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Perturbative expansion of the plaquette to O(α35) in four-dimensional SU(3) gauge theory

Gunnar S. Bali*

Clemens Bauer

Antonio Pineda†

  • Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany and Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

  • Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany

  • Grup de Física Teòrica, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain

  • *gunnar.bali@ur.de
  • †AntonioMiguel.Pineda@uab.es
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Phys. Rev. D 89, 054505 – Published 17 March, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.054505

Abstract

Using numerical stochastic perturbation theory, we determine the first 35 infinite volume coefficients of the perturbative expansion in powers of the strong-coupling constant α of the plaquette in SU(3) gluodynamics. These coefficients are obtained in lattice regularization with the standard Wilson gauge action. The onset of the dominance of the dimension-four renormalon associated to the gluon condensate is clearly observed. We determine the normalization of the corresponding singularity in the Borel plane and convert this into the MS¯ scheme. We also comment on the impact of the renormalon on nonperturbative determinations of the gluon condensate.

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References (58)

  1. G. ’t Hooft, in Proceedings of the International School of Subnuclear Physics: The Whys of Subnuclear Physics, Erice, 1977, edited by A. Zichichi (Plenum, New York, 1979).
  2. C. Bauer, G. S. Bali, and A. Pineda, Phys. Rev. Lett. 108, 242002 (2012).
  3. G. S. Bali, C. Bauer, A. Pineda, and C. Torrero, Phys. Rev. D 87, 094517 (2013).
  4. G. S. Bali, C. Bauer, and A. Pineda, arXiv:1311.0114.
  5. I. I. Bigi, M. A. Shifman, N. G. Uraltsev, and A. I. Vainshtein, Phys. Rev. D 50, 2234 (1994).
  6. M. Beneke and V. M. Braun, Nucl. Phys. B426, 301 (1994).
  7. F. Di Renzo, G. Marchesini, P. Marenzoni, and E. Onofri, Nucl. Phys. B, Proc. Suppl. 34, 795 (1994).
  8. F. Di Renzo, E. Onofri, G. Marchesini, and P. Marenzoni, Nucl. Phys. B426, 675 (1994).
  9. F. Di Renzo and L. Scorzato, J. High Energy Phys. 10 (2004) 073.
  10. A. I. Vainshtein, V. I. Zakharov, and M. A. Shifman, Pis’ma Zh. Eksp. Teor. Fiz. 27, 60 (1978) [JETP Lett. 27, 55 (1978)].
  11. A. Di Giacomo and G. C. Rossi, Phys. Lett. B 100, 481 (1981).
  12. B. Allés, M. Campostrini, A. Feo, and H. Panagopoulos, Phys. Lett. B 324, 433 (1994).
  13. F. Di Renzo, E. Onofri, and G. Marchesini, Nucl. Phys. B457, 202 (1995).
  14. G. Burgio, F. Di Renzo, G. Marchesini, and E. Onofri, Phys. Lett. B 422, 219 (1998).
  15. F. Di Renzo and L. Scorzato, J. High Energy Phys. 10 (2001) 038.
  16. P. E. L. Rakow, Proc. Sci. LAT2005 (2006) 284 [arXiv:hep-lat/0510046].
  17. R. Horsley, G. Hotzel, E. M. Ilgenfritz, R. Millo, H. Perlt, P. E. L. Rakow, Y. Nakamura, G. Schierholz, and A. Schiller (QCDSF Collaboration), Phys. Rev. D 86, 054502 (2012).
  18. M. Beneke and M. Jamin, J. High Energy Phys. 09 (2008) 044.
  19. A. Pich, Proc. Sci. Confinement X 2012 (2012) 022 [arXiv:1303.2262].
  20. D. J. Broadhurst, A. L. Kataev, and C. J. Maxwell, Nucl. Phys. B592, 247 (2000).
  21. J. Zinn-Justin and U. D. Jentschura, Ann. Phys. (Amsterdam) 313, 197 (2004).
  22. G. Başar, G. V. Dunne, and M. Ünsal, J. High Energy Phys. 10 (2013) 041.
  23. G. V. Dunne and M. Ünsal, J. High Energy Phys. 11 (2012) 170.
  24. I. Aniceto and R. Schiappa, arXiv:1308.1115.
  25. A. Cherman, D. Dorigoni, G. V. Dunne, and M. Ünsal, Phys. Rev. Lett. 112, 021601 (2014).
  26. F. Di Renzo and L. Scorzato, J. High Energy Phys. 10 (2004) 073.
  27. G. ’t Hooft, Nucl. Phys. B153, 141 (1979).
  28. A. Gonzáles-Arroyo, J. Jurkiewiecz, and C. P. Korthals Altes, in Structural Elements in Particle Physics and Statistical Mechanics: Proceedings of the NATO Advanced Summer Study Institute on Theoretical Physics, Freiburg, 1981, edited by J. Honerkamp, K. Pohlmeier, and H. Römer (Plenum, New York, 1983).
  29. A. Coste, A. González-Arroyo, J. Jurkiewicz, and C. P. Korthals Altes, Nucl. Phys. B262, 67 (1985).
  30. M. Lüscher and P. Weisz, Nucl. Phys. B266, 309 (1986).
  31. C. Torrero and G. S. Bali, Proc. Sci. LATTICE 2008 (2008) 215 [arXiv:0812.1680].
  32. U. Wolff (ALPHA Collaboration), Comput. Phys. Commun. 156, 143 (2004); (ALPHA Collaboration), 176, 383(E) (2007).
  33. W. Zimmermann, Ann. Phys. (N.Y.) 77, 570 (1973); Lect. Notes Phys. 558, 278 (2000).
  34. T. van Ritbergen, J. A. M. Vermaseren, and S. A. Larin, Phys. Lett. B 400, 379 (1997).
  35. M. Lüscher and P. Weisz, Nucl. Phys. B452, 234 (1995).
  36. C. Christou, A. Feo, H. Panagopoulos, and E. Vicari, Nucl. Phys. B525, 387 (1998); 608, 479(E) (2001).
  37. A. Bode and H. Panagopoulos, Nucl. Phys. B625, 198 (2002).
  38. M. Guagnelli, R. Petronzio, and N. Tantalo, Phys. Lett. B 548, 58 (2002).
  39. A. Di Giacomo, H. Panagopoulos, and E. Vicari, Phys. Lett. B 240, 423 (1990).
  40. A. Di Giacomo, H. Panagopoulos, and E. Vicari, Nucl. Phys. B338, 294 (1990).
  41. M. Lüscher and P. Weisz, Commun. Math. Phys. 97, 59 (1985); 98, 433(E) (1985).
  42. S. Narison and R. Tarrach, Phys. Lett. B 125, 217 (1983).
  43. H. D. Trottier, N. H. Shakespeare, G. P. Lepage, and P. B. Mackenzie, Phys. Rev. D 65, 094502 (2002).
  44. B. Allés, A. Feo, and H. Panagopoulos, Phys. Lett. B 426, 361 (1998); 553, 337(E) (2003).
  45. U. M. Heller and F. Karsch, Nucl. Phys. B251, 254 (1985).
  46. M. Beneke, Phys. Rep. 317, 1 (1999).
  47. G. ’t Hooft, Commun. Math. Phys. 81, 267 (1981).
  48. P. van Baal, Commun. Math. Phys. 85, 529 (1982).
  49. A. Hasenfratz and P. Hasenfratz, Phys. Lett. B 93, 165 (1980).
  50. T. Lee, Phys. Rev. D 56, 1091 (1997).
  51. D. J. Broadhurst, Z. Phys. C 58, 339 (1993).
  52. M. Beneke, D. Boito, and M. Jamin, J. High Energy Phys. 01 (2013) 125.
  53. M. Jamin, private communication.
  54. T. Lee, Phys. Lett. B 711, 360 (2012).
  55. S. Necco and R. Sommer, Nucl. Phys. B622, 328 (2002).
  56. S. Capitani, M. Lüscher, R. Sommer, and H. Wittig (ALPHA Collaboration), Nucl. Phys. B544, 669 (1999).
  57. A. Pineda, J. High Energy Phys. 06 (2001) 022.
  58. P. Weisz, Nucl. Phys. B212, 1 (1983).

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Phys. Rev. D 89, 054505– Published 17 March, 2014
  • Received 31 January 2014

© 2014 American Physical Society

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