One loop gluon form factor and freezing of alpha_s in the Gribov-Zwanziger QCD Lagrangian

Abstract

We use the Gribov-Zwanziger Lagrangian in QCD to evaluate the one loop correction to the gluon propagator as a function of the Gribov volume and verify that the propagator vanishes in the infrared limit. Using the corresponding correction to the Faddeev-Popov ghost propagator we construct the renormalization group invariant coupling constant, alpha^eff_S(p^2), from the gluon and ghost form factors and verify, using the Gribov mass gap condition, that it freezes out at zero momentum to a non-zero value. This is qualitatively consistent with other approaches. We also show that there is an enhancement of the propagator of one of the Zwanziger ghosts at two loops similar to that which occurs for the Faddeev-Popov ghosts. From the exact evaluation of the form factors we examine power corrections for the gluon propagator and the effective coupling. We find that both have the same qualitative behaviour in that the leading power correction is O(1/p^2) and not O(1/(p^2)^2).

30 latex pages

References in corpus (16)

• Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory
• A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations
• The Gribov parameter and the dimension two gluon condensate in Euclidean Yang-Mills theories in the Landau gauge
• The massive analytic invariant charge in QCD
• A study of the Gribov copies in linear covariant gauges in Euclidean Yang-Mills theories
• Center Vortices and the Gribov Horizon
• Two loop correction to the Gribov mass gap equation in Landau gauge QCD
• The influence of the Gribov copies on the gluon and ghost propagators in Euclidean Yang-Mills theory in the maximal Abelian gauge
• Non-perturbative Power Corrections to Ghost and Gluon Propagators
• The one loop MSbar static potential in the Gribov-Zwanziger Lagrangian
• Landau gauge ghost and gluon propagators and the Faddeev-Popov operator spectrum
• The QCD analytic running coupling and chiral symmetry breaking
• Short comment about the lattice gluon propagator at vanishing momentum
• Gauge-variant propagators and the running coupling from lattice QCD
• Gribov horizon under the (lattice) microscope
• The vector coupling in IR region from splittings in bottomonium

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