Properties of the free energy density using the principle ofmaximum conformality

  • We present a detailed study on the properties of the free energy density at high temperature by applying the principle of maximum conformality (PMC) scale-setting method within effective field theory. The PMC utilizes the renormalization group equation recursively to identify the occurrence and pattern of the non-conformal {βi}-terms, and determines the optimal renormalization scale at each order. Our analysis shows that a more accurate free energy density up to gs5-order level without renormalization scale dependence can be achieved by applying the PMC. We also observe that by using a smaller factorization scale around the effective parameter mE, the PMC prediction is consistent with the lattice QCD prediction derived at low temperature.
      PCAS:
  • 加载中
  • [1] K. Kajantie, M. Laine, K. Rummukainen, and Y. Schroder, Phys. Rev. Lett., 86:10 (2001)
    [2] E. Braaten and A. Nieto, Phys. Rev. D, 53:3421 (1996)
    [3] G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Legeland, M. Lutgemeier, and B. Petersson, Nucl. Phys. B, 469:419 (1996)
    [4] M. Okamoto et al (CP-PACS Collaboration), Phys. Rev. D, 60:094510 (1999)
    [5] C. Bernard et al (MILC Collaboration), Phys. Rev. D, 71:034504 (2005)
    [6] Y. Aoki, Z. Fodor, S. D. Katz, and K. K. Szabo, JHEP, 0601:089 (2006)
    [7] C. Bernard et al, Phys. Rev. D, 75:094505 (2007)
    [8] M. Cheng et al, Phys. Rev. D, 77:01451 (2008)
    [9] G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, PoS LATTICE, 2007:228 (2007)
    [10] F. Di Renzo, M. Laine, Y. Schroder, and C. Torrero, JHEP, 0809:061 (2008)
    [11] A. Hietanen, K. Kajantie, M. Laine, K. Rummukainen, and Y. Schroder, Phys. Rev. D, 79:045018 (2009)
    [12] A. Bazavov et al, Phys. Rev. D, 80:014504 (2009)
    [13] S. Borsanyi, G. Endrodi, Z. Fodor, A. Jakovac, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, JHEP, 1011:077 (2010)
    [14] S. BorsSnyi, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szab_, PoS Lattice, 2010:171 (2014)
    [15] S. Borsanyi, G. Endrodi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, JHEP, 1208:053 (2012)
    [16] S. Borsanyi, G. Endrodi, Z. Fodor, S. D. Katz, and K. K. Szabo, JHEP, 1207:056 (2012)
    [17] S. Borsanyi et al, JHEP, 1208:126 (2012)
    [18] A. Bazavov et al (HotQCD Collaboration), Phys. Rev. D, 86:034509 (2012)
    [19] A. Bazavov et al, Phys. Rev. Lett., 109:192302 (2012)
    [20] O. Philipsen, Prog. Part. Nucl. Phys., 70:55 (2013)
    [21] S. Borsanyi, Z. Fodor, S. D. Katz, S. Krieg, C. Ratti, and K. K. Szabo, Phys. Rev. Lett., 111:062005 (2013)
    [22] A. Bazavov et al, Phys. Rev. Lett., 111:082301 (2013)
    [23] U. Gursoy, Acta Phys. Polon. B, 47:2509 (2016)
    [24] E. V. Shuryak, Sov. Phys. JETP, 47:212 (1978)
    [25] J. I. Kapusta, Nucl. Phys. B, 148:461 (1979)
    [26] T. Toimela, Phys. Lett., 124B:407 (1983)
    [27] P. B. Arnold and C. X. Zhai, Phys. Rev. D, 50:7603 (1994)
    [28] P. B. Arnold and C. X. Zhai, Phys. Rev. D, 51:1906 (1995)
    [29] C. X. Zhai and B. M. Kastening, Phys. Rev. D, 52:7232 (1995)
    [30] E. Braaten and A. Nieto, Phys. Rev. Lett., 76:1417 (1996)
    [31] K. Kajantie, M. Laine, K. Rummukainen, and Y. Schroder, Phys. Rev. D, 67:105008 (2003)
    [32] A. D. Linde, Rept. Prog. Phys., 42:389 (1979)
    [33] A. D. Linde, Phys. Lett., 96B:289 (1980)
    [34] D. J. Gross, R. D. Pisarski, and L. G. Yaffe, Rev. Mod. Phys., 53:43 (1981)
    [35] T. Matsubara, Prog. Theor. Phys., 14:351 (1955)
    [36] W. Celmaster and R. J. Gonsalves, Phys. Rev. D, 20:1420 (1979)
    [37] L. F. Abbott, Phys. Rev. Lett., 44:1569 (1980)
    [38] A. J. Buras, Rev. Mod. Phys., 52:199 (1980)
    [39] G. Grunberg, Phys. Lett., 95B:70 (1980)
    [40] P. M. Stevenson, Phys. Rev. D, 23:2916 (1981)
    [41] S. J. Brodsky, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D, 28:228 (1983)
    [42] X. G. Wu, S. J. Brodsky, and M. Mojaza, Prog. Part. Nucl. Phys., 72:44 (2013)
    [43] X. G. Wu, Y. Ma, S. Q. Wang, H. B. Fu, H. H. Ma, S. J. Brodsky, and M. Mojaza, Rept. Prog. Phys., 78 (2015) 126201.
    [44] M. Gell-Mann and F. E. Low, Phys. Rev., 95:1300 (1954)
    [45] M. Beneke, Phys. Rept., 317:1 (1999)
    [46] E. Gardi and G. Grunberg, Phys. Lett. B, 517:215 (2001)
    [47] F. Karsch, A. Patkos, and P. Petreczky, Phys. Lett. B, 401:69 (1997)
    [48] S. Chiku and T. Hatsuda, Phys. Rev. D, 58:076001 (1998)
    [49] J. O. Andersen, E. Braaten, and M. Strickland, Phys. Rev. D, 61:074016 (2000)
    [50] J. O. Andersen, E. Braaten, and M. Strickland, Phys. Rev. Lett., 83:2139 (1999)
    [51] J. O. Andersen, E. Braaten, and M. Strickland, Phys. Rev. D, 63:105008 (2001)
    [52] J. O. Andersen, L. E. Leganger, M. Strickland, and N. Su, Phys. Lett. B, 696:468 (2011)
    [53] J. O. Andersen, L. E. Leganger, M. Strickland, and N. Su, JHEP, 1108:053 (2011)
    [54] N. Haque, M. G. Mustafa, and M. Strickland, Phys. Rev. D, 87:no. 10, 105007 (2013)
    [55] N. Haque, A. Bandyopadhyay, J. O. Andersen, M. G. Mustafa, M. Strickland, and N. Su, JHEP, 1405:027 (2014)
    [56] M. Strickland, J. O. Andersen, A. Bandyopadhyay, N. Haque, M. G. Mustafa, and N. Su, Nucl. Phys. A, 931:841 (2014)
    [57] N. Haque, PoS ICPAQGP, 2015:057 (2017)
    [58] B. M. Kastening, Phys. Rev. D, 56:8107 (1997)
    [59] T. Hatsuda, Phys. Rev. D, 56:8111 (1997)
    [60] G. Cvetic and R. Kogerler, Phys. Rev. D, 66:105009 (2002)
    [61] G. Cvetic and R. Kogerler, Phys. Rev. D, 70:114016 (2004)
    [62] T. Hatsuda and T. Kunihiro, Phys. Rept., 247:221 (1994)
    [63] K. Fukushima, Phys. Rev. D, 68:045004 (2003)
    [64] K. Fukushima, Phys. Lett. B, 591:277 (2004)
    [65] C. Ratti, M. A. Thaler, and W. Weise, Phys. Rev. D, 73:014019 (2006)
    [66] S. Mukherjee, M. G. Mustafa, and R. Ray, Phys. Rev. D, 75:094015 (2007)
    [67] A. Bhattacharyya, P. Deb, S. K. Ghosh, and R. Ray, Phys. Rev. D, 82:014021 (2010)
    [68] A. Bhattacharyya, P. Deb, A. Lahiri, and R. Ray, Phys. Rev. D, 83:014011 (2011)
    [69] M. Bluhm and B. Kampfer, Phys. Rev. D, 77:034004 (2008)
    [70] V. M. Bannur, JHEP, 0709:046 (2007)
    [71] V. M. Bannur, Phys. Rev. C, 78:045206 (2008)
    [72] F. G. Gardim and F. M. Steffens, Nucl. Phys. A, 825:222 (2009)
    [73] B. J. Schaefer, M. Wagner, and J. Wambach, PoS CPOD, 2009:017 (2009)
    [74] B. J. Schaefer, M. Wagner, and J. Wambach, Phys. Rev. D, 81:074013 (2010)
    [75] V. Skokov, B. Friman, and K. Redlich, Phys. Rev. C, 83:054904 (2011)
    [76] S. J. Brodsky and X. G. Wu, Phys. Rev. D, 85:034038 (2012)
    [77] S. J. Brodsky and X. G. Wu, Phys. Rev. Lett., 109:042002 (2012)
    [78] M. Mojaza, S. J. Brodsky, and X. G. Wu, Phys. Rev. Lett., 110:192001 (2013)
    [79] S. J. Brodsky, M. Mojaza, and X. G. Wu, Phys. Rev. D, 89:014027 (2014)
    [80] X. G. Wu, J. M. Shen, B. L. Du, and S. J. Brodsky, arXiv:1802.09154[hep-ph].
    [81] X. G. Wu, S. Q. Wang, and S. J. Brodsky, Front. Phys., 11:111201 (2016)
    [82] P. H. Ginsparg, Nucl. Phys. B, 170:388 (1980)
    [83] T. Appelquist and R. D. Pisarski, Phys. Rev. D, 23:2305 (1981)
    [84] S. Nadkarni, Phys. Rev. D, 27:917 (1983)
    [85] A. Bazavov, N. Brambilla, X. Garcia i Tormo, P. Petreczky, J. Soto, and A. Vairo, Phys. Rev. D, 907:074038 (2014)
    [86] S. Q. Wang, X. G. Wu, S. J. Brodsky, and M. Mojaza, Phys. Rev. D, 94:053003 (2016)
    [87] S. Q. Wang, X. G. Wu, X. C. Zheng, G. Chen, and J. M. Shen, J. Phys. G, 41:075010 (2014)
  • 加载中

Get Citation
Shi Bu, Xing-Gang Wu, Jian-Ming Shen and Jun Zeng. Properties of the free energy density using the principle ofmaximum conformality[J]. Chinese Physics C, 2018, 42(8): 083105. doi: 10.1088/1674-1137/42/8/083105
Shi Bu, Xing-Gang Wu, Jian-Ming Shen and Jun Zeng. Properties of the free energy density using the principle ofmaximum conformality[J]. Chinese Physics C, 2018, 42(8): 083105.  doi: 10.1088/1674-1137/42/8/083105 shu
Milestone
Received: 2018-04-08
Fund

    Supported by Natural Science Foundation of China (11625520)

Article Metric

Article Views(835)
PDF Downloads(11)
Cited by(0)
Policy on re-use
To reuse of Open Access content published by CPC, for content published under the terms of the Creative Commons Attribution 3.0 license (“CC CY”), the users don’t need to request permission to copy, distribute and display the final published version of the article and to create derivative works, subject to appropriate attribution.
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Email This Article

Title:
Email:

Properties of the free energy density using the principle ofmaximum conformality

  • 1. Department of Physics, Chongqing University, Chongqing 401331, China
Fund Project:  Supported by Natural Science Foundation of China (11625520)

Abstract: We present a detailed study on the properties of the free energy density at high temperature by applying the principle of maximum conformality (PMC) scale-setting method within effective field theory. The PMC utilizes the renormalization group equation recursively to identify the occurrence and pattern of the non-conformal {βi}-terms, and determines the optimal renormalization scale at each order. Our analysis shows that a more accurate free energy density up to gs5-order level without renormalization scale dependence can be achieved by applying the PMC. We also observe that by using a smaller factorization scale around the effective parameter mE, the PMC prediction is consistent with the lattice QCD prediction derived at low temperature.

    HTML

Reference (87)

目录

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return