Abstract.
The long standing problem of non perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. The approach provides new physical insight into nature of gauge theory and the potential energy of QCD and QED near the origin. The so obtained formalism is applied to physical mesons with a different flavor of quark and anti-quark. The excitation spectrum of the ρ-meson with its excellent agreement between theory and experiment is discussed as a pedagogical example.
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References
1. H.C. Pauli and S.J. Brodsky: Phys. Rev. D 32, 1993 (1985)
2. P.A.M. Dirac: Rev. Mod. Phys. 21, 392 (1949)
3. S.J. Brodsky, H.C. Pauli, and S.S. Pinsky: Phys. Rep. 301, 299–486 (1998)
4. A.H. Mueller: Nucl. Phys. B 415, 373 (1994)
5. H.C. Pauli: in: New directions in Quantum Chromodynamics, C.R. Ji and D.P. Min, Eds., American Institute of Physics, 1999, pp. 80–139; hep-ph/9910203
6. G.P. Lepage and S.J. Brodsky: Phys.Rev. D 22, 2157 (1980)
7. A.C. Kalloniatis: Phys. Rev. D 54, 2876 (1996)
8. J. Hiller: Nucl. Phys. B (Proc.Suppl.) 90, 170 (2000)
9. K. Wilson: in Lattice ‘89, R. Petronzio, Ed.; Nucl. Phys. B (Proc. Suppl.) 17, 82. (1990)
10. K.G. Wilson, T. Walhout, A. Harindranath, W.M. Zhang, R.J. Perry, and S.D. Glazek: Phys. Rev. D 49, 6720 (1994)
11. H.C. Pauli: “Compendium of Light-Cone Quantization”, Nucl. Phys. B (Proc. Suppl.) 90, 259 (2000)
12. H.C. Pauli: Eur. Phys. J. C 7, 289 (1998)
13. H.C. Krahl: master thesis (University of Heidelberg, 2004)
14. F. Wegner: Nucl. Phys. B (Proc. Suppl.) 90, 141 (2000); H.C. Pauli: Nucl. Phys. B (Proc. Suppl.) 90, 147 (2000)
15. M. Krautgärtner, H.C. Pauli, and F. Wölz: Phys. Rev. D 45, 3755 (1992)
16. U. Trittmann and H.C. Pauli: Nucl. Phys. B (Proc. Suppl.) 90, 161 (2000)
17. H.C. Pauli: Nucl. Phys. B (Proc. Suppl.) 90, 154 (2000)
18. H.C. Pauli: Nucl. Phys. B (Proc. Suppl.) 108, 273 (2002)
19. M. Frewer, T. Frederico, and H.C. Pauli: Nucl. Phys. B (Proc. Supp.) 108, 234 (2002) A. Krassnigg and H.C. Pauli: Nucl. Phys. B (Proc. Supp.) 108, 251 (2002)
20. H.C. Pauli and J. Merkel: Phys. Rev. D 55, 2486 (1997)
21. H.C. Pauli: 2003, in preparation
22. T. Frederico, H.C. Pauli, and S.G. Zhou: Phys. Rev. D 62, 116011–8 (2002)
23. C. Caso et al: Eur. Phys. J. C 3, 1 (1998)
24. A.V. Anisovich, V.V. Anisovich, and A.V. Sarantsev: Phys. Rev. D 66, 051502–5 (2002)
25. H. Omer: master thesis (University of Heidelberg 2004)
26. S. Godfrey and N. Isgur: Phys. Rev. D 32, 189 (1985)
27. K. Schilling: Nucl. Phys. B (Proc.Suppl.) 83, 140 (2000)
28. G. Schierholz: Nucl. Phys. B (Proc.Suppl.) 90, 207 (2000)
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Pauli, HC. Succesful renormalization of a QCD-inspired Hamiltonian. Eur. Phys. J. A 19 (Suppl 1), 15–22 (2004). https://doi.org/10.1140/epjad/s2004-03-003-3
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DOI: https://doi.org/10.1140/epjad/s2004-03-003-3