Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature

  • Based on the Dyson-Schwinger Equations (DSEs), the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite-temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum m02-also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc=131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the "in-hadron condensate" for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m02(T) is almost flat in the temperature region from 0 to Tc, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m02(T)=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.
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  • [1] Shifman M A, Vainshtein A I, Zakharvov V. Nucl. Phys. B, 1979, 147: 385[2] Reinders L J, Rubinstein H, Yazaki S. Phys. Rep., 1985, 127: 1[3] Narison S. QCD Special Sum Rules. Singapore: World Scientific: 1989[4] ZHOU Li-Juan, Kisslinger L S, MA Wei-Xing. Phys. Rev. D, 2010, 82: 034037 [arXiv:hep-ph/0904.3558][5] Kisslinger L S, Linsuain O. arXiv: hep-ph/0110111; Kisslinger L S, Harly M A. arXiv: hep-ph/9906457; Novikov V A, Shifman M A, Vainshtein V I et al. Nucl. Phys. B, 1984, 237: 525[6] Takumi D, Noriyoshi I, Makoto O, Suganuma H. Nucl. Phys. A, 2003, 721: 934C ; Belyaev V M, Ioffe B L. Sov. Phys. JEPT, 1982, 56: 493; Roberts C D, Cahill R T, Sevior M E, Iannelle N. Phys. Rev. D, 1994, 49: 125; Polykov M V, Weiss C. Phys. Lett. B, 1996, 387: 841[7] GAO F, QIN S X, LIU Y X, Roberts C D et al. arXiv:nucl-th/1401.2406[8] Burden C J, Qian L, Roberts C D et al. Phys. Rev. C, 1997, 55: 2649 [arXiv:nucl-th/9605027][9] Blaschke D, Burau G, Kalinovsky Y L et al. Int. J. Mod. Phys. A, 2001, 16: 2267 [arXiv:nucl-th/0002024][10] ZHOU Li-Juan, PING Rong-Gang, MA Wei-Xing. Commun. Theor. Phys., 2004, 42: 875[11] Kisslinger L S, Meissner T. Phys. Rev. C, 1998, 57: 1528; Frank M R, Meissner T. Phys. Rev. C, 1996, 53: 2410 [arXiv: hep-ph/9511016]; Kisslinger L S, Aw M, Harey A, Linsuain O. Phys. Rev. C, 1999, 60: 065204[12] Roberts C, Schmidt S. Dyson-Schwinger equations: Density, temperature and continuum strong QCD, Progr. Part. Nucl. Phys., 2000, 45(Supplement1): 13[13] Matsubara T. Prog. Theor. Phys., 1955, 14: 351[14] Horvatic D, Blaschke D, Klabucar D, Radzhabov A E. Phys. Part. Nucl., 2008, 39: 1033 [arXiv:hep-ph/0703115][15] Kisslinger L S, Meissner T. Phys. Rev. C, 1998, 57: 1528 [arXiv:hep-ph/9706423][16] Meissner T. Phys. Lett. B, 1997, 405: 8[17] ZONG H S, LU X F, GU J Z, CHANG C H et al. Phys. Rev. C, 1999, 60: 055208 [arXiv:nucl-th/9906078][18] ZONG H S, LU X F, ZHAO E G, WANG F. Commun. Theor. Phys., 2000, 33: 687[19] ZHANG Z, ZHAO W Q. Phys. Lett. B, 2005, 610: 235 [arXiv:hep-ph/0406210][20] Narison S, Tarrach R. Phys. Lett. B, 1983, 125: 217[21] Gomez Nicola A, Pelaez J R, Ruiz de Elvira J. Phys. Rev. D, 2010, 82: 074012 [arXiv:hep-ph/1005.4370][22] Gomez Nicola A, Pelaez J R, Ruiz de Elvira J. Phys. Rev. D, 2013, 87: 016001 [arXiv:hep-ph/1210.7977][23] Maris P, Roberts C D. Phys. Rev. C, 1997, 56: 3369 [arXiv:nucl-th/9708029][24] Maris P, Roberts C D, Tandy P C. Phys. Lett. B, 1998, 420: 267 [arXiv:nucl-th/9707003][25] Brodsky S J, Roberts C D, Shrock R, Tandy P C. Phys. Rev. C, 2010, 82: 022201 [arXiv:nucl-th/1005.4610][26] Doi T, Ishii N, Oka M, Suganuma H. Phys. Rev. D, 2004, 70: 034510 [arXiv:hep-lat/0402005]
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ZHOU Li-Juan, ZHENG Bo, ZHONG Hong-Wei and MA Wei-Xing. Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature[J]. Chinese Physics C, 2015, 39(3): 033101. doi: 10.1088/1674-1137/39/3/033101
ZHOU Li-Juan, ZHENG Bo, ZHONG Hong-Wei and MA Wei-Xing. Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature[J]. Chinese Physics C, 2015, 39(3): 033101.  doi: 10.1088/1674-1137/39/3/033101 shu
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Received: 2014-03-28
Revised: 2014-08-20
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Temperature dependence of quarks and gluon vacuum condensate in the Dyson-Schwinger Equations at finite temperature

Abstract: Based on the Dyson-Schwinger Equations (DSEs), the two-quark vacuum condensate, the four-quark vacuum condensate, and the quark gluon mixed vacuum condensate in the non-perturbative QCD vacuum state are investigated by solving the DSEs with rainbow truncation at zero- and finite-temperature, respectively. These condensates are important input parameters in QCD sum rule with zero and finite temperature, and in studying hadron physics, as well as predicting the quark mean squared momentum m02-also called quark virtuality in the QCD vacuum state. The present calculated results show that these physical quantities are almost independent of the temperature below the critical point temperature Tc=131 MeV, and above Tc the chiral symmetry is restored. For comparison we calculate the temperature dependence of the "in-hadron condensate" for pion. At the same time, we also calculate the ratio of the quark gluon mixed vacuum condensate to the two-quark vacuum condensate by using these condensates, and the unknown quark mean squared momentum in the QCD vacuum state has been obtained. The results show that the ratio m02(T) is almost flat in the temperature region from 0 to Tc, although there are drastic changes of the quark vacuum condensate and the quark gluon mixed vacuum condensate at the region. Our predicted ratio comes out to be m02(T)=2.41 GeV2 at the Chiral limit, which is consistent with other theory model predictions, and strongly indicates the significance that the quark gluon mixed vacuum condensate has played in the virtuality calculations.

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