The Elusiveness of Infrared Critical Exponents in Landau Gauge Yang--Mills Theories

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dc.creatorFischer, C. S.
dc.creatorAlkofer, R.
dc.creatorReinhardt, H.
dc.date2002-02-20
dc.date.accessioned2026-07-07T11:09:14Z
dc.date.available2026-07-07T11:09:14Z
dc.descriptionWe solve a truncated system of coupled Dyson-Schwinger equations for the gluon and ghost propagators in SU($N_c$) Yang-Mills theories in Faddeev-Popov quantization on a four-torus. This compact space-time manifold provides an efficient mean to solve the gluon and ghost Dyson-Schwinger equations without any angular approximations. We verify that analytically two power-like solutions in the very far infrared seem possible. However, only one of these solutions can be matched to a numerical solution for non-vanishing momenta. For a bare ghost-gluon vertex this implies that the gluon propagator is only weakly infrared vanishing, $D_{gl}(k^2) \propto (k^2)^{2κ-1}$, $κ\approx 0.595$, and the ghost propagator is infrared singular, $D_{gh}(k^2) \propto (k^2)^{-κ-1}$. For non-vanishing momenta our solutions are in agreement with the results of recent SU(2) Monte-Carlo lattice calculations. The running coupling possesses an infrared fixed point. We obtain $α(0) = 8.92/N_c$ for all gauge groups SU($N_c$). Above one GeV the running coupling rapidly approaches its perturbative form.
dc.description30 pages, REVTEX4 style, 11 figures
dc.identifierhttps://arxiv.org/abs/hep-ph/0202195
dc.identifierhttp://arxiv.org/abs/hep-ph/0202195
dc.identifierPhys.Rev.D65:094008,2002
dc.identifierdoi:10.1103/PhysRevD.65.094008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/190393
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectHigh Energy Physics - Lattice
dc.subjectHigh Energy Physics - Theory
dc.subjectNuclear Theory
dc.titleThe Elusiveness of Infrared Critical Exponents in Landau Gauge Yang--Mills Theories
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