The one loop MS̄ static potential in the Gribov-Zwanziger Lagrangian

Journal of High Energy Physics

Volumn 2010, Issue 2, 2010, Pages

  Gracey, J A ^a  

^a UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

Confinement; NLO computations; QCD

Indexed keywords

EID: 77954944577     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1007/JHEP02(2010)009     Document Type: Article

References (91)

1. D.J. Gross and F. Wilczek, Ultraviolet behavior of non-abelian gauge theories, Phys. Rev. Lett. 30 (1973) 1343 [SPIRES].
2. H.D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett. 30 (1973) 1346 [SPIRES].
3. S. Perantonis and C. Michael, Static potentials and hybrid mesons from pure SU(3) lattice gauge theory, Nucl. Phys. B 347 (1990) 854 [SPIRES].
4. C. Michael, The running coupling from lattice gauge theory, Phys. Lett. B 283 (1992) 103 [hep-lat/9205010] [SPIRES].
5. G.S. Bali, K. Schilling and A. Wachter, Complete O(v2) corrections to the static interquark potential from SU(3) gauge theory, Phys. Rev. D 56 (1997) 2566 [hep-lat/9703019] [SPIRES].
6. S. Mandelstam, General introduction to confinement, Phys. Rept. 67 (1980) 109 [SPIRES].
7. R. Anishetty, M. Baker, S.K. Kim, J.S. Ball and F. Zachariasen, Infrared properties of the coupling constant in nonabelian gauge theories, Phys. Lett. B 86 (1979) 52 [SPIRES].
8. S. Mandelstam, Approximation scheme for QCD, Phys. Rev. D 20 (1979) 3223 [SPIRES].
9. G.B. West, Confinement, the Wilson loop and the gluon propagator, Phys. Lett. B 115 (1982) 468 [SPIRES].
10. V.N. Gribov, Quantization of non-Abelian gauge theories, Nucl. Phys. B 139 (1978) 1 [SPIRES].
11. D. Zwanziger, Nonperturbative modification of the Faddeev-Popov formula and banishment of the naive vacuum, Nucl. Phys. B 209 (1982) 336 [SPIRES].
12. D. Zwanziger, Action from the Gribov horizon, Nucl. Phys. B 321 (1989) 591 [SPIRES].
13. D. Zwanziger, Local and renormalizable action from the Gribov horizon, Nucl. Phys. B 323 (1989) 513 [SPIRES].
14. G. Dell'Antonio and D. Zwanziger, Ellipsoidal bound on the Gribov horizon contradicts the perturbative renormalization group, Nucl. Phys. B 326 (1989) 333 [SPIRES].
15. G. Dell'Antonio and D. Zwanziger, Every gauge orbit passes inside the Gribov horizon, Commun. Math. Phys. 138 (1991) 291 [SPIRES].
16. D. Zwanziger, Vanishing of zero momentum lattice gluon propagator and color confinement, Nucl. Phys. B 364 (1991) 127 [SPIRES].
17. D. Zwanziger, Critical limit of lattice gauge theory, Nucl. Phys. B 378 (1992) 525 [SPIRES].
18. D. Zwanziger, Renormalizability of the critical limit of lattice gauge theory by BRS invariance, Nucl. Phys. B 399 (1993) 477 [SPIRES].
19. D. Zwanziger, Fundamental modular region, Boltzmann factor and area law in lattice gauge theory, Nucl. Phys. B 412 (1994) 657 [SPIRES].
20. D. Zwanziger, Non-perturbative Landau gauge and infrared critical exponents in QCD, Phys. Rev. D 65 (2002) 094039 [hep-th/0109224] [SPIRES].
21. D. Zwanziger, Non-perturbative Faddeev-Popov formula and infrared limit of QCD, Phys. Rev. D 69 (2004) 016002 [hep-ph/0303028] [SPIRES].
22. A. Cucchieri and T. Mendes, What's up with IR gluon and ghost propagators in Landau gauge? A puzzling answer from huge lattices, PoS(LATTICE 2007)297 [arXiv:0710.0412] [SPIRES].
23. I.L. Bogolubsky, E.M. Ilgenfritz, M. Müller-Preussker and A. Sternbeck, The Landau gauge gluon and ghost propagators in 4D SU(3) gluodynamics in large lattice volumes, PoS(LATTICE 2007)290 [arXiv:0710.1968] [SPIRES].
24. A. Cucchieri and T. Mendes, Constraints on the IR behavior of the gluon propagator in Yang-Mills theories, Phys. Rev. Lett. 100 (2008) 241601 [arXiv:0712.3517] [SPIRES].
25. A. Cucchieri and T. Mendes, Constraints on the IR behavior of the ghost propagator in Yang-Mills theories, Phys. Rev. D 78 (2008) 094503 [arXiv:0804.2371] [SPIRES].
26. O. Oliveira and P.J. Silva, Does the lattice zero momentum gluon propagator for pure gauge SU(3) Yang-Mills theory vanish in the infinite volume limit?, Phys. Rev. D 79 (2009) 031501 [arXiv:0809.0258] [SPIRES].
27. P. Boucaud et al., On the IR behaviour of the Landau-gauge ghost propagator, JHEP 06 (2008) 099 [arXiv:0803.2161] [SPIRES].
28. A.C. Aguilar, D. Binosi and J. Papavassiliou, Gluon and ghost propagators in the Landau gauge: deriving lattice results from Schwinger-Dyson equations, Phys. Rev. D 78 (2008) 025010 [arXiv:0802.1870] [SPIRES].
29. C.S. Fischer, A. Maas and J.M. Pawlowski, On the infrared behavior of Landau gauge Yang-Mills theory, Annals Phys. 324 (2009) 2408 [arXiv:0810.1987] [SPIRES].
30. N. Maggiore and M. Schaden, Landau gauge within the Gribov horizon, Phys. Rev. D 50 (1994) 6616 [hep-th/9310111] [SPIRES].
31. D. Dudal, R.F. Sobreiro, S.P. Sorella and H. Verschelde, The Gribov parameter and the dimension two gluon condensate in euclidean Yang-Mills theories in the Landau gauge, Phys. Rev. D 72 (2005) 014016 [hep-th/0502183] [SPIRES].
32. J.A. Gracey, Two loop correction to the Gribov mass gap equation in Landau gauge QCD, Phys. Lett. B 632 (2006) 282 [hep-ph/0510151] [SPIRES].
33. s in the Gribov-Zwanziger QCD lagrangian, JHEP 05 (2006) 052 [hep-ph/0605077] [SPIRES].
34. T. Kugo and I. Ojima, Local covariant operator formalism of nonabelian gauge theories and quark confinement problem, Prog. Theor. Phys. Suppl. 66 (1979) 1 [Erratum ibid. 77 (1984) 1121] [SPIRES].
35. T. Kugo, The universal renormalization factors Z1/Z3 and color confinement condition in non-abelian gauge theory, hep-th/9511033 [SPIRES].
36. L. Susskind, Coarse grained quantum chromodynamics, in Les Houches 1976, Proceedings Weak and Electromagnetic Interactions at High Energy, North-Holland Publishing Company, Amsterdam, The Netherlands (1977).
37. W. Fischler, Quark-anti-quark potential in QCD, Nucl. Phys. B 129 (1977) 157 [SPIRES].
38. T. Appelquist, M. Dine and I.J. Muzinich, The static limit of quantum chromodynamics, Phys. Rev. D 17 (1978) 2074 [SPIRES].
39. M. Peter, The static quark-antiquark potential in QCD to three loops, Phys. Rev. Lett. 78 (1997) 602 [hep-ph/9610209] [SPIRES].
40. M. Peter, The static potential in QCD: a full two-loop calculation, Nucl. Phys. B 501 (1997) 471 [hep-ph/9702245] [SPIRES].
41. Y. Schröder, The static potential in QCD, DESY-THESIS-1999-2021 [SPIRES].
42. Y. Schröder, The static potential in QCD to two loops, Phys. Lett. B 447 (1999) 321 [hep-ph/9812205] [SPIRES].
43. B.A. Kniehl, A.A. Penin, Y. Schröder, V.A. Smirnov and M. Steinhauser, Two-loop static QCD potential for general colour state, Phys. Lett. B 607 (2005) 96 [hep-ph/0412083] [SPIRES].
44. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Fermionic contributions to the three-loop static potential, Phys. Lett. B 668 (2008) 293 [arXiv:0809.1927] [SPIRES].
45. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Applying Mellin-Barnes technique and Gröbner bases to the three-loop static potential, PoS(RAD COR 2007)024 [arXiv:0805.1871] [SPIRES].
46. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Evaluating the three-loop static quark potential, Nucl. Phys. Proc. Suppl. 183 (2008) 308 [arXiv:0807.0365] [SPIRES].
47. C. Anzai, Y. Kiyo and Y. Sumino, Static QCD potential at three-loop order, arXiv:0911.4335 [SPIRES].
48. A.V. Smirnov, V.A. Smirnov and M. Steinhauser, Three-loop static potential, arXiv:0911.4742 [SPIRES].
49. Y.M. Makeenko, Introduction to gauge theory, Surveys High Energ. Phys. 10 (1997) 1 [SPIRES].
50. D. Zwanziger, Some exact infrared properties of gluon and ghost propagators and long-range force in QCD, arXiv:0904.2380 [SPIRES].
51. J.C. Taylor, Ward Identities and charge renormalization of the Yang-Mills field, Nucl. Phys. B 33 (1971) 436 [SPIRES].
52. D. Dudal, S.P. Sorella, N. Vandersickel and H. Verschelde, New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach, Phys. Rev. D 77 (2008) 071501 [arXiv:0711.4496] [SPIRES].
53. D. Dudal, J.A. Gracey, S.P. Sorella, N. Vandersickel and H. Verschelde, A refinement of the Gribov-Zwanziger approach in the Landau gauge: infrared propagators in harmony with the lattice results, Phys. Rev. D 78 (2008) 065047 [arXiv:0806.4348] [SPIRES].
54. J.G.M. Gatheral, Exponentiation of eikonal cross-sections in nonabelian gauge theories, Phys. Lett. B 133 (1983) 90 [SPIRES].
55. J. Frenkel and J.C. Taylor, Nonabelian eikonal exponentiation, Nucl. Phys. B 246 (1984) 231 [SPIRES].
56. S. Titard and F.J. Yndurain, Rigorous QCD evaluation of spectrum and ground state properties of heavy qq̄ systems: with a precision determination of mb, M(ηb), Phys. Rev. D 49 (1994) 6007 [hep-ph/9310236] [SPIRES].
57. J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [SPIRES].
58. R.F. Sobreiro and S.P. Sorella, A study of the Gribov copies in linear covariant gauges in euclidean Yang-Mills theories, JHEP 06 (2005) 054 [hep-th/0506165] [SPIRES].
59. P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [SPIRES].
60. S.A. Larin and J.A.M. Vermaseren, The three loop QCD β-function and anomalous dimensions, Phys. Lett. B 303 (1993) 334 [hep-ph/9302208] [SPIRES].
61. A.D. Dolgov, A. Lepidi and G. Piccinelli, Electrodynamics at non-zero temperature, chemical potential and Bose condensate, JCAP 02 (2009) 027 [arXiv:0811.4406] [SPIRES].
62. G. Gabadadze and R.A. Rosen, Effective lagrangian and quantum screening in charged condensate, JCAP 02 (2009) 016 [arXiv:0811.4423] [SPIRES].
63. P. Gaete and E. Spallucci, From screening to confinement in a Higgs-like model, Phys. Lett. B 675 (2009) 145 [arXiv:0902.0905] [SPIRES].
64. G. Gabadadze and D. Pirtskhalava, Quantum liquid signatures in dwarf stars, JCAP 05 (2009) 017 [arXiv:0904.4267] [SPIRES].
65. A.D. Dolgov, A. Lepidi and G. Piccinelli, Screening effects in plasma with charged Bose condensate, Phys. Rev. D 80 (2009) 125009 [arXiv:0905.4422] [SPIRES].
66. M. Lüscher, Symmetry breaking aspects of the roughening transition in gauge theories, Nucl. Phys. B 180 (1981) 317 [SPIRES].
67. J.M. Cornwall and A. Soni, Glueballs as bound states of massive gluons, Phys. Lett. B 120 (1983) 431 [SPIRES].
68. W. Buchmüller, G. Grunberg and S.H.H. Tye, The Regge slope and the lambda parameter in QCD: an empirical approach via quarkonia, Phys. Rev. Lett. 45 (1980) 103 [Erratum ibid. 45 (1980) 587] [SPIRES].
69. S.J. Brodsky, G.P. Lepage and P.B. Mackenzie, On the elimination of scale ambiguities in perturbative quantum chromodynamics, Phys. Rev. D 28 (1983) 228 [SPIRES].
70. W. Celmaster and R.J. Gonsalves, The renormalization prescription dependence of the QCD coupling constant, Phys. Rev. D 20 (1979) 1420 [SPIRES].
71. E. Braaten and J.P. Leveille, Minimal subtraction and momentum subtraction in QCD at two loop order, Phys. Rev. D 24 (1981) 1369 [SPIRES].
72. s and of ∧QCD in the MOM scheme, JHEP 04 (2000) 006 [hep-ph/0003020] [SPIRES].
73. P. Boucaud et al., Artefacts and ≤ A2 > power corrections: revisiting the MOM Z (p2) and Z(V ), Phys. Rev. D 74 (2006) 034505 [hep-lat/0504017] [SPIRES].
74. P. Boucaud et al., Non-perturbative power corrections to ghost and gluon propagators, JHEP 01 (2006) 037 [hep-lat/0507005] [SPIRES].
75. J.A. Gracey, Recent results for Yang-Mills theory restricted to the Gribov region, arXiv:0711.3622 [SPIRES].
76. F.A. Berends, M. Buza, M. Böhm and R. Scharf, Closed expressions for specific massive multiloop selfenergy integrals, Z. Phys. C 63 (1994) 227 [SPIRES].
77. D. Dudal, S.P. Sorella, N. Vandersickel and H. Verschelde, Gribov no-pole condition, Zwanziger horizon function, Kugo-Ojima confinement criterion, boundary conditions, BRST breaking and all that, Phys. Rev. D 79 (2009) 121701 [arXiv:0904.0641] [SPIRES].
78. T. van Ritbergen, A.N. Schellekens and J.A.M. Vermaseren, Group theory factors for Feynman diagrams, Int. J. Mod. Phys. A 14 (1999) 41 [hep-ph/9802376] [SPIRES].
79. A. Soni and M.D. Tran, Gluon condensate and the interquark potential in quantum chromodynamics, Phys. Lett. B 109 (1982) 393 [SPIRES].
80. R. Akhoury and V.I. Zakharov, On non perturbative corrections to the potential for heavy quarks, Phys. Lett. B 438 (1998) 165 [hep-ph/9710487] [SPIRES].
81. S. Narison and V.I. Zakharov, Duality between QCD perturbative series and power corrections, Phys. Lett. B 679 (2009) 355 [arXiv:0906.4312] [SPIRES].
82. 2 corrections, Nucl. Phys. B 550 (1999) 353 [hep-ph/9811275] [SPIRES].
83. S. Narison, Masses, decays and mixings of gluonia in QCD, Nucl. Phys. B 509 (1998) 312 [hep-ph/9612457] [SPIRES].
84. F.R. Graziani, The gluon condensate and the effective gluon mass, Z. Phys. C 33 (1987) 397 [SPIRES].
85. V.P. Spiridonov and K.G. Chetyrkin, Nonleading mass corrections and renormalization of the operators m ψ̄ψ and G2 μν , Sov. J. Nucl. Phys. 47 (1988) 522 [SPIRES].
86. J. Liu and W. Wetzel, Gluon-mass effects in quarkonia decays, e+e- annihilation and the scalar glueball current, hep-ph/9611250 [SPIRES].
87. H. Verschelde, Perturbative calculation of nonperturbative effects in quantum field theory, Phys. Lett. B 351 (1995) 242 [SPIRES].
88. H. Verschelde, S. Schelstraete and M. Vanderkelen, Non-perturbative calculation of the mass-gap in the Gross-Neveu model, Z. Phys. C 76 (1997) 161 [SPIRES].
89. 2, Phys. Lett. B 516 (2001) 307 [hep-th/0105018] [SPIRES].
90. T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The four-loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [SPIRES].
91. A.J. MacFarlane, A. Sudbery and P.H. Weisz, On Gell-Mann's gamma matrices, d tensors and f tensors, octets and parametrizations of SU(3), Commun. Math. Phys. 11 (1968) 77 [SPIRES].