Few-Body Systems

, 58:65 | Cite as

From Asymptotic Freedom Toward Heavy Quarkonia Within the Renormalization-Group Procedure for Effective Particles

  • María Gómez-RochaEmail author
Part of the following topical collections:
  1. Light Cone 2016


The renormalization group procedure for effective particles (RGPEP), developed as a nonperturbative tool for constructing bound states in quantum field theories, is applied to QCD. The approach stems from the similarity renormalization group and introduces the concept of effective particles. It has been shown that the RGPEP passes the test of exhibiting asymptotic freedom. We present the running of the Hamiltonian coupling constant with the renormalization-group scale and we summarize the basic elements needed in the formulation of the bound-state problem.


  1. 1.
    S.D. Głazek, Reinterpretation of gluon condensate in dynamics of hadronic constituents. Acta Phys. Polon. B 42, 1933 (2011)CrossRefGoogle Scholar
  2. 2.
    S.D. Głazek, Perturbative formulae for relativistic interactions of effective particles. Acta Phys. Polon. B 43, 1843 (2012)CrossRefGoogle Scholar
  3. 3.
    A.P. Trawiński, S.D. Głazek, S.J. Brodsky, G.F. de Téramond, H.G. Dosch, Effective confining potentials for QCD. Phys. Rev. D 90(7), 074017 (2014)ADSCrossRefGoogle Scholar
  4. 4.
    S.D. Głazek, Calculation of size for bound-state constituents. Phys. Rev. D 90(4), 045020 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    M. Gómez-Rocha, S.D. Głazek, Asymptotic freedom in the front-form Hamiltonian for quantum chromodynamics of gluons. Phys. Rev. D 92(6), 065005 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    S.D. Głazek, K.G. Wilson, Renormalization of hamiltonians. Phys. Rev. D 48, 5863 (1993)ADSCrossRefGoogle Scholar
  7. 7.
    K.G. Wilson, T.S. Walhout, A. Harindranath, W.M. Zhang, R.J. Perry, S.D. Głazek, Nonperturbative QCD: a weak-coupling treatment on the light front. Phys. Rev. D 49, 6720 (1994)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    S.D. Głazek, A.P. Trawiński, Effective particles in quantam field theory, in Proceedings of Light Cone (2016), arXiv:1612.06211
  9. 9.
    P.A.M. Dirac, Forms of relativistic dynamics. Rev. Mod. Phys. 21, 392 (1949)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    N. Brambilla et al., Heavy quarkonium: progress, puzzles, and opportunities. Eur. Phys. J. C 71, 1534 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    A. Pineda, Review of heavy quarkonium at weak coupling. Prog. Part. Nucl. Phys. 67, 735 (2012)ADSCrossRefGoogle Scholar
  12. 12.
    M. Blank, A. Krassnigg, Bottomonium in a Bethe-Salpeter-equation study. Phys. Rev. D 84, 096014 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    T. Hilger, C. Popovici, M. Gomez-Rocha, A. Krassnigg, Spectra of heavy quarkonia in a Bethe-Salpeter-equation approach. Phys. Rev. D 91(3), 034013 (2015)ADSCrossRefGoogle Scholar
  14. 14.
    T. Hilger, M. Gomez-Rocha, A. Krassnigg, Masses of \(\text{ J }^{PC}= 1^{-+}\) exotic quarkonia in a Bethe-Salpeter-equation approach. Phys. Rev. D 91(11), 114004 (2015)ADSCrossRefGoogle Scholar
  15. 15.
    M. Gomez-Rocha, T. Hilger, A. Krassnigg, Effects of a dressed quark-gluon vertex in pseudoscalar heavy-light mesons. Phys. Rev. D 92(5), 054030 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    M. Gómez-Rocha, T. Hilger, A. Krassnigg, Effects of a dressed quark-gluon vertex in vector heavy-light mesons and theory average of the B\(_c^*\) meson mass. Phys. Rev. D 93(7), 074010 (2016)ADSCrossRefGoogle Scholar
  17. 17.
    C.S. Fischer, S. Kubrak, R. Williams, Spectra of heavy mesons in the Bethe-Salpeter approach. Eur. Phys. J. A 51, 10 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    S.D. Glazek, J. Mlynik, Boost-invariant Hamiltonian approach to heavy quarkonia. Phys. Rev. D 74, 105015 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Li, P. Maris, X. Zhao, J.P. Vary, Heavy quarkonium in a holographic basis. Phys. Lett. B 758, 118 (2016)ADSCrossRefGoogle Scholar
  20. 20.
    C. Popovici, P. Watson, H. Reinhardt, Quarks in Coulomb gauge perturbation theory. Phys. Rev. D 79, 045006 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    J. Segovia, D.R. Entem, F. Fernandez, E. Ruiz Arriola, Renormalized quarkonium. Phys. Rev. D 86, 094027 (2012)ADSCrossRefGoogle Scholar
  22. 22.
    J. Greensite, A.P. Szczepaniak, Constituent gluons and the static quark potential. Phys. Rev. D 93(7), 074506 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    P. Guo, A.P. Szczepaniak, G. Galata, A. Vassallo, E. Santopinto, Heavy quarkonium hybrids from Coulomb gauge QCD. Phys. Rev. D 78, 056003 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    S.J. Brodsky, H.C. Pauli, S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone. Phys. Rept. 301, 299 (1998)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    S.D. Głazek, Dynamics of effective gluons. Phys. Rev. D 63, 116006 (2001)ADSCrossRefGoogle Scholar
  26. 26.
    D.J. Gross, F. Wilczek, Ultraviolet behavior of non-abelian gauge theories. Phys. Rev. Lett. 30, 1343 (1973)ADSCrossRefGoogle Scholar
  27. 27.
    H.D. Politzer, Reliable perturbative results for strong interactions? Phys. Rev. Lett. 30, 1346 (1973)ADSCrossRefGoogle Scholar
  28. 28.
    K.G. Wilson, Model of coupling-constant renormalization. Phys. Rev. D 2, 1438 (1970)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    S.D. Glazek, Harmonic oscillator force between heavy quarks. Phys. Rev. D 69, 065002 (2004)ADSCrossRefGoogle Scholar
  30. 30.
    S.D. Glazek, A.P. Szczepaniak, Special relativity constraints on an effective constituent theory of hybrids. Phys. Rev. D 67, 034019 (2003)ADSCrossRefGoogle Scholar
  31. 31.
    S.D. Glazek, J. Narebski, Special relativity in decays of hybrids. Acta Phys. Polon. B 37, 389 (2006)ADSGoogle Scholar

Copyright information

© Springer-Verlag Wien 2017

Authors and Affiliations

  1. 1.European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*)VillazzanoItaly

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