Abstract.
The interquark static potential for heavy mesons described by a massive one-gluon exchange interaction obtained from the propagator of the truncated Dyson-Schwinger equations does not reproduced the expected Cornell potential. I show that no formulation based on a finite propagator will lead to confinement of quenched QCD. I propose a mechanism based on a singular nonperturbative coupling constant which has the virtue of giving rise to a finite gluon propagator and (almost) linear confinement. The mechanism can be slightly modified to produce the screened potentials of unquenched QCD.
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References
J.M. Cornwall, Phys. Rev. D 26, 1453 (1982)
A.C. Aguilar, J. Papavassiliou, JHEP 12, 012 (2006)
P. Gonzalez, V. Mathieu, V. Vento, Phys. Rev. D 84, 114008 (2011) arXiv:1108.2347 [hep-ph]
I.L. Bogolubsky, E.M. Ilgenfritz, M. Muller-Preussker, A. Sternbeck, PoS LATTICE, 290 (2007)
J.D. Bjorken, S.D. Drell, Relativistic quantum fields, (McGraw-Hill, 1965) Chapt. 19, ISBN-0070054940
Y. Ding, T. Huang, Z. Chen, Phys. Lett. B 196, 191 (1987)
A.A. Belkov, M. Dillig, F. Pilotto, Acta Phys. Pol. B 27, 3371 (1996)
F. Pilotto, PhD thesis, Universidade do Rio Grande do Sul (Porto Alegre, Brazil, 2001) and M. Dillig, F. Pilotto, C.A.Z. Vasconcellos, Multigluon Exchange Forces in Heavy Mesons, Preprint (Univ. UFRGS Porto Alegre, 2002)
J.A. Gracey, Eur. Phys. J. C 70, 451 (2010) arXiv:1010.1104 [hep-th]
V.N. Gribov, Eur. Phys. J. C 10, 91 (1999) hep-ph/9902279
H. Hersbach, Phys. Rev. D 47, 3027 (1993)
J.M. Cornwall, Phys. Rev. D 83, 076001 (2011) arXiv:1011.3524 [hep-ph]
A. Doff, F.A. Machado, A.A. Natale, Ann. Phys. 327, 1030 (2012) arXiv:1106.2860 [hep-ph]
A.C. Aguilar, D. Binosi, J. Papavassiliou, JHEP 01, 050 (2012) arXiv:1108.5989 [hep-ph]
R. Sommer, Nucl. Phys. B 411, 839 (1994) arXiv:hep-lat/9310022
E. Eichten, K. Gottfried, T. Kinoshita, J.B. Kogut, K.D. Lane, T.-M. Yan, Phys. Rev. Lett. 34, 369 (1975)
C. Quigg, J.L. Rosner, Phys. Rep. 56, 167 (1979)
E. Eichten, K. Gottfried, T. Kinoshita, K.D. Lane, T.-M. Yan, Phys. Rev. D 21, 203 (1980)
E. Eichten, S. Godfrey, H. Mahlke, J.L. Rosner, Rev. Mod. Phys. 80, 1161 (2008) arXiv:hep-ph/0701208
J. Greensite, S. Olejnik, Phys. Rev. D 67, 094503 (2003) hep-lat/0302018
D.V. Shirkov, I.L. Solovtsov, Phys. Rev. Lett. 79, 1209 (1997) hep-ph/9704333
S.J. Brodsky, G.F. de Teramond, A. Deur, Phys. Rev. D 81, 096010 (2010) arXiv:1002.3948 [hep-ph]
A. Courtoy, S. Scopetta, V. Vento, Eur. Phys. J. A 47, 49 (2011) arXiv:1102.1599 [hep-ph]
K.D. Born, E. Laermann, N. Pirch, T.F. Walsh, P.M. Zerwas, Phys. Rev. D 40, 1653 (1989)
E.S. Swanson, J. Phys. G 31, 854 (2005) hep-ph/0504097
R. Alkofer, C.S. Fischer, F.J. Llanes-Estrada, K. Schwenzer, Ann. Phys. 324, 106 (2009) arXiv:0804.3042 [hep-ph]
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Vento, V. Confinement, the gluon propagator and the interquark potential for heavy mesons. Eur. Phys. J. A 49, 71 (2013). https://doi.org/10.1140/epja/i2013-13071-2
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DOI: https://doi.org/10.1140/epja/i2013-13071-2