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Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

  • Regular Article - Theoretical Physics
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Abstract

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.

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References

  1. A. Bazavov et al., arXiv:0903.4379 [hep-lat]

  2. Y. Aoki, Z. Fodor, S.D. Katz, K.K. Szabo, Phys. Lett. B 643, 46 (2006). arXiv:hep-lat/0609068

    Article  ADS  Google Scholar 

  3. M. Cheng et al., arXiv:0911.2215 [hep-lat]

  4. M. Cheng et al., arXiv:0911.3450 [hep-lat]

  5. Y. Aoki, S. Borsanyi, S. Durr, Z. Fodor, S.D. Katz, S. Krieg, K.K. Szabo, J. High Energy Phys. 0906, 088 (2009). arXiv:0903.4155 [hep-lat]

    Article  ADS  Google Scholar 

  6. Y. Aoki, G. Endrodi, Z. Fodor, S.D. Katz, K.K. Szabo, Nature 443, 675 (2006). arXiv:hep-lat/0611014

    Article  ADS  Google Scholar 

  7. F. Karsch, M. Lütgemeier, Nucl. Phys. Proc. Suppl. 73, 444 (1999)

    Article  MATH  ADS  Google Scholar 

  8. F. Karsch, M. Lütgemeier, Nucl. Phys. B 550, 449 (1999)

    Article  ADS  Google Scholar 

  9. J. Engels, S. Holtmann, T. Schulze, Nucl. Phys. B 724, 357 (2005). arXiv:hep-lat/0505008

    Article  ADS  Google Scholar 

  10. F. Karsch, E. Laermann, arXiv:hep-lat/0305025

  11. E. Bilgici, F. Bruckmann, C. Gattringer, C. Hagen, Phys. Rev. D 77, 094007 (2008). arXiv:0801.4051 [hep-lat]

    Article  ADS  Google Scholar 

  12. C. Gattringer, Phys. Rev. Lett. 97, 032003 (2006). arXiv:hep-lat/0605018

    Article  MathSciNet  ADS  Google Scholar 

  13. F. Bruckmann, C. Gattringer, C. Hagen, Phys. Lett. B 647, 56 (2007). arXiv:hep-lat/0612020

    Article  MathSciNet  ADS  Google Scholar 

  14. F. Synatschke, A. Wipf, C. Wozar, Phys. Rev. D 75, 114003 (2007). arXiv:hep-lat/0703018

    Article  ADS  Google Scholar 

  15. F. Synatschke, A. Wipf, K. Langfeld, Phys. Rev. D 77, 114018 (2008). arXiv:0803.0271 [hep-lat]

    Article  ADS  Google Scholar 

  16. E. Bilgici, C. Gattringer, J. High Energy Phys. 0805, 030 (2008). arXiv:0803.1127 [hep-lat]

    Article  ADS  Google Scholar 

  17. J. Danzer, C. Gattringer, A. Maas, J. High Energy Phys. 0901, 024 (2009). arXiv:0810.3973 [hep-lat]

    Article  MathSciNet  ADS  Google Scholar 

  18. E. Bilgici, C. Gattringer, E.M. Ilgenfritz, A. Maas, J. High Energy Phys. 0911, 035 (2009). arXiv:0904.3450 [hep-lat]

    Article  ADS  Google Scholar 

  19. C.S. Fischer, Phys. Rev. Lett. 103, 052003 (2009). arXiv:0904.2700 [hep-ph]

    Article  ADS  Google Scholar 

  20. C.S. Fischer, J.A. Mueller, Phys. Rev. D 80, 074029 (2009). arXiv:0908.0007 [hep-ph]

    Article  ADS  Google Scholar 

  21. E. Bilgici, F. Bruckmann, J. Danzer, C. Gattringer, C. Hagen, E.M. Ilgenfritz, A. Maas, Few Body Syst. 47, 125 (2010). arXiv:0906.3957 [hep-lat]

    Article  ADS  Google Scholar 

  22. W. Söldner, PoS LAT2007, 222 (2007). arXiv:0710.2707 [hep-lat]

    Google Scholar 

  23. J. Braun, L.M. Haas, F. Marhauser, J.M. Pawlowski, arXiv:0908.0008 [hep-ph]

  24. A. Roberge, N. Weiss, Nucl. Phys. B 275, 734 (1986)

    Article  ADS  Google Scholar 

  25. P. de Forcrand, O. Philipsen, Nucl. Phys. B 642, 290 (2002). arXiv:hep-lat/0205016

    Article  MATH  ADS  Google Scholar 

  26. A. Cucchieri, A. Maas, T. Mendes, Phys. Rev. D 75, 076003 (2007). arXiv:hep-lat/0702022

    Article  ADS  Google Scholar 

  27. R. Alkofer, L. von Smekal, Phys. Rept. 353, 281 (2001). arXiv:hep-ph/0007355

    Article  MATH  ADS  Google Scholar 

  28. C.S. Fischer, J. Phys. G 32, R253 (2006). arXiv:hep-ph/0605173

    Article  ADS  Google Scholar 

  29. C.D. Roberts, S.M. Schmidt, Prog. Part. Nucl. Phys. 45, S1 (2000). arXiv:nucl-th/0005064

    Article  ADS  Google Scholar 

  30. B.J. Schaefer, J. Wambach, Phys. Part. Nucl. 39, 1025 (2008). arXiv:hep-ph/0611191

    Article  Google Scholar 

  31. H. Gies, arXiv:hep-ph/0611146

  32. J.M. Pawlowski, Ann. Phys. 322, 2831 (2007). arXiv:hep-th/0512261

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. I. Zahed, D. Zwanziger, Phys. Rev. D 61, 037501 (2000). arXiv:hep-th/9905109

    Article  ADS  Google Scholar 

  34. A. Maas, J. Wambach, R. Alkofer, Eur. Phys. J. C 42, 93 (2005). arXiv:hep-ph/0504019

    Article  ADS  Google Scholar 

  35. A. Maas, J. Wambach, B. Grüter, R. Alkofer, Eur. Phys. J. C 37(3), 335 (2004). arXiv:hep-ph/0408074

    Article  ADS  Google Scholar 

  36. A. Maas, arXiv:0911.0348 [hep-lat]

  37. S. Furui, H. Nakajima, Few Body Syst. 40, 101 (2006). arXiv:hep-lat/0612009

    Article  ADS  Google Scholar 

  38. A. Cucchieri, A. Maas, T. Mendes, Phys. Rev. D 74, 014503 (2006). arXiv:hep-lat/0605011

    Article  ADS  Google Scholar 

  39. F. Karsch, J. Rank, Nucl. Phys. Proc. Suppl. 42, 508 (1995)

    Article  ADS  Google Scholar 

  40. A. Cucchieri, F. Karsch, P. Petreczky, Phys. Lett. B 497, 80 (2001). arXiv:hep-lat/0004027

    Article  ADS  Google Scholar 

  41. A. Cucchieri, F. Karsch, P. Petreczky, Phys. Rev. D 64, 036001 (2001). arXiv:hep-lat/0103009

    Article  ADS  Google Scholar 

  42. A. Cucchieri, T. Mendes, Nucl. Phys. B 471, 263 (1996). arXiv:hep-lat/9511020

    Article  ADS  Google Scholar 

  43. A. Maas, arXiv:0907.5185 [hep-lat]

  44. A. Maas, Phys. Rev. D 79, 014505 (2009). arXiv:0808.3047 [hep-lat]

    Article  ADS  Google Scholar 

  45. I.L. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker, A. Sternbeck, PoS LATTICE2009, 237 (2009). arXiv:0912.2249 [hep-lat]

    Google Scholar 

  46. I.L. Bogolubsky, V.G. Bornyakov, G. Burgio, E.M. Ilgenfritz, M. Muller-Preussker, V.K. Mitrjushkin, Phys. Rev. D 77, 014504 (2008). Erratum. ibid. D 77 (2008) 039902. arXiv:0707.3611 [hep-lat]

    Article  ADS  Google Scholar 

  47. P.J. Silva, O. Oliveira, Nucl. Phys. B 690, 177 (2004). arXiv:hep-lat/0403026

    Article  MATH  ADS  Google Scholar 

  48. A. Maas, Š. Olejník, J. High Energy Phys. 0802, 070 (2008). arXiv:0711.1451 [hep-lat]

    Article  ADS  Google Scholar 

  49. J. Fingberg, U.M. Heller, F. Karsch, Nucl. Phys. B 392, 493 (1993). arXiv:hep-lat/9208012

    Article  ADS  Google Scholar 

  50. B. Lucini, M. Teper, U. Wenger, J. High Energy Phys. 0401, 061 (2004). arXiv:hep-lat/0307017

    Article  MathSciNet  ADS  Google Scholar 

  51. A. Cucchieri, T. Mendes, A.R. Taurines, Phys. Rev. D 67, 091502 (2003). arXiv:hep-lat/0302022

    Article  ADS  Google Scholar 

  52. A. Maas, work in progress

  53. M.N. Chernodub, E.M. Ilgenfritz, Phys. Rev. D 78, 034036 (2008). arXiv:0805.3714 [hep-lat]

    Article  ADS  Google Scholar 

  54. D. Dudal, J.A. Gracey, N. Vandersickel, D. Vercauteren, H. Verschelde, Phys. Rev. D 80, 065017 (2009). arXiv:0907.0380 [hep-th]

    Article  ADS  Google Scholar 

  55. R. Alkofer, W. Detmold, C.S. Fischer, P. Maris, Nucl. Phys. Proc. Suppl. 141, 122 (2005). arXiv:hep-ph/0309078

    Article  ADS  Google Scholar 

  56. R. Alkofer, W. Detmold, C.S. Fischer, P. Maris, Phys. Rev. D 70, 014014 (2004). arXiv:hep-ph/0309077

    Article  ADS  Google Scholar 

  57. J.S. Ball, T.W. Chiu, Phys. Rev. D 22, 2542 (1980)

    Article  ADS  Google Scholar 

  58. C.S. Fischer, R. Williams, Phys. Rev. D 78, 074006 (2008). arXiv:0808.3372 [hep-ph]

    Article  ADS  Google Scholar 

  59. P.V. Buividovich, E.V. Luschevskaya, M.I. Polikarpov, Phys. Rev. D 78, 074505 (2008). arXiv:0809.3075 [hep-lat]

    Article  ADS  Google Scholar 

  60. J. Braun, H. Gies, J.M. Pawlowski, Phys. Lett. B 684, 262 (2010). arXiv:0708.2413 [hep-th]

    Article  ADS  Google Scholar 

  61. F. Marhauser, J.M. Pawlowski, arXiv:0812.1144 [hep-ph]

  62. R. Brun, F. Rademakers, Nucl. Instrum. Methods A 389, 81 (1997)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289, Darmstadt, Germany

    Christian S. Fischer & Jens A. Müller

  2. GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291, Darmstadt, Germany

    Christian S. Fischer

  3. Institut für Physik, Karl-Franzens Universität Graz, Universitätsplatz 5, 8010, Graz, Austria

    Axel Maas

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  1. Christian S. Fischer
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  2. Axel Maas
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  3. Jens A. Müller
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Correspondence to Jens A. Müller.

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Fischer, C.S., Maas, A. & Müller, J.A. Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3). Eur. Phys. J. C 68, 165–181 (2010). https://doi.org/10.1140/epjc/s10052-010-1343-1

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  • DOI: https://doi.org/10.1140/epjc/s10052-010-1343-1

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