Chiral crossover transition in a finite volume

  • Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature Tc of the crossover, showing a significant decrease in Tc as L decreases below 3 fm.
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  • [1] J. Adams et al (STAR Collaboration), Nucl. Phys. A, 757:102 (2005)
    [2] E. Shuryak, Prog. Part. Nucl. Phys., 62:48 (2009)
    [3] E. Shuryak, Prog. Part. Nucl. Phys., 53:273 (2004)
    [4] W. A. Zajc, Nucl. Phys. A, 805:283 (2008)
    [5] E. Bilgici, F. Bruckmann, C. Gattringer, and C. Hagen, Phys. Rev. D, 77:094007 (2008)
    [6] C. S. Fischer, Phys. Rev. Lett., 103:052003 (2009)
    [7] G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, JHEP, 1104:001 (2011)
    [8] M. Asakawa and K. Yazaki, Nucl. Phys. A, 504:668 (1989)
    [9] A. Bazavov et al (HotQCD Collaboration), Phys. Rev. D, 90:094503 (2014)
    [10] C. Shi, Y. L. Wang, Y. Jiang, Z. F. Cui, and H. S. Zong, JHEP, 1407:014 (2014)
    [11] S. A. Bass et al, Prog. Part. Nucl. Phys., 41:255 (1998)
    [12] G. Graef, M. Bleicher, and Q. Li, Phys. Rev. C, 85:044901 (2012)
    [13] L. F. Palhares, E. S. Fraga, and T. Kodama, J. Phys. G, 38:085101 (2011)
    [14] J. Gasser and H. Leutwyler, Phys. Lett. B, 188:477 (1987)
    [15] F. C. Hansen, Nucl. Phys. B, 345:685 (1990).
    [16] P. H. Damgaard and H. Fukaya, JHEP, 0901:052 (2009)
    [17] J. Braun, B. Klein, and B. J. Schaefer, Phys. Lett. B, 713:216 (2012)
    [18] J. Braun, B. Klein, H.-J. Pirner, and A. H. Rezaeian, Phys. Rev. D, 73:074010 (2006)
    [19] A. Bhattacharyya, R. Ray, and S. Sur, Phys. Rev. D, 91(5):051501 (2015)
    [20] A. Bhattacharyya, P. Deb, S. K. Ghosh, R. Ray, and S. Sur, Phys. Rev. D, 87(5):054009 (2013)
    [21] Z. Pan, Z. F. Cui, C. H. Chang, and H. S. Zong, Int. J. Mod. Phys. A, 32(13):1750067 (2017)
    [22] C. D. Roberts, Prog. Part. Nucl. Phys., 61:50 (2008)
    [23] C. S. Fischer and J. Luecker, Phys. Lett. B, 718:1036 (2013)
    [24] C. Shi, Y. L. Du, S. S. Xu, X. J. Liu, and H. S. Zong, Phys. Rev. D, 93(3):036006 (2016)
    [25] J. Luecker, C. S. Fischer, and R. Williams, Phys. Rev. D, 81:094005 (2010)
    [26] B. Klein, Phys. Rept., 09:002 (2017)
    [27] C. D. Roberts and S. M. Schmidt, Prog. Part. Nucl. Phys., 45:S1 (2000)
    [28] P. Maris and P. C. Tandy, Phys. Rev. C, 60:055214 (1999)
    [29] A. Bazavov et al.:Phys. Rev. D 85:054503 (2012)
    [30] H.-T. Ding, A. Bazavov, F. Karsch, Y. Maezawa, S. Mukherjee, and P. Petreczky, PoS LATTICE, 2013:157 (2014)
    [31] A. Bazavov, H.-T. Ding, P. Hegde, F. Karsch, E. Laermann, S. Mukherjee, P. Petreczky, and C. Schmidt, Phys. Rev. D, 95(7):074505 (2017)
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11. Shi, C., He, X.-T., Jia, W.-B. et al. Chiral transition and the chiral charge density of the hot and dense QCD matter.[J]. Journal of High Energy Physics, 2020, 2020(6): 122. doi: 10.1007/JHEP06(2020)122
12. Zhao, Y.-P., Yin, P.-L., Yu, Z.-H. et al. Finite volume effects on chiral phase transition and pseudoscalar mesons properties from the Polyakov-Nambu-Jona-Lasinio model[J]. Nuclear Physics B, 2020. doi: 10.1016/j.nuclphysb.2020.114919
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Get Citation
Chao Shi, Wenbao Jia, An Sun, Liping Zhang and Hongshi Zong. Chiral crossover transition in a finite volume[J]. Chinese Physics C, 2018, 42(2): 023101. doi: 10.1088/1674-1137/42/2/023101
Chao Shi, Wenbao Jia, An Sun, Liping Zhang and Hongshi Zong. Chiral crossover transition in a finite volume[J]. Chinese Physics C, 2018, 42(2): 023101.  doi: 10.1088/1674-1137/42/2/023101 shu
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Received: 2017-11-09
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    Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment Technology in Huazhong University of Science Technology (DMETKF2015015)

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Chiral crossover transition in a finite volume

    Corresponding author: Chao Shi,
    Corresponding author: Wenbao Jia,
    Corresponding author: Hongshi Zong,
  • 1.  College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
  • 2.  College of Materials Science and Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
  • 3.  Key laboratory of road construction &
  • 4. College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China
  • 5. Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, CAS, Beijing 100190, China
  • 6. Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing 210093, China
Fund Project:  Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment Technology in Huazhong University of Science Technology (DMETKF2015015)

Abstract: Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature Tc of the crossover, showing a significant decrease in Tc as L decreases below 3 fm.

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