Renormalization group equation and QCD coupling constant in the presence of SU(3) chromo-electric field

Regular Article - Theoretical Physics

Abstract

We solve the renormalization group equation in QCD in the presence of a SU(3) constant chromo-electric field E a with arbitrary color index a=1,2,…,8 and find that the QCD coupling constant α s depends on two independent Casimir/gauge invariants C 1=[E a E a ] and C 2=[d abc E a E b E c ]2 instead of one gauge invariant C 1=[E a E a ]. The β function is derived from the one-loop effective action. This coupling constant may be useful to study hadron formation from color flux tubes/strings at high energy colliders and to study quark–gluon plasma formation at RHIC and LHC.

PACS

11.15.-q 11.15.Me 12.38.Cy 11.15.Tk 

References

  1. 1.
    G.C. Nayak, P. van Nieuwenhuizen, Phys. Rev. D 71, 125001 (2005) CrossRefADSGoogle Scholar
  2. 2.
    F. Cooper, G.C. Nayak, Phys. Rev. D 73, 065005 (2006) CrossRefMathSciNetADSGoogle Scholar
  3. 3.
    G.C. Nayak, Phys. Rev. D 72, 125010 (2005) CrossRefADSGoogle Scholar
  4. 4.
    J. Schwinger, Phys. Rev. 82, 664 (1951) MATHCrossRefMathSciNetADSGoogle Scholar
  5. 5.
    W. Heisenberg, H. Euler, Z. Phys. 98, 714 (1936) CrossRefADSGoogle Scholar
  6. 6.
    A. Casher, H. Neuberger, S. Nussinov, Phys. Rev. D 20, 179 (1979) CrossRefADSGoogle Scholar
  7. 7.
    B. Andersson, The Lund Model (Cambridge University Press, Cambridge, 1998) MATHGoogle Scholar
  8. 8.
  9. 9.
    F. Cooper, E. Mottola, G.C. Nayak, Phys. Lett. B 555, 181 (2003) MATHCrossRefADSGoogle Scholar
  10. 10.
    G.C. Nayak et al., Nucl. Phys. A 687, 457 (2001) CrossRefADSGoogle Scholar
  11. 11.
    L. McLerran, R. Venugopalan, Phys. Rev. D 49, 2233 (1994) CrossRefADSGoogle Scholar
  12. 12.
    L. McLerran, R. Venugopalan, Phys. Rev. D 49, 3352 (1994) CrossRefADSGoogle Scholar
  13. 13.
    E. Iancuu, A. Leonidov, L. McLerran, Phys. Lett. B 510, 133 (2001) CrossRefADSGoogle Scholar
  14. 14.
    E. Iancuu, A. Leonidov, L. McLerran, Nucl. Phys. A 692, 583 (2001) CrossRefADSGoogle Scholar
  15. 15.
    J. Jalilian-Marian, A. Kovner, L. Mcerran, H. Weigert, Phys. Rev. D 55, 5414 (1997) CrossRefADSGoogle Scholar
  16. 16.
    G. ’t Hooft, Nucl. Phys. B 62, 444 (1973) CrossRefADSGoogle Scholar
  17. 17.
    L.F. Abbott, Nucl. Phys. B 185, 189 (1981) CrossRefADSGoogle Scholar
  18. 18.
    S. Coleman, E. Weinberg, Phys. Rev. D 7, 1888 (1973) CrossRefADSGoogle Scholar
  19. 19.
    T. Muta, Foundations of Quantum Chromodynamics, World Scientific Lecture Notes in Physics, vol. 5 Google Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2009

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of ArizonaTucsonUSA

Personalised recommendations