Hatsuda T, Miake Y 2008 Quark-Gluon Plasma: From Big Bang to Little Bang (Vol. 23) (Cambridge: Cambridge University Press) pp12−20
[2] Fukushima K, Hatsuda T 2011 Rep. Prog. Phys. 74 014001
Google Scholar
[3] Braun-Munzinger P, Koch V, Schäfer T, Stachel J 2016 Phys. Rep. 621 76
Google Scholar
[4] Fodor Z, Katz S D 2009 arXiv: 0908.3341v1 [hep-ph]
[5] Ding H T, Karsch F, Mukherjee S 2015 Int. J. Mod. Phys. E 24 1530007
[6] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 122 345
Google Scholar
[7] Nambu Y, Jona-Lasinio G 1961 Phys. Rev. 124 246
Google Scholar
[8] Vogl U, Weise W 1991 Prog. Part. Nucl. Phys. 27 195
Google Scholar
[9] Klevansky S P 1992 Rev. Mod. Phys. 64 649
Google Scholar
[10] Hatsuda T, Kunihiro T 1994 Phys. Rep. 247 221
Google Scholar
[11] Buballa M 2005 Phys. Rep. 407 205
[12] Gell-Mann M, Lévy M 1960 Nuovo Cimento 16 705
Google Scholar
[13] Scavenius O, Mocsy A, Mishustin I N, Rischke D H 2001 Phys. Rev. C 64 045202
[14] Ring P, Schuck P 1980 The Nuclear Many- Body Problem (Heidelberg: Springer) pp189−215
[15] Serot B D, Walecka J D 1986 Advances in Nuclear Physics (Vol. l6) (New York: Plenum) pp1−311
[16] Serot B D, Walecka J D 1997 Int. J. Mod. Phys. E 6 515
[17] Scavenius O, Dumitru A, Fraga E S, Lenaghan J T, Jackson A D 2001 Phys. Rev. D 63 116003
Google Scholar
[18] Skokov V, Friman B, Nakano E, Redlich K, Schaefer B J 2010 Phys. Rev. D 82 034029
Google Scholar
[19] Luo X, Xu N 2017 Nucl. Sci. Tech. 28 112
Google Scholar
[20] Coleman S 1977 Phys. Rev. D 15 2929
[21] Coleman S 1977 Phys. Rev. D 16 1248
[22] Callan C G, Coleman J, Coleman S 1977 Phys. Rev. D 16 1762
Google Scholar
[23] Coleman S 1988 Aspects of Symmetry (Cambridge: Cambridge University Press) p416
[24] Linde A D 1983 Nucl. Phys. B 216 421
Google Scholar
[25] Palhares L F, Fraga E S 2010 Phys. Rev. D 82 125018
Google Scholar
[26] Garcia A F, Pinto M B 2013 Phys. Rev. C 88 025207
Google Scholar
[27] Schaefer B J, Pawlowski J M, Wambach J 2007 Phys. Rev. D 76 074023
Google Scholar
[28] Mao H, Jin S J, Huang M 2010 J. Phys. G: Nucl. Part. Phys. 37 035001
Google Scholar
[29] Jin S J, Mao H 2016 Phys. Rev. C 93 015202
Google Scholar
[30] Li Y Y, Hu J N, Mao H 2018 Phys. Rev. C 97 054313
[31] Mintz B W, Stiele R, Ramos R O, Schaffner-Bielich J 2013 Phys. Rev. D 87 036004
Google Scholar
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