Four-loop vacuum energy density of the SU(Nc) + adjoint Higgs theory

Journal of High Energy Physics

Volumn 7, Issue 4, 2003, Pages 795-823

  Kajantie, Keijo ^a   Laine, Mikko ^b   Rummukainen, Kari ^c   Schröder, York ^d  

^a Department of Physical Sciences ^*  (Finland)

^b CERN   (Switzerland)

^c UNIVERSITY OF HELSINKI   (Finland)

^d MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Field Theories in Lower Dimensions; NLO Computations; QCD; Thermal Field Theory

Indexed keywords

EID: 23044441055     PISSN: 10298479     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2003/04/036     Document Type: Article

References (49)

1. S. Bronoff, R. Buffa and C.P. Korthals Altes, Phase diagram of 3d SU(3) gauge-adjoint Higgs system, hep-ph/9809452;
2. S. Bronoff and C.P. Korthals Altes, Phase diagram of 3d SU(3) gauge-adjoint Higgs system and C-violation in hot QCD, Phys. Lett. B 448 (1999) 85 [hep-ph/9811243].
3. A. Rajantie, SU(5) + adjoint Higgs model at finite temperature, Nucl. Phys. B 501 (1997) 521 [hep-ph/9702255];
4. K. Kajantie, M. Laine, A. Rajantie, K. Rummukainen and M. Tsypin, The phase diagram of three-dimensional SU(3) + adjoint Higgs theory, J. High Energy Phys. 11 (1998) 011 [hep-lat/9811004].
5. E. Braaten and A. Nieto, Free energy of QCD at high temperature, Phys. Rev. D 53 (1996) 3421 [hep-ph/9510408].
6. K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, How to resum long-distance contributions to the QCD pressure?, Phys. Rev. Lett. 86 (2001) 10 [hep-ph/0007109].
7. P. Arnold and C.-X. Zhai, The three loop free energy for pure gauge QCD, Phys. Rev. D 50 (1994) 7603 [hep-ph/9408276];
8. The three loop free energy for high temperature QED and QCD with fermions, Phys. Rev. D 51 (1995) 1906 [hep-ph/9410360].
9. 5, Phys. Rev. D 52 (1995) 7232 [hep-ph/9507380].
10. K. Kajantie, M. Laine, K. Rummukainen and M.E. Shaposhnikov, 3d SU(N) + adjoint Higgs theory and finite-temperature QCD, Nucl. Phys. B 503 (1997) 357 [hep-ph/9704416].
11. A.D. Linde, Infrared problem in thermodynamics of the Yang-Mills gas, Phys. Lett. B 96 (1980) 289.
12. D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and instantons at finite temperature, Rev. Mod. Phys. 53 (1981) 43.
13. P. Ginsparg, First order and second order phase transitions in gauge theories at finite temperature, Nucl. Phys. B 170 (1980) 388;
14. T. Appelquist and R.D. Pisarski, High-temperature Yang-Mills theories and three-dimensional Quantum Chromodynamics, Phys. Rev. D 23 (1981) 2305.
15. 6 ln(1/g), hep-ph/0211321.
16. Y. Schröder, Logarithmic divergence in the energy density of the three-dimensional Yang-Mills theory, in preparation.
17. K. Kajantie, M. Laine, K. Rummukainen and Y. Schröder, Measuring infrared contributions to the QCD pressure, Nucl. Phys. 106 (Proc. Suppl.) (2002) 525 [hep-lat/0110122];
18. Four-loop logarithms in 3d gauge + Higgs theory, hep-lat/0209072.
19. K. Kajantie, M. Laine and Y. Schröder, A simple way to generate high order vacuum graphs, Phys. Rev. D 65 (2002) 045008 [hep-ph/0109100].
20. M. Achhammer, The QCD partition function at high temperatures, Ph.D. thesis, University of Regensburg, July 2000, Logos-Verlag, Berlin 2001.
21. Y. Schröder, Automatic reduction of four-loop bubbles, Nucl. Phys. 116 (Proc. Suppl.) (2003) 402 [hep-ph/0211288].
22. J.A.M. Vermaseren, New features of form, math-ph/0010025, http://www.nikhef.nl/~form/.
23. K.G. Chetyrkin and F.V. Tkachov, Integration by parts: the algorithm to calculate beta functions in 4 loops, Nucl. Phys. B 192 (1981) 159;
24. F.V. Tkachov, A theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65.
25. S. Laporta, High-precision calculation of multi-loop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033].
26. MS̄ to four loops, Z. Physik C 54 (1992) 599.
27. K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3d physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis, Nucl. Phys. B 442 (1995) 317 [hep-lat/9412091].
28. M. Laine and A. Rajantie, Lattice-continuum relations for 3d SU(N) + Higgs theories, Nucl. Phys. B 513 (1998) 471 [hep-lat/9705003].
29. S.A. Larin and J.A.M. Vermaseren, The three loop QCD beta function and anomalous dimensions, Phys. Lett. B 303 (1993) 334 [hep-ph/9302208];
30. S.A. Larin, F.V. Tkachov and J.A.M. Vermaseren, The FORM version of Mincer, preprint NIKHEF-H-91-18.
31. E. Braaten and A. Nieto, Effective field theory approach to high temperature thermodynamics, Phys. Rev. D 51 (1995) 6990 [hep-ph/9501375].
32. 6 ln(g), hep-ph/0212283.
33. J.P. Blaizot, E. Iancu and A. Rebhan, On the apparent convergence of perturbative QCD at high temperature, hep-ph/0303045.
34. G. Cvetič and R. Kögerler, Resummations of free energy at high temperature, Phys. Rev. D 66 (2002) 105009 [hep-ph/0207291].
35. M. Strickland, Reorganizing finite temperature field theory, Int. J. Mod. Phys. A 16S1C (2001) 1277;
36. E. Braaten, Thermodynamics of hot QCD, Nucl. Phys. A 702 (2002) 13;
37. A. Peshier, Resummation of the QCD thermodynamic potential, Nucl. Phys. A 702 (2002) 128 [hep-ph/0110342];
38. J.O. Andersen, Hard thermal loops and QCD thermodynamics, hep-ph/0210195;
39. J.-P. Blaizot, E. Iancu and A. Rebhan, Thermodynamics of the high-temperature quark gluon plasma, hep-ph/0303185.
40. K. Farakos, K. Kajantie, K. Rummukainen and M.E. Shaposhnikov, 3d physics and the electroweak phase transition: perturbation theory, Nucl. Phys. B 425 (1994) 67 [hep-ph/9404201].
41. P.-N. Tan, B. Tekin and Y. Hosotani, Maxwell-Chern-Simons scalar electrodynamics at two loops, Nucl. Phys. B 502 (1997) 483 [hep-th/9703121].
42. J.O. Andersen, 3d effective field theory for finite temperature scalar electrodynamics, Phys. Rev. D 59 (1999) 065015 [hep-ph/9709418].
43. K. Kajantie, M. Karjalainen, M. Laine and J. Peisa, Three-dimensional U(1) gauge + Higgs theory as an effective theory for finite temperature phase transitions, Nucl. Phys. B 520 (1998) 345 [hep-lat/9711048].
44. c in 4-ε dimensions with minimal subtraction, Phys. Rev. B 65 (2002) 174512 [cond-mat/0109372].
45. S. Laporta, High-precision ε-expansions of massive four-loop vacuum bubbles, Phys. Lett. B 549 (2002) 115 [hep-ph/0210336].
46. A. Devoto and D.W. Duke, Table of integrals and formulae for Feynman diagram calculations, Riv. Nuovo Cim. 7N6 (1984) 1.
47. A. Vuorinen, Four-loop Feynman diagrams in three dimensions, Master's Thesis, Helsinki University, 2001 (unpublished) http://ethesis.helsinki.fi/ julkaisut/mat/fysii/pg/vuorinen/fourloop.pdf.
48. S. Groote, J.G. Korner and A.A. Pivovarov, Configuration space based recurrence relations for sunset-type diagrams, Eur. Phys. J. C 11 (1999) 279 [hep-ph/9903412].
49. A.K. Rajantie, Feynman diagrams to three loops in three-dimensional field theory, Nucl. Phys. B 480 (1996) 729 [hep-ph/9606216], erratum ibid. 513 (1996) 761.