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A purely algebraic construction of a gauge and renormalization group invariant scalar glueball operator

  • D. DudalEmail author
  • S. P. Sorella
  • N. Vandersickel
  • H. Verschelde
Regular Article - Theoretical Physics

Abstract

This paper presents a complete algebraic proof of the renormalizability of the gauge invariant d=4 operator F μ ν 2 (x) to all orders of perturbation theory in pure Yang–Mills gauge theory, whereby working in the Landau gauge. This renormalization is far from being trivial as mixing occurs with other d=4 gauge variant operators, which we identify explicitly. We determine the mixing matrix Z to all orders in perturbation theory by using only algebraic arguments and consequently we can uncover a renormalization group invariant by using the anomalous dimension matrix Γ derived from Z. We also present a future plan for calculating the mass of the lightest scalar glueball with the help of the framework we have set up.

PACS

11.10.Gh 

References

  1. 1.
    V. Mathieu, N. Kochelev, V. Vento, Int. J. Mod. Phys. E 18, 1 (2009) CrossRefADSGoogle Scholar
  2. 2.
    D. Bettoni, J. Phys. Conf. Ser. 9, 309 (2005) CrossRefADSGoogle Scholar
  3. 3.
    M.S. Chanowitz, Int. J. Mod. Phys. A 21, 5535 (2006) CrossRefADSGoogle Scholar
  4. 4.
    D.S. Carman, AIP Conf. Proc. 814, 173 (2006) CrossRefADSGoogle Scholar
  5. 5.
    B. Alessandro et al., J. Phys. G 32, 1295 (2006) [ALICE Collaboration] CrossRefADSGoogle Scholar
  6. 6.
    C.J. Morningstar, M.J. Peardon, Phys. Rev. D 60, 034509 (1999) CrossRefADSGoogle Scholar
  7. 7.
    C. McNeile, Nucl. Phys. A 711, 303 (2002) CrossRefADSGoogle Scholar
  8. 8.
    Y. Chen et al., Phys. Rev. D 73, 014516 (2006) CrossRefADSGoogle Scholar
  9. 9.
    M.J. Teper, arXiv:hep-th/9812187
  10. 10.
    H.B. Meyer, J. High. Energy Phys. 0901, 071 (2009) CrossRefADSGoogle Scholar
  11. 11.
    G.B. West, Nucl. Phys. Proc. Suppl. 54A, 353 (1997) CrossRefADSGoogle Scholar
  12. 12.
    R.L. Jaffe, K. Johnson, Phys. Lett. B 60, 201 (1976) CrossRefADSGoogle Scholar
  13. 13.
    J.M. Cornwall, Phys. Rev. D 26, 1453 (1982) CrossRefADSGoogle Scholar
  14. 14.
    C.W. Bernard, Phys. Lett. B 108, 431 (1982) CrossRefADSGoogle Scholar
  15. 15.
    J.M. Cornwall, A. Soni, Phys. Lett. B 120, 431 (1983) CrossRefADSGoogle Scholar
  16. 16.
    T. Barnes, Z. Phys. C 10, 275 (1981) CrossRefADSGoogle Scholar
  17. 17.
    A. Szczepaniak, E.S. Swanson, C.R. Ji, S.R. Cotanch, Phys. Rev. Lett. 76, 2011 (1996) CrossRefADSGoogle Scholar
  18. 18.
    A.B. Kaidalov, Yu.A. Simonov, Phys. At. Nucl. 63, 1428 (2000) (Yad. Fiz. 63, 1428 (2000)) CrossRefGoogle Scholar
  19. 19.
    V.A. Novikov, M.A. Shifman, A.I. Vainshtein, V.I. Zakharov, Nucl. Phys. B 165, 67 (1980) CrossRefADSGoogle Scholar
  20. 20.
    S. Narison, Nucl. Phys. Proc. Suppl. 186, 306 (2009) CrossRefADSGoogle Scholar
  21. 21.
    E.V. Shuryak, Nucl. Phys. B 203, 116 (1982) CrossRefADSGoogle Scholar
  22. 22.
    R.C. Brower, S.D. Mathur, C.I. Tan, Nucl. Phys. B 587, 249 (2000) zbMATHCrossRefMathSciNetADSGoogle Scholar
  23. 23.
    H. Forkel, Phys. Rev. D 78, 025001 (2008) CrossRefMathSciNetADSGoogle Scholar
  24. 24.
    D. Zwanziger, Nucl. Phys. B 323, 513 (1989) CrossRefMathSciNetADSGoogle Scholar
  25. 25.
    V.N. Gribov, Nucl. Phys. B 139, 1 (1978) CrossRefMathSciNetADSGoogle Scholar
  26. 26.
    D. Dudal, S.P. Sorella, N. Vandersickel, H. Verschelde, Phys. Rev. D 77, 071501 (2008) CrossRefADSGoogle Scholar
  27. 27.
    D. Dudal, J.A. Gracey, S.P. Sorella, N. Vandersickel, H. Verschelde, Phys. Rev. D 78, 065047 (2008) CrossRefADSGoogle Scholar
  28. 28.
    J.C. Collins, Phys. Rev. D 14, 1965 (1976) CrossRefMathSciNetADSGoogle Scholar
  29. 29.
    H. Kluberg-Stern, J.B. Zuber, Phys. Rev. D 12, 467 (1975) CrossRefADSGoogle Scholar
  30. 30.
    J.C. Collins, Renormalization. An Introduction to Renormalization, the Renormalization Group, and the Operator Product Expansion (Cambridge University Press, Cambridge, 1984) zbMATHGoogle Scholar
  31. 31.
    J.A. Gracey, Nucl. Phys. B 634, 192 (2002) (Erratum Nucl. Phys. B 696, 295 (2004)) zbMATHCrossRefMathSciNetADSGoogle Scholar
  32. 32.
    S.D. Joglekar, B.W. Lee, Ann. Phys. 97, 160 (1976) CrossRefMathSciNetADSGoogle Scholar
  33. 33.
    W.S. Deans, J.A. Dixon, Phys. Rev. D 18, 1113 (1978) CrossRefMathSciNetADSGoogle Scholar
  34. 34.
    D. Espriu, Phys. Rev. D 28, 349 (1983) CrossRefADSGoogle Scholar
  35. 35.
    M. Henneaux, Phys. Lett. B 313, 35 (1993) (Erratum Phys. Lett. B 316, 633 (1993)) CrossRefMathSciNetADSGoogle Scholar
  36. 36.
    J.C. Collins, R.J. Scalise, Phys. Rev. D 50, 4117 (1994) CrossRefADSGoogle Scholar
  37. 37.
    J.C. Collins, A. Duncan, S.D. Joglekar, Phys. Rev. D 16, 438 (1977) CrossRefADSGoogle Scholar
  38. 38.
    R. Tarrach, Nucl. Phys. B 196, 45 (1982) CrossRefADSGoogle Scholar
  39. 39.
    O. Piguet, S.P. Sorella, In: Lecture Notes in Physics, vol. M28, p. 1 (Springer, Berlin, 1995) Google Scholar
  40. 40.
    L.S. Brown, Ann. Phys. 126, 135 (1980) CrossRefADSGoogle Scholar
  41. 41.
    D. Zwanziger, Nucl. Phys. B 399, 477 (1993) CrossRefMathSciNetADSGoogle Scholar
  42. 42.
    D. Dudal, S.P. Sorella, N. Vandersickel, H. Verschelde, arXiv:0906.4257 [hep-th]

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2009

Authors and Affiliations

  • D. Dudal
    • 1
    • 2
    Email author
  • S. P. Sorella
    • 3
  • N. Vandersickel
    • 2
  • H. Verschelde
    • 2
  1. 1.Center for Theoretical PhysicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of Mathematical Physics and AstronomyGhent UniversityGentBelgium
  3. 3.Departamento de Física Teórica, Instituto de FísicaUERJ—Universidade do Estado do Rio de JaneiroRio de JaneiroBrasil

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