Publication: Two infrared Yang-Mills solutions in stochastic quantization and in an effective action formalism
Full text at PDC
Advisors (or tutors)
Amer Physical Soc
Three decades of work on the quantum field equations of pure Yang-Mills theory have distilled two families of solutions in Landau gauge. Both coincide for hig (Euclidean) momentum with known perturbation theory, and both predict an infrared suppressed transverse gluon propagator, but whereas the solution known as scaling features an infrared power law for the gluon and ghost propagators, the massive solution rather describes the gluon as a vector boson that features a finite Debye screening mass. In this work we examine the gauge dependence of these solutions by adopting stochastic quantization. What we find, in four dimensions and in a rainbow approximation, is that stochastic quantization supports both solutions in Landau gauge but the scaling solution abruptly disappears when the parameter controlling the drift force is separated from zero (soft gauge-fixing), recovering only the perturbative propagators; the massive solution seems to survive the extension outside Landau gauge. These results are consistent with the scaling solution being related to the existence of a Gribov horizon, with the massive one being more general. We also examine the effective action in Faddeev-Popov quantization that generates the rainbow and we find, for a bare vertex approximation, that the massive-type solutions minimize the quantum effective action.
© 2012 American Physical Society. We wish to thank D. Zwanziger for his continued support and contributions to this work. We also thank R. Alkofer, C. Fischer and L. von Smekal for discussions and a critical reading of this manuscript. This work has been supported by Grants No. FPA2011-27853-01, No. FIS2008-01323 (Spain) and by the Austrian Science Fund FWF under Project No. M1333-N16.
 A. P. Szczepaniak and E. S. Swanson, Phys. Rev. D 65, 025012 (2001).  L. von Smekal, A. Hauck, and R. Alkofer, Ann. Phys.(N.Y.) 267, 1 (1998); 269, 182(E) (1998).  L. von Smekal, R. Alkofer, and A. Hauck, Phys. Rev. Lett. 79, 3591 (1997).  J. E. Mandula and M. Ogilvie, Phys. Lett. B 185, 127 (1987).  J. M. Cornwall, Phys. Rev. D 26, 1453 (1982).  D. Dudal, S. P. Sorella, N. Vandersickel, and H. Verschelde, Phys. Rev. D 77, 071501 (2008).  D. Dudal, J. A. Gracey, S. P. Sorella, N. Vandersickel, and H. Verschelde, Phys. Rev. D 78, 065047 (2008).  A. C. Aguilar, D. Binosi, and J. Papavassiliou, Phys. Rev. D 78, 025010 (2008).  P. Boucaud, J. P. Leroy, A. Le Yaouanc, J. Micheli, O.Pene, and J. Rodriguez-Quintero, J. High Energy Phys.06 (2008) 099.  A. C. Aguilar, D. Binosi, and J. Papavassiliou, J.High Energy Phys. 01 (2012) 050.  R. Alkofer, Proc. Sci., FACESQCD (2010) 030.  C. S. Fischer, A. Maas, and J. M. Pawlowski, Ann. Phys.(N.Y.) 324, 2408 (2009).  A. Maas, A. Cucchieri, and T. Mendes, Braz. J. Phys. 37, 219 (2007).  A. Cucchieri and T. Mendes, Phys. Rev. D 81, 01600(2010).  E.-M. Ilgenfritz, C. Menz,M.Muller-Preussker, A. Schiller, and A. Sternbeck, Phys. Rev. D 83, 054506 (2011).  I. L. Bogolubsky, E.-M. Ilgenfritz, M. Muller Preussker, and A. Sternbeck, Proc. Sci., LAT 2009 (2009) 237.  O. Oliveira and P. Bicudo, J. Phys. G 38, 045003 (2011).  O. Oliveira, P. J. Silva, and P. Bicudo, Proc. Sci., FACESQCD (2010) 009.  R. Alkofer, C. S. Fischer, and F. J. Llanes-Estrada, Phys. Lett. B 611, 279 (2005); 670, 460(E) (2009).  C. S. Fischer and J. M. Pawlowski, Phys. Rev. D 75,025012 (2007).  P. Watson and R. Alkofer, Phys. Rev. Lett. 86, 5239(2001).  N. Alkofer and R. Alkofer, Phys. Lett. B 702, 158 (2011).  L. H. Thomas, Proc. Cambridge Philos. Soc. 23, 542(1927).  For completeness we note that x ≡ r∕a, with a = a_0(9 π^2∕(128Z))⅓, in terms of the nuclear charge Z and Bohr’s radius a_0, and Ф ≡ rV(r)/(Ze) rescales the Coulomb potential due to the spherically symmetric (though not pointlike) charge distribution.  D. Zwanziger, Nucl. Phys. B321, 591 (1989).  D. Zwanziger, Phys. Rev. D 65, 094039 (2002).  A. Maas, Phys. Lett. B 689, 107 (2010).  A. Maas, arXiv:1106.3942.  G. Parisi and Y.-s. Wu, Sci. Sin. 24, 483 (1981).  A. M. Sudupe and R. F. Alvarez-Estrada, Phys. Lett. 166B, 186 (1986).  A. M. Sudupe, Phys. Lett. 167B, 221 (1986).  R. F. Alvarez-Estrada and A. M. Sudupe, Phys. Rev. D 37, 2340 (1988).  N. Vandersickel and D. Zwanziger, arXiv:1202.1491.  D. Zwanziger, Phys. Rev. D 67, 105001 (2003).  P. Boucaud, J-P. Leroy, A. L. Yaouanc, J. Micheli, O. Pene, and J. Rodriguez-Quintero, J. High Energy Phys. 06(2008) 012.  As a side remark we comment that the disappearance of the scaling solution in four dimensions in the setting of stochastic quantization is perhaps expected because of the analysis of von Smekal et al.  since the scaling solution seems to be a feature of ghost-antighost symmetric Faddeev-Popov quantization, and such symmetry is not implemented in the stochastic scheme.  R. Alkofer, C. S. Fischer, H. Reinhardt, and L. von Smekal, Phys. Rev. D 68, 045003 (2003).  M. Q. Huber, K. Schwenzer, and R. Alkofer, Eur. Phys. J. C 68, 581 (2010).  R. Alkofer, M.Q. Huber, V. Mader, and A. Windisch,Proc. Sci., QCD-TNT-II (2011)003.  C. S. Fischer and D. Zwanziger, Phys. Rev. D 72, 054005 (2005).  A. Cucchieri, A. Maas, and T. Mendes, Comput. Phys. Commun. 180, 215 (2009).  A. Cucchieri, T. Mendes, G. M. Nakamura, and E. M. S. Santos, Proc. Sci., FACESQCD (2010) 026.  C. S. Fischer, R. Alkofer, T. Dahm, and P. Maris, Phys. Rev. D 70, 073007 (2004).  D. Atkinson and J. C. R. Bloch, Phys. Rev. D 58, 094036 (1998).  J. M. Pawlowski, D. Spielmann, and I.-O. Stamatescu, Nucl. Phys. B830, 291 (2010).  H. Aiso, J. Fromm, M. Fukuda, T. Iwamiya, A. Nakamura,M. Stingl, and M. Yoshida, Nucl. Phys. B, Proc. Suppl.53,570 (1997).  A. Weber, J. Phys. Conf. Ser. 378, 012042 (2012).  J. Berges, Phys. Rev. D 70, 105010 (2004).  A. Maas, Phys. Rev. D 79, 014505 (2009).  J. Kuipers, T. Ueda, J. A. M. Vermaseren, and J. Vollinga, arXiv:1203.6543.